Math Homework Answers - Recent questions and answers in Geometry Answers
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Powered by Question2AnswerAnswered: A 75-lb child is sitting on a teeter board at (-2.5, 3.5) and the fulcrum is at (4.5, -1.5), where units are in feet.
https://www.mathhomeworkanswers.org/243324/child-sitting-teeter-board-and-fulcrum-where-units-are-feet?show=243353#a243353
<p style="text-align:justify">The formulae for answering this question and similar questions are:
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(x-x1)/(x2-x1)=(y-y1)/(y2-y1)=M2/(M1+M2)=a/R, and a^2=(x-x1)^2+(y-y1)^2 and R^2=(x2-x1)^2+(y2-y1)^2.
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Where mass M1 is at point (x1,y1), mass M2 is at point (x2,y2), the fulcrum is at (x,y); a is M1's distance from the fulcrum; R is the distance between M1 and M2.</p>
<p style="text-align:justify">In this question M1=75lb, M2=37.5lb, x1=-2.5', y1=3.5', x=4.5', y=-1.5'.</p>
<p style="text-align:justify">(4.5+2.5)/(x2+2.5)=37.5/(75+37.5)=(-1.5-3.5)/(y2-3.5).</p>
<p style="text-align:justify">7*112.5=37.5x2+2.5*37.5, 787.5-93.75=37.5x2, x2=18.5'.</p>
<p style="text-align:justify">37.5y2-3.5*37.5=112.5(-5), 37.5y2=-431.25, y2=-11.5'. So the location of the second child is (18.5',-11.5').</p>
<p style="text-align:justify">The distance of the second child from the fulcrum is R-a=√(21^2+15^2)-√(7^2+5^2)=17.20' approx. Note that a/R=1/3, so R=3a and M1=2M2, so the results are as expected: the second child has to sit twice as far away from the fulcrum as the first child, because the first child is twice as heavy.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243324/child-sitting-teeter-board-and-fulcrum-where-units-are-feet?show=243353#a243353Thu, 22 Jun 2017 22:16:10 +0000Answered: A 65.75 lb child is sitting on a teeter board at(-1,-4) and the fulcrum is at (6.5, 3.5) where units are in feet.
https://www.mathhomeworkanswers.org/243329/child-sitting-teeter-board-and-the-fulcrum-where-units-feet?show=243347#a243347
<p style="text-align:justify">Use the formulae (x-x1)/(x2-x1)=M2/(M1+M2), (y-y1)/(y2-y1)=M2/(M1+M2) (see the question about the two children weighing 22 and 47.5 kilos, showing a representative diagram and derivation of the formulae). We have x=6.5, y=3.5, M1=65.75lb, M2=39.4lb, x1=-1, y1=-4. M1+M2=105.15lb.</p>
<p style="text-align:justify">(6.5+1)/(x2+1)=39.4/105.15=(3.5+4)/(y2+4).</p>
<p style="text-align:justify">Cross-multiplying:</p>
<p style="text-align:justify">105.15*7.5=39.4x2+39.4 and 105.15*7.5=39.4y2+39.4*4.</p>
<p style="text-align:justify">x2=19.016' and y2=16.016' approximately. So the coordinates are (19.016,16.016) feet.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243329/child-sitting-teeter-board-and-the-fulcrum-where-units-feet?show=243347#a243347Thu, 22 Jun 2017 17:01:25 +0000Answered: A 22 kilos child is sitting at A(-7, -3) and a 47.5 kilos child is at B(1,4), where units are in feet
https://www.mathhomeworkanswers.org/243326/kilos-child-sitting-and-kilos-child-is-where-units-are-in-feet?show=243335#a243335
<p style="text-align:justify">For a general solution to this problem let A be the point (x1,y1) and B be (x2,y2). Let AB=R and let a on AB be the distance between A and the fulcrum F(x,y).</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=18117121478703915139" style="height:313px; width:450px"></p>
<p style="text-align:justify">The masses are M1 at A and M2 at B. The moments about the fulcrum must be equal for equilibrium, so M1a=M2(R-a) and M1a+M2a=M2R, making a/R=M2/(M1+M2). By similar triangles (y-y1)/(y2-y1)=(x-x1)/(x2-x1)=a/R=M2/(M1+M2). Also, R=√(y2-y1)^2+(x2-x1)^2) and a=√(y-y1)^2+(x-x1)^2).</p>
<p style="text-align:justify">Therefore (x-x1)(M1+M2)=(x2-x1)M2; x(M1+M2)-x1M1-x1M2=x2M2-x1M2.</p>
<p style="text-align:justify">So x=(x1M1+x2M2)/(M1+M2) and y=(y1M1+y2M2)/(M1+M2).</p>
<p style="text-align:justify">Therefore the coordinates of F are ((x1M1+x2M2)/(M1+M2),(y1M1+y2M2)/(M1+M2)).</p>
<p style="text-align:justify">These formulae can be used in all problems of this nature.</p>
<p style="text-align:justify">We have M1=22kg and M2=47.5kg, so M1+M2=69.5kg.</p>
<p style="text-align:justify">x1=-7, y1=-3, x2=1, y2=4, so F is ((-7*22+47.5)/69.5,(-3*22+4*47.5)/69.5)=(-213/139,248/139)=(-1.53',1.78').</p>
<p style="text-align:justify">Note that the formula can be used to find any of the values M1, M2, x1, x2, x, y1, y2, y given the coordinates of A and B or F or M1 or M2.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243326/kilos-child-sitting-and-kilos-child-is-where-units-are-in-feet?show=243335#a243335Thu, 22 Jun 2017 13:51:04 +0000A 35 kilos child is sitting on a teeter board at (4.-5, 3.7) and the fulcrum is at (-4.2, 5.6), where units are in feet.
https://www.mathhomeworkanswers.org/243330/kilos-child-sitting-teeter-board-fulcrum-where-units-are-feet
A 35 kilos child is sitting on a teeter board at (4.-5, 3.7) and the fulcrum is at (-4.2, 5.6), where units are in feet. At what point should a 26.5 kilos child sit to be in equilibrium? What is the distance of the second child from the fulcrum?Geometry Answershttps://www.mathhomeworkanswers.org/243330/kilos-child-sitting-teeter-board-fulcrum-where-units-are-feetThu, 22 Jun 2017 11:49:13 +0000A 48.2 lb child is sitting on a teeter board at (-1.5,-4) and the fulcrum is at (6.7,-5) where units are in feet.
https://www.mathhomeworkanswers.org/243327/child-sitting-teeter-board-and-fulcrum-where-units-are-feet
A 48.2 lb child is sitting on a teeter board at (-1.5,-4) and the fulcrum is at (6.7,-5) where units are in feet. At what point should a 32lb child sit to be in equilibrium?Geometry Answershttps://www.mathhomeworkanswers.org/243327/child-sitting-teeter-board-and-fulcrum-where-units-are-feetThu, 22 Jun 2017 11:38:22 +0000A 52-lb child is sitting on a teeter board at (-7.5, 1.7) and the fulcrum is at (-1.7, 4.1), where units are In feet.
https://www.mathhomeworkanswers.org/243325/child-sitting-teeter-board-and-fulcrum-where-units-are-feet
A 52-lb child is sitting on a teeter board at (-7.5, 1.7) and the fulcrum is at (-1.7, 4.1), where units are in feet. At what point should a 40 lb child sit to be in equilibrium? What is the distance of the second child from the fulcrum?Geometry Answershttps://www.mathhomeworkanswers.org/243325/child-sitting-teeter-board-and-fulcrum-where-units-are-feetThu, 22 Jun 2017 11:29:33 +0000Answered: Using determinant show that the points (1,0) (0,2) and (1,0) lie on a straight line.
https://www.mathhomeworkanswers.org/243308/using-determinant-show-that-the-points-and-lie-straight-line?show=243320#a243320
<p style="text-align:justify">The line joining (1,0) and (0,2) has a slope (2-0)/(0-1)=-2. The line joining (0,2) and (1,0) has a slope (0-2)/(1-0)=-2. So these points are colinear because (0,2) is a common point and the lines have the same slope.</p>
<p style="text-align:justify">The determinant is:</p>
<p style="text-align:justify">| 1 0 1 |</p>
<p style="text-align:justify">| 0 2 1 | = 1(2-0)-0+1(0-2)=2-2=0 which confirms collinearity.</p>
<p style="text-align:justify">| 1 0 1 |</p>
<p style="text-align:justify"> </p>
<p style="text-align:justify"> </p>Geometry Answershttps://www.mathhomeworkanswers.org/243308/using-determinant-show-that-the-points-and-lie-straight-line?show=243320#a243320Thu, 22 Jun 2017 10:08:52 +0000Answered: A circle in quadrant II is tangent to both axes. It touches the y-axis at (0,3). a.At what point does it meet the x-axis? b. Find the coordinates of the center of the circle.
https://www.mathhomeworkanswers.org/243304/circle-quadrant-tangent-touches-coordinates-center-circle?show=243317#a243317
<p style="text-align: justify;">If an axis is at a tangent, it is right angles to the radius, so the y axis (x=0) is a distance of 3 units to the right of the centre, making the centre 3 units to the left at x=-3. Because the axis is also a tangent it must be above the x-axis by 3 units (y=3), so the centre is at (-3,3).</p>Geometry Answershttps://www.mathhomeworkanswers.org/243304/circle-quadrant-tangent-touches-coordinates-center-circle?show=243317#a243317Thu, 22 Jun 2017 09:40:50 +0000Answered: A rectangle with sides parallel to the axes has vertices at (3,-2) and (-1,-7). a. Find the coordinates of the other two vertices. b. Find the area of the rectangle
https://www.mathhomeworkanswers.org/243303/rectangle-parallel-vertices-coordinates-vertices-rectangle?show=243316#a243316
<p style="text-align:justify">(a) The other two vertices are at (-1,-2) and (3,-7) so combining the given coordinates.
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(b) The area is (3-(-1)) * (-2-(-7))=4*5=20 sq units.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=13886319500752037138" style="height:551px; width:375px"></p>Geometry Answershttps://www.mathhomeworkanswers.org/243303/rectangle-parallel-vertices-coordinates-vertices-rectangle?show=243316#a243316Thu, 22 Jun 2017 09:34:49 +0000Answered: A person 6 ft tall is standing near a street light so that the ration of his height to the pole is 2/3.
https://www.mathhomeworkanswers.org/243307/person-tall-standing-near-street-light-that-ration-height-pole?show=243315#a243315
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=1551357372730325276" style="height:265px; width:375px"></p>
<p style="text-align:justify">The picture shows the details. (a) DE=(2/3)AC, so AC=(3/2)DE=3*6/2=9'.</p>
<p style="text-align:justify">(b) DE=FC=6'; AF=AC-FC=9-6=3'; DF^2=AB^2-AF^2 (Pythagoras)=25-9=16, so DF=4'.</p>
<p style="text-align:justify">(c) BE/(BE+4)=2/3 (similar triangles BDE and BAC); 3BE=2BE+8; BE=8' (shadow length).</p>
<p style="text-align:justify">(d) all points shown on the picture with coordinates.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243307/person-tall-standing-near-street-light-that-ration-height-pole?show=243315#a243315Thu, 22 Jun 2017 09:23:25 +0000Answered: A person 6 ft tall is standing near a street light so that the ration of his height to the pole is 2/3.
https://www.mathhomeworkanswers.org/243309/person-tall-standing-near-street-light-that-ration-height-pole?show=243314#a243314
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=1551357372730325276" style="height:265px; width:375px"></p>
<p style="text-align:justify">The picture shows the details. (a) DE=(2/3)AC, so AC=(3/2)DE=3*6/2=9'.</p>
<p style="text-align:justify">(b) DE=FC=6'; AF=AC-FC=9-6=3'; DF^2=AB^2-AF^2 (Pythagoras)=25-9=16, so DF=4'.</p>
<p style="text-align:justify">(c) BE/(BE+4)=2/3 (similar triangles BDE and BAC); 3BE=2BE+8; BE=8' (shadow length).</p>
<p style="text-align:justify">(d) all points shown on the picture with coordinates.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243309/person-tall-standing-near-street-light-that-ration-height-pole?show=243314#a243314Thu, 22 Jun 2017 09:18:00 +0000Answered: The line through the points (1, 1) and (2, 0) cuts the y- axis at the point (0, b). Find b by using similar triangles.
https://www.mathhomeworkanswers.org/243224/through-points-cuts-axis-point-find-using-similar-triangles?show=243232#a243232
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=16182601298244544606" style="height:351px; width:400px"></p>
<p style="text-align: justify;">The axes have been removed in the picture, but the coordinates of the points are shown.</p>
<p style="text-align: justify;">In the similar triangles CNB and COA, CN/CO=NB/OA; that is, 1/2=1/b or 2/1=b/1, so b=2.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243224/through-points-cuts-axis-point-find-using-similar-triangles?show=243232#a243232Tue, 20 Jun 2017 12:04:02 +0000Find m angle 1 in the figure below. PQ and RS are parallel
https://www.mathhomeworkanswers.org/243030/find-m-angle-1-in-the-figure-below-pq-and-rs-are-parallel
Parallel and perpendicular linesGeometry Answershttps://www.mathhomeworkanswers.org/243030/find-m-angle-1-in-the-figure-below-pq-and-rs-are-parallelFri, 16 Jun 2017 00:22:47 +00002x^3-\sqrt{2}
https://www.mathhomeworkanswers.org/242575/2x-3-sqrt-2
. If \sqrt{2x+2} is a factor of the polynomial 2x^3-\sqrt{2} then find the other factor.Geometry Answershttps://www.mathhomeworkanswers.org/242575/2x-3-sqrt-2Mon, 05 Jun 2017 14:56:28 +0000Answered: A convex heptagon has interior angles that measure x, 160, 150, 2x, 150, 160, and 2x. What is x
https://www.mathhomeworkanswers.org/72726/convex-heptagon-interior-angles-that-measure-150-160-and-what?show=242416#a242416
<p style="text-align: justify;"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=9153977402977912744" style="height:139px; width:200px">The picture shows how a heptagon can be split into 5 triangles. Each triangle has an angle sum of 180° so 5 triangles total 900°, which is also the sum of the interior angles of the heptagon. Therefore, if we add all the given angles we get 5x+620=900, from which 5x=280 and x=56°.</p>Geometry Answershttps://www.mathhomeworkanswers.org/72726/convex-heptagon-interior-angles-that-measure-150-160-and-what?show=242416#a242416Thu, 01 Jun 2017 10:43:23 +0000Answered: one interior angle of a convex pentagon is 110 degree and the remaining angles is x.Find the value of x
https://www.mathhomeworkanswers.org/242338/interior-angle-convex-pentagon-degree-remaining-angles-value?show=242353#a242353
<p style="text-align:justify">A pentagon is made up of 3 triangles and since the angles of each triangle add up to 180 degrees, the interior angles of the pentagon must add up to 3*180=540 degrees. Therefore 4x+110=540 and 4x=430, so x=430/4=107.5°.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=6126618249872773188" style="height:181px; width:200px"></p>Geometry Answershttps://www.mathhomeworkanswers.org/242338/interior-angle-convex-pentagon-degree-remaining-angles-value?show=242353#a242353Wed, 31 May 2017 09:19:29 +0000Answered: find the sum of all positive numbers from 5 to 1,555 that are divisible by 5
https://www.mathhomeworkanswers.org/242285/find-the-sum-all-positive-numbers-from-555-that-are-divisible?show=242289#a242289
<p><em>find the sum of all positive numbers from 5 to 1,555 that are divisible by 5 </em></p>
<p>The numbers from 5 to 1555 that are divisible by 5 are: 5, 10, 15, 20, ... 1545, 1550, 1555</p>
<p>which is five times 1, 2, 3, 4, ..., 309, 310, 311.</p>
<p>So, the sum of all positive numbers from 5 to 1,555 that are divisible by 5 is 5 times the sum of all positive numbers from 1 to 311.</p>
<p>The sum of all positive numbers from 1 to n is: (1/2)n(n+1)</p>
<p>The sum of all positive numbers from 1 to 311 is: (1/2)*311*(311 + 1) = 311*156 = 48,516</p>
<p><span style="text-decoration: underline;"><strong>Answer: 242, 580</strong></span></p>Geometry Answershttps://www.mathhomeworkanswers.org/242285/find-the-sum-all-positive-numbers-from-555-that-are-divisible?show=242289#a242289Tue, 30 May 2017 07:21:45 +0000Answered: how many diagonals form in triangle?
https://www.mathhomeworkanswers.org/241799/how-many-diagonals-form-in-triangle?show=242203#a242203
3 diagonals are there in a circleGeometry Answershttps://www.mathhomeworkanswers.org/241799/how-many-diagonals-form-in-triangle?show=242203#a242203Sun, 28 May 2017 07:41:40 +0000Answered: Find the measure of the indicated angle to the nearest degree: Hypotenuse = 47; Leg1 = 18 (with a 90 degree angle) and L2 = ?
https://www.mathhomeworkanswers.org/242141/measure-indicated-angle-nearest-degree-hypotenuse-degree?show=242148#a242148
<p>Leg2=√(47^2-18^2)=√1885=43.42 approx.</p>
<p style="text-align: justify;">Angle = sin^-1(18/47)=23° or 67° depending on which angle is marked.</p>Geometry Answershttps://www.mathhomeworkanswers.org/242141/measure-indicated-angle-nearest-degree-hypotenuse-degree?show=242148#a242148Sat, 27 May 2017 01:44:20 +0000Answered: co ordinate grid problem
https://www.mathhomeworkanswers.org/241967/co-ordinate-grid-problem?show=241979#a241979
<p style="text-align: justify;">Because (i), (ii) and (iii) are part of (b), I think you should follow the transformations through. So you reflect A'B'C'D' to give you A"B"C"D", then rotate A"B"C"D". When you get to part (c) you will be able to appreciate what the final image looks like compared to the original ABCD. Certainly, you should calculate the coordinates as well as drawing so that you can check the accuracy of your drawings.</p>Geometry Answershttps://www.mathhomeworkanswers.org/241967/co-ordinate-grid-problem?show=241979#a241979Tue, 23 May 2017 13:51:59 +000011.7 geometric probability answers
https://www.mathhomeworkanswers.org/241975/11-7-geometric-probability-answers
11.7 holt mcdougalGeometry Answershttps://www.mathhomeworkanswers.org/241975/11-7-geometric-probability-answersTue, 23 May 2017 12:50:52 +0000Answered: if p denotes the length of perpendicular line drawn from origin to a line x÷a+y÷b=1 then show that 1÷a^2+1÷b^2=I ÷p^2
https://www.mathhomeworkanswers.org/241968/denotes-length-perpendicular-line-drawn-from-origin-line-then?show=241973#a241973
<p><em>if p denotes the length of perpendicular line drawn from origin to a line x÷a+y÷b=1 then show that 1÷a^2+1÷b^2=I ÷p^2</em></p>
<p>The equation is,</p>
<p>x/a + y/b = 1 rearranging,</p>
<p><span style="text-decoration: underline;">y = (-b/a)x + b</span></p>
<p>this is a straight line of slope m = -b/a and y-intercept c = b</p>
<p>if two lines, y = mx + c and y2 = m2.x + c2 are mutually perpindicular then <span style="text-decoration: underline;">m.m2 = -1</span></p>
<p>Since m = -b/a, the the slope of the perpindicular line is <span style="text-decoration: underline;">m2 = a/b</span></p>
<p>Since the line y2 = m2.x + c2 passes through the origin then c2 = 0. Then,</p>
<p><span style="text-decoration: underline;">y2 = (a/b)x</span></p>
<p> </p>
<p><span style="text-decoration: underline;">The intersection of y and y2</span></p>
<p>when y = y2, then</p>
<p>-(b/a)x + b = (a/b)x</p>
<p>x(a/b + b/a) = b</p>
<p>x(a^2 + b^2)/ab = b</p>
<p><span style="text-decoration: underline;">x = ab^2/(a^2 + b^2)</span></p>
<p>Since y = (a/b).x, then</p>
<p><span style="text-decoration: underline;">y = a^2.b/(a^2 + b^2)</span></p>
<p>The distance p, from the origin to the point of intersection, is the square root of the sum of the squares of the x- and y-coordinates, i.e.</p>
<p>p^2 = x^2 + y^2</p>
<p>p^2 = a^2b^4/(a^2 + b^2)^2 + a^4b^2/(a^2 + b^2)^2</p>
<p>p^2 = (a^2b^4 + a^4b^2)/(a^2 + b^2)^2</p>
<p>p^2 = a^2b^2(b^2 + a^2)/(a^2 + b^2)^2</p>
<p>p^2 = a^2b^2/(a^2 + b^2)</p>
<p>1/p^2 = (a^2 + b^2)/(a^2b^2)</p>
<p><span style="text-decoration: underline;"><strong>1/p^2 = 1/b^2 + 1/a^2</strong></span></p>Geometry Answershttps://www.mathhomeworkanswers.org/241968/denotes-length-perpendicular-line-drawn-from-origin-line-then?show=241973#a241973Tue, 23 May 2017 11:56:50 +0000Answered: question related to right triangle
https://www.mathhomeworkanswers.org/241749/question-related-to-right-triangle?show=241751#a241751
<p style="text-align:justify">There are an infinite number of places for C, if any of the three angles can be a right angle. If A or B are right angles all the points for C lie on the line y=x+5 or y=x-1, which are parallel to one another.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=17231538561915172349" style="height:325px; width:500px"></p>
<p style="text-align:justify">I've added 4 more points as examples. Also, if you draw a circle (centre (-3.5,-1.5)) with AB as the diameter, any point on the circumference will be a right angle, so C can be anywhere on the circumference. The equation of the circle is (x+3.5)^2+(y+1.5)^2=4.5 or (2x+7)^2+(2y+3)^2=18.</p>Geometry Answershttps://www.mathhomeworkanswers.org/241749/question-related-to-right-triangle?show=241751#a241751Fri, 12 May 2017 20:02:57 +0000Answered: The measure of a regular polygon’s interior angle is four times bigger than the measure of its external angle. How many sides does the polygon have?
https://www.mathhomeworkanswers.org/241728/measure-regular-polygons-interior-measure-external-polygon?show=241730#a241730
<p><em>The measure of a regular polygon’s interior angle is four times bigger than the measure of its external angle. How many sides does the polygon have? </em></p>
<p> </p>
<p>Let θ be the interior angle and α be the exterior angle, then</p>
<p>α + θ = π, and</p>
<p>θ = 4α, i.e.</p>
<p>θ = 4(π - θ) = 4π - 4θ</p>
<p><span style="text-decoration: underline;">θ = 4π/5 </span></p>
<p>Sum of interior angles of an n-sided polygon is: nθ = (n - 2)π, so</p>
<p>n(4π/5 ) = (n - 2)π</p>
<p>n(4/5 ) = (n - 2)</p>
<p>4n = 5n - 10</p>
<p><span style="text-decoration: underline;">n = 10</span></p>
<p><span style="text-decoration: underline;"><strong>The polygon has 10 sides</strong></span></p>Geometry Answershttps://www.mathhomeworkanswers.org/241728/measure-regular-polygons-interior-measure-external-polygon?show=241730#a241730Fri, 12 May 2017 09:10:32 +0000Answered: reflection and translation
https://www.mathhomeworkanswers.org/241698/reflection-and-translation?show=241702#a241702
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=1651504769099132751" style="height:580px; width:400px"></p>
<p style="text-align:justify">The geometrical figure above with its reflections is an example. The figure in red is the original figure and the reflection of the figure in both axes is shown in black. The axes act like mirrors in a kaleidoscope to produce a symmetrical figure. Tesselation is possible in this case if the "tile" enclosing the figure (rectangle measuring 4 by 2 units) is repeated along each axis so that the pointed parts touch, as illustrated below (axes removed, but original figure shown in red):</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=9709781076844705700" style="height:252px; width:250px"></p>Geometry Answershttps://www.mathhomeworkanswers.org/241698/reflection-and-translation?show=241702#a241702Wed, 10 May 2017 20:28:38 +0000Answered: Given that AD//CD, find the values of the unknowns in this figure
https://www.mathhomeworkanswers.org/241593/given-that-ad-cd-find-the-values-of-the-unknowns-in-this-figure?show=241596#a241596
Angle a = 180° - (108° + 37°) Angle a = 180° - 145° Angle a = 35° By the transversal rule, the measure of angle b is 71°.Geometry Answershttps://www.mathhomeworkanswers.org/241593/given-that-ad-cd-find-the-values-of-the-unknowns-in-this-figure?show=241596#a241596Sat, 06 May 2017 18:12:58 +0000Answered: what does BIG/JOKE=.HAHAHA mean
https://www.mathhomeworkanswers.org/50577/what-does-big-joke-hahaha-mean?show=241573#a241573
I don't knowGeometry Answershttps://www.mathhomeworkanswers.org/50577/what-does-big-joke-hahaha-mean?show=241573#a241573Fri, 05 May 2017 00:12:45 +0000Answered: The cost of three books was 90000 if the books were later sold at 25000each
https://www.mathhomeworkanswers.org/241501/cost-three-books-was-90000-the-books-were-later-sold-25000each?show=241529#a241529
<p style="text-align: justify;">Selling price of 3 books=75000. So the loss is 1-75000/90000=1-5/6=1/6 or 16.67% (16 2/3%). The actual loss is 90000-75000=15000 which is 1/6 of the cost price.</p>Geometry Answershttps://www.mathhomeworkanswers.org/241501/cost-three-books-was-90000-the-books-were-later-sold-25000each?show=241529#a241529Wed, 03 May 2017 22:23:54 +0000Answered: Which letter has rotational symmetry? Q,H,G,A
https://www.mathhomeworkanswers.org/76329/which-letter-has-rotational-symmetry-q-h-g-a?show=241176#a241176
<p><span style="font-family:georgia,serif"><span style="font-size:20px">Rotational symmetry</span></span></p>
<p> </p>Geometry Answershttps://www.mathhomeworkanswers.org/76329/which-letter-has-rotational-symmetry-q-h-g-a?show=241176#a241176Wed, 26 Apr 2017 23:36:43 +0000Answered: How to find the slant height of a cone?
https://www.mathhomeworkanswers.org/241112/how-to-find-the-slant-height-of-a-cone?show=241118#a241118
<p style="text-align:justify">The slant length L, the vertical height h, the base radius r are related by Pythagoras: L^2=h^2+r^2. This formula means that, given any two of L, h, r, the third one can be found.</p>
<p style="text-align:justify">Cone volume=πr^2h/3=πr^2√(L^2-r^2)/3. </p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=17183079208042715311" style="height:393px; width:400px"></p>
<p style="text-align:justify">The picture shows a major sector of a circle that forms the surface area of a cone. The radius of the circle is the slant length L. The cone is formed by joining the arms of the sector. The arc of the sector forms the circular base of the cone, so the arc length is 2πr. The minor sector has an arc length s. Its area is represnted by A. The ratio of the minor sector area to the area of the large circle is the same as the ratio of the sector angle <span style="font-size:12pt">β</span> to 2π:</p>
<p style="text-align:justify">A/(πL^2)=<span style="font-size:16px">β</span>/2π from which A=<span style="font-size:16px">β</span>L^2/2. But s=L<span style="font-size:16px">β</span>=2π(L-r), from which <span style="font-size:16px">β</span>=2π(L-r)/L. Therefore A=2π(L-r)/L.L^2/2=πL(L-r). The surface area of the cone itself is πL^2-A=πL^2-πL^2+πLr=πLr. However, this excludes the area of the base which is πr^2 and the total surface area is πLr+πr^2=πr(L+r).</p>
<p style="text-align:justify">These formulae show how the slant length comes into calculations of volume and surface area of a cone.</p>Geometry Answershttps://www.mathhomeworkanswers.org/241112/how-to-find-the-slant-height-of-a-cone?show=241118#a241118Tue, 25 Apr 2017 19:45:21 +0000Answered: cari nilai k
https://www.mathhomeworkanswers.org/78149/cari-nilai-k?show=241117#a241117
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=8169843138717760554" style="height:427px; width:400px"></p>
<p>Areas: QSUT-(QSP+PUR+QRT)=PQR=10</p>
<p>5(1-k)-(½-k/2+4-5/2-5k/2)=3-2k=10, 2k=-7, k=-7/2.</p>Geometry Answershttps://www.mathhomeworkanswers.org/78149/cari-nilai-k?show=241117#a241117Tue, 25 Apr 2017 19:18:24 +0000Answered: find expressions in terms of x
https://www.mathhomeworkanswers.org/241079/find-expressions-in-terms-of-x?show=241094#a241094
<p style="text-align: justify;">i) TS=PR=x+150
<br>
<br>
ii) length of fencing = 500 = QR+RS+TS+PT. RS=PT, the width of the pen.
<br>
<br>
So 500=x+2RS+x+150. Therefore 2x+2RS=350, x+RS=175 and RS=175-x.
<br>
<br>
iii) area=length x width=(x+150)(175-x)=26250+25x-x^2.
<br>
<br>
iv) we can write the area in a different way: 26250-(x^2-25x)=26250+12.5^2-(x^2-25x+12.5^2).
<br>
<br>
So we get area=26250+12.5^2-(x-12.5)^2; 26406.25-(x-12.5)^2.
<br>
<br>
The maximum value of the area is 26406.25 sq m when x=12.5m. This is the stationary value. Any other value of x will reduce the area from 26406.25 sq m.
<br>
<br>
v) 26406.25 sq m is the maximum area, = 162.5^2, length=width, a perfect square.</p>Geometry Answershttps://www.mathhomeworkanswers.org/241079/find-expressions-in-terms-of-x?show=241094#a241094Tue, 25 Apr 2017 14:01:16 +0000Answered: *Given: LMNB is a square, LM = 20 cm, P∈ LM , LP = 4 cm, K∈ PN , PK= 1 5 PN Find: Area of LPKB.
https://www.mathhomeworkanswers.org/241023/given-lmnb-is-square-lm-20-cm-p%E2%88%88-lm-cm-k%E2%88%88-pn-pk-pn-find-area-of-lpkb?show=241029#a241029
Not quite sure what you mean by your last statement what do you mean by PK= 1 5 PN. If PK is 15 time longer than PN you are way outside the square and could be argued that PK is not a member of PN.Geometry Answershttps://www.mathhomeworkanswers.org/241023/given-lmnb-is-square-lm-20-cm-p%E2%88%88-lm-cm-k%E2%88%88-pn-pk-pn-find-area-of-lpkb?show=241029#a241029Mon, 24 Apr 2017 09:29:46 +0000Answered: why in every graph the sum of the degrees of all the vertices equals twice the number of edges?
https://www.mathhomeworkanswers.org/54935/every-graph-degrees-vertices-equals-twice-the-number-edges?show=240930#a240930
Every edge is connected to exactly two vertices.Geometry Answershttps://www.mathhomeworkanswers.org/54935/every-graph-degrees-vertices-equals-twice-the-number-edges?show=240930#a240930Thu, 20 Apr 2017 14:29:31 +0000Answered: how to solve 4X-5y=11 AND 7x+9y=3 USING ELIMINATION
https://www.mathhomeworkanswers.org/240918/how-to-solve-4x-5y-11-and-7x-9y-3-using-elimination?show=240923#a240923
<p><em>how to solve 4X-5y=11,7x+9y=3 USING ELIMINATION</em></p>
<p>The eqns are:</p>
<p>4x - 5y = 11</p>
<p>7x + 9y = 3</p>
<p>Let's eliminate the y's say, by multiplying the 1st eqn by 9 and the 2nd eqn by 5.</p>
<p>This gives us,</p>
<p>36x - 45y = 99</p>
<p>35x + 45y = 15</p>
<p>Now simply add the two eqns together, to give</p>
<p>71x = 114</p>
<p><span style="text-decoration: underline;">x = 114/71</span></p>
<p>Substituting for x = 114/71 in the 1st eqn, we get</p>
<p>4(114/71) - 5y = 11</p>
<p>456/71 - 11*(71/71) = 5y</p>
<p>456 - 781 = 71*5y</p>
<p>-325 = 71*5y</p>
<p>-65 = 71y</p>
<p><span style="text-decoration: underline;">y = -65/71</span></p>
<p><span style="text-decoration: underline;"><strong>Answers: x = 114/71, y = -65/71</strong></span></p>Geometry Answershttps://www.mathhomeworkanswers.org/240918/how-to-solve-4x-5y-11-and-7x-9y-3-using-elimination?show=240923#a240923Thu, 20 Apr 2017 06:20:11 +0000Answered: an orange is 7 cm in diameter,if 2/9 of it is made up of juice how much juice can you get from squeezing 7 similar such oranges?
https://www.mathhomeworkanswers.org/240786/orange-diameter-juice-much-juice-squeezing-similar-oranges?show=240789#a240789
<p><span style="text-decoration: underline;">an orange is 7 cm in diameter,if 2/9 of it is made up of juice how much juice can you get from squeezing 7 similar such oranges?</span><span style="text-decoration: underline;"> </span></p>
<p>Volume of orange is V = pi.D^2/4</p>
<p>V = pi*(7)^2/4 = <span style="text-decoration: underline;">49pi/4</span></p>
<p>2/9 of that volume is juice, i.e.</p>
<p><span style="text-decoration: underline;">Vj = 2V/9 = 49pi/18</span></p>
<p>Total volume from 7 such oranges is Vt, where</p>
<p>Vt = 7Vj = <span style="text-decoration: underline;">343pi/18</span></p>
<p><span style="text-decoration: underline;"><strong>Volume = 343pi/18 cm^3 = 59.86 cm^3</strong></span></p>Geometry Answershttps://www.mathhomeworkanswers.org/240786/orange-diameter-juice-much-juice-squeezing-similar-oranges?show=240789#a240789Mon, 17 Apr 2017 04:59:19 +0000Answered: how do you find the order and magnitude of symmetry for a star
https://www.mathhomeworkanswers.org/240471/how-do-you-find-the-order-and-magnitude-of-symmetry-for-a-star?show=240517#a240517
<p style="text-align:justify">A star is basically a ball of very hot gas in constant motion. From a distance it is a point of light, with the exception of the sun, our nearest star. The sun has a generally uniform appearance so its rotational symmetry could be considered of infinite order. But if its granular appearance is considered then there would be no symmetry since there is so much randomness.</p>
<p style="text-align:justify">Its magnitude (brightness) is -27, while the full moon's magnitude is -13. The brighter an object the more negative is its magnitude. So faint stars have positive magnitude. A step of 5 in the magnitude between two stars is a change in brightness by a factor of 100, so a step of 1 is 100^(1/5). A piano keyboard can be used as an analogous system. The lower notes correspond to brighter stars while the higher notes correspond to dimmer stars. A piano keyboard is logarithmic as is the magnitude system. To use the magnitude system we need to define a reference magnitude. Middle C on a piano could represent magnitude 0. The note below would be a star with magnitude -1, or roughly 2.5 times brighter than a star with magnitude 0. The note above would be about 2.5 times dimmer. A star with magnitude -5 is a hundred times brighter than a magnitude 0 star, magnitude 5 100 times dimmer. The magnitude is not restricted to integers.</p>
<p style="text-align:justify">The formula apparent magnitude, M=M0-2.5log[10](I[m]/I[m0]) applies, where I denotes measurable intensity, M0 is the reference magnitude (star with magnitude 0). Absolute magnitude requires knowledge of a star's distance. To determine the apparent magnitude of a star you would need to measure the brightness of a reference object (e.g., the moon) using, for example, power per unit area, then use the same units to measure the star's brightness. Knowing the magnitude of the moon's brightness, M0=-13, plug the values into the equation to find M.</p>Geometry Answershttps://www.mathhomeworkanswers.org/240471/how-do-you-find-the-order-and-magnitude-of-symmetry-for-a-star?show=240517#a240517Sat, 08 Apr 2017 12:24:11 +0000Answered: In triangle ABC, angle A = 30, angle B= 60 and segment = BC 4, what is the length of AC to the nearest hundredth
https://www.mathhomeworkanswers.org/240392/triangle-angle-angle-segment-what-length-nearest-hundredth?show=240415#a240415
<p style="text-align:justify">Angle C=180-(60+30)=90 degrees, so AC/4=tan60=√3, and AC=4√3=6.93 units approx.</p>Geometry Answershttps://www.mathhomeworkanswers.org/240392/triangle-angle-angle-segment-what-length-nearest-hundredth?show=240415#a240415Wed, 05 Apr 2017 17:35:25 +0000Answered: If possible, draw an example of 2 noncongruent triangles that satisfy the following conditions. If not possible, then explain why.
https://www.mathhomeworkanswers.org/240336/possible-noncongruent-triangles-following-conditions-possible?show=240339#a240339
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=3756937594753605339" style="height:330px; width:500px"></p>
<p style="text-align: justify;">Triangles 1 shows two similar triangles formed because of the parallel lines, so the large triangle and nested inner triangle have all three angles congruent, but the side lengths are different, so the triangles are not congruent.</p>
<p style="text-align: justify;">Similarly Triangles 2 shows two similar triangles and one pair of sides congruent. But the sides are not in corresponding positions and the triangles are not congruent even though they have 4 congruencies.</p>
<p style="text-align: justify;">Triangles 3 also has three congruencies: two sides and an angle, but they are not in corresponding positions.</p>
<p style="text-align: justify;">For 5 congruencies we have to have 3 sides and 2 angles, or 2 sides and 3 angles. If 2 angles are congruent the third angle must also be congruent. And if all angles are congruent the two sides must include one of the angles, making the triangles congruent; so with 5 matching parts there will always be congruency.</p>Geometry Answershttps://www.mathhomeworkanswers.org/240336/possible-noncongruent-triangles-following-conditions-possible?show=240339#a240339Mon, 03 Apr 2017 10:58:04 +0000Answered: Research and explain how it creates parallel rays of light, name 4 uses for retroreflectors and why were they placed on moon's surface.
https://www.mathhomeworkanswers.org/240303/research-explain-creates-parallel-retroreflectors-surface?show=240314#a240314
<p style="text-align:justify">The three mirrors are arranged to form the corner of a cuboid, or more specifically a cube with the reflecting surfaces facing inwards. An incident ray of light can be considered to have an x, y and z component, where x, y and z are Cartesian components of the ray vector. The ray will strike one mirror first and then be reflected on to another, which in turn reflects on to the third mirror. With each reflection one component of the original ray is reversed. So (x,y,z)→(-x,y,z)→(-x,-y,z)→(-x,-y,-z). In the last reflection all three components of the ray have been reversed, meaning that the ray is reflected back parallel to the path it arrived.</p>
<p style="text-align:justify">A retroreflector on the moon, for example, would bounce a laser ray back the way it came and by timing the journey from source back to source using accurate timing devices, the distance of the moon to the earth can be calculated because the speed of light in a vacuum is known. Using satellites instead of terrestrial sources gives better results because there is no atmosphere to cause variation in the speed of light.</p>
<p style="text-align:justify">Retroreflectors on the moon are usually in arrays so that they capture and reflect light over a wide area.</p>
<p style="text-align:justify">Retroreflectors can be used similarly for navigation systems to provide great accuracy in determining location. So they can be installed in satellites for just such a purpose.</p>
<p style="text-align:justify">They can also be used to determine the speed of light in various media where distances between points are known and the timing is measured.</p>
<p style="text-align:justify">They're used in reflectors on the road surface and in vehicle reflectors. They can also be used in hi-viz clothing.</p>Geometry Answershttps://www.mathhomeworkanswers.org/240303/research-explain-creates-parallel-retroreflectors-surface?show=240314#a240314Sun, 02 Apr 2017 13:40:25 +0000Answered: How much would density be of each planet have to change to have same volume as Earth?
https://www.mathhomeworkanswers.org/240302/much-would-density-planet-have-change-have-same-volume-earth?show=240312#a240312
<p style="text-align:justify">The general form for density D=M/V. Applying this formula to the Earth, DE=ME/VE. So, if V is the volume of a planet, V/VE is the proportion of its volume in relation to Earth. If the planet is bigger than Earth, then V/VE>1 and compressing its mass into the same volume as the Earth would increase its density by the same factor. So the density would change to D.V/VE. There would be a decrease in density if V<VE. But D=M/V, so the change in density would simply be M/VE. This is of course the mass of the planet squeezed or expanded into Eath's volume.</p>
<p style="text-align:justify">The density of water is 1g/cc=1E12kg/km^3. The density of the planets is best shown using the density of water as the unit. Treating every planet as a perfect sphere and knowing the mean radius of each we can work out the volume and calculate the density.</p>
<table border="1" cellpadding="1" cellspacing="1" style="width:500px">
<tbody>
<tr>
<td style="text-align:center">PLANET</td>
<td style="text-align:center">Radius (km)</td>
<td style="text-align:center">Mass (kg)</td>
<td style="text-align:center">Volume (km^3)</td>
<td style="text-align:center">Density (compared to water)</td>
<td style="text-align:center">Changed density</td>
</tr>
<tr>
<td style="text-align:center">Mercury</td>
<td style="text-align:center">2440</td>
<td style="text-align:center">3.30E23</td>
<td style="text-align:center">6.09E10</td>
<td style="text-align:center">5.42</td>
<td style="text-align:center">0.30</td>
</tr>
<tr>
<td style="text-align:center">Venus</td>
<td style="text-align:center">6052</td>
<td style="text-align:center">4.87E24</td>
<td style="text-align:center">9.29E11</td>
<td style="text-align:center">5.25</td>
<td style="text-align:center">4.48</td>
</tr>
<tr>
<td style="text-align:center">EARTH</td>
<td style="text-align:center">6378</td>
<td style="text-align:center">5.97E24</td>
<td style="text-align:center">1.09E12</td>
<td style="text-align:center">5.49</td>
<td style="text-align:center">5.49</td>
</tr>
<tr>
<td style="text-align:center">Mars</td>
<td style="text-align:center">3397</td>
<td style="text-align:center">6.42E23</td>
<td style="text-align:center">1.64E11</td>
<td style="text-align:center">3.91</td>
<td style="text-align:center">0.59</td>
</tr>
<tr>
<td style="text-align:center">Jupiter</td>
<td style="text-align:center">71492</td>
<td style="text-align:center">1.90E27</td>
<td style="text-align:center">1.53E15</td>
<td style="text-align:center">1.24</td>
<td style="text-align:center">1748</td>
</tr>
<tr>
<td style="text-align:center">Saturn</td>
<td style="text-align:center">60268</td>
<td style="text-align:center">5.68E26</td>
<td style="text-align:center">9.17E14</td>
<td style="text-align:center">0.62</td>
<td style="text-align:center">523</td>
</tr>
<tr>
<td style="text-align:center">Uranus</td>
<td style="text-align:center">25559</td>
<td style="text-align:center">8.68E25</td>
<td style="text-align:center">6.99E13</td>
<td style="text-align:center">1.24</td>
<td style="text-align:center">80</td>
</tr>
<tr>
<td style="text-align:center">Neptune</td>
<td style="text-align:center">24766</td>
<td style="text-align:center">1.02E26</td>
<td style="text-align:center">6.36E13</td>
<td style="text-align:center">1.60</td>
<td style="text-align:center">94</td>
</tr>
<tr>
<td style="text-align:center">Pluto</td>
<td style="text-align:center">1150</td>
<td style="text-align:center">1.27E22</td>
<td style="text-align:center">6.37E9</td>
<td style="text-align:center">1.99</td>
<td style="text-align:center">1.17</td>
</tr>
</tbody>
</table>
<p style="text-align:justify"> </p>Geometry Answershttps://www.mathhomeworkanswers.org/240302/much-would-density-planet-have-change-have-same-volume-earth?show=240312#a240312Sun, 02 Apr 2017 11:09:19 +0000Research traffic signs to determine the meaning and most common uses of traffic signs in the following shapes:
https://www.mathhomeworkanswers.org/240301/research-traffic-determine-meaning-common-traffic-following
While driving, we rely on traffic signs to help us arrive at our destinations safely. Each type of traffic sign communicates a message through its shape as well as its color. The Federal Highway Administration publishes the Manual on Uniform Traffic Control Devices, MUTCD, which defines traffic sign standards. Research traffic signs to determine the meaning and most common uses of traffic signs in the following shapes: circle, rectangle, square, octagon, pentagon, rhombus, trapezoid, equilateral triangle and isosceles triangle.<br />
<br />
~~From book College Geometry A Problem-Solving Approach 2nd Edition Section 2.2 problem 39.Geometry Answershttps://www.mathhomeworkanswers.org/240301/research-traffic-determine-meaning-common-traffic-followingSun, 02 Apr 2017 04:18:29 +0000Answered: triangle; radius = 4 inches
https://www.mathhomeworkanswers.org/240225/triangle-radius-4-inches?show=240269#a240269
<p style="text-align:justify">I assume an equilateral triangle and its circumscribed circle. The centre of the triangle and circle are the same point and the radius is from the centre to a vertex. Joining two radii to vertices we get an isosceles triangle with angle at the centre=120 degrees (360/3) and the equal angles are 30 degrees. The isosceles triangle can be divided into two back-to-back right-angled triangles with hypotenuse (radius) = 4". The height of the right triangle is 4sin30=2 inches and the base = 4cos30 = 2√3 inches. The area of one such triangle = 2√3. There are 6 right triangles formed by the radii and vertices, so the area of the equilateral triangle is 6*2√3=12√3=20.78 sq in (approx).</p>Geometry Answershttps://www.mathhomeworkanswers.org/240225/triangle-radius-4-inches?show=240269#a240269Sat, 01 Apr 2017 15:29:56 +0000Answered: Prove that line AB ~= line AD.
https://www.mathhomeworkanswers.org/240256/prove-that-line-ab-line-ad?show=240268#a240268
<p style="text-align: justify;">Triangles ABC and ADC are similar because of the equal angles, also angles ADC and ABC are equal because ADC=180-(DAC+ACD) and ABC=180-(BAC+ACB). But side AC is common to both, so the triangles are congruent. That means corresponding sides have the same length. Therefore AB=AD.</p>Geometry Answershttps://www.mathhomeworkanswers.org/240256/prove-that-line-ab-line-ad?show=240268#a240268Sat, 01 Apr 2017 09:17:31 +0000Answered: square; radius = 8 mm
https://www.mathhomeworkanswers.org/240226/square-radius-8-mm?show=240262#a240262
<p style="text-align: justify;">If by radius you mean the distance from the centre to a corner then it's the radius of the circumscribed circle.</p>
<p style="text-align: justify;">The length of the diagonal is 16mm, and the side of the square is 16/√2 mm. The area of the square is the square of this side=256/2=128 sq mm. The length of the diagonal is also the length of the diameter of the circle.</p>Geometry Answershttps://www.mathhomeworkanswers.org/240226/square-radius-8-mm?show=240262#a240262Fri, 31 Mar 2017 23:57:02 +0000Answered: Form the intersection for the following sets. R = {10, 15, 20} S = {20, 25}
https://www.mathhomeworkanswers.org/74500/form-the-intersection-for-the-following-sets-r-10-15-20-s-20-25?show=239805#a239805
<p><span style="background-color:rgb(255, 255, 255); color:rgb(2, 10, 27); font-family:proximanova,helvetica,arial,sans-serif; font-size:16px">For the intersection of R and S, we need to find what number set R and set S has in common. Since 20 is in R and 20 is in S then </span>
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<span style="background-color:rgb(255, 255, 255); color:rgb(2, 10, 27); font-family:proximanova,helvetica,arial,sans-serif; font-size:16px">R ∩ S=20. </span></p>Geometry Answershttps://www.mathhomeworkanswers.org/74500/form-the-intersection-for-the-following-sets-r-10-15-20-s-20-25?show=239805#a239805Thu, 23 Mar 2017 14:07:02 +0000Answered: area of square problem
https://www.mathhomeworkanswers.org/239729/area-of-square-problem?show=239734#a239734
<p style="text-align:justify">You are using squared graph paper, right? When you have drawn a 2x2 square you just count how many squares of graph paper are enclosed. If the side of the square is 2 then the area enclosed is 4 squares.</p>
<p style="text-align:justify">But how do you draw a square with area 2? What you do is draw the diagonals of each of the 4 enclosed squares. For the top left and bottom right squares you draw the diagonal from the bottom left corner to the top right corner; and for the other two squares you draw the other diagonal. This gives you a square inside the bigger square tilted by 45 degrees.</p>
<p style="text-align:justify">You have also divided the area of 4 squares into 8 triangles. So 8 triangles have a total area of 4 little squares. Each triangle has an area of ½. The tilted square contains 4 of these triangles. So if 8 triangles is equivalent to 4, then 4 triangles is equivalent to 2. That's how you know the area of your tilted square is 2. So its sides have length √2, the length of each diagonal. No Pythagoras!</p>
<p style="text-align:justify">Looking at squares geometrically probably also helps you to answer your other question, when you start with the tilted square. Because the area of the tilted square is 2, its side length is √2. But the side is the diagonal of a unit square. This means to get the length of the side of the square knowing the length of its diagonal, you just divide the length of the diagonal by √2.</p>Geometry Answershttps://www.mathhomeworkanswers.org/239729/area-of-square-problem?show=239734#a239734Wed, 22 Mar 2017 07:44:31 +0000Answered: Suppose you know the length of the diagonal of a square. How can you find the side length of the square? Explain.
https://www.mathhomeworkanswers.org/239726/suppose-length-diagonal-square-find-length-square-explain?show=239730#a239730
d^2 = a^2 + a^2<br />
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d^2 = 2a^2<br />
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a^2 = d^2/2<br />
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a= sgrt(d^2/2) = d/sgrt2 = (d*sgrt2)/2Geometry Answershttps://www.mathhomeworkanswers.org/239726/suppose-length-diagonal-square-find-length-square-explain?show=239730#a239730Tue, 21 Mar 2017 22:00:21 +0000Answered: round 4.123 rounded to the nearest hundredth place
https://www.mathhomeworkanswers.org/21368/round-4-123-rounded-to-the-nearest-hundredth-place?show=239721#a239721
<p><span style="color:#EE82EE"><span style="font-family:georgia,serif"><span style="font-size:26px">4.12<img alt="cool" src="https://www.mathhomeworkanswers.org/qa-plugin/ckeditor4/plugins/smiley/images/shades_smile.gif" style="height:20px; width:20px" title="cool">+</span></span></span></p>Geometry Answershttps://www.mathhomeworkanswers.org/21368/round-4-123-rounded-to-the-nearest-hundredth-place?show=239721#a239721Tue, 21 Mar 2017 16:04:58 +0000Answered: If a trapezoid is isosceles, then each pair of base angles is_________?
https://www.mathhomeworkanswers.org/239565/trapezoid-isosceles-then-each-pair-base-angles-is_________?show=239574#a239574
CongruentGeometry Answershttps://www.mathhomeworkanswers.org/239565/trapezoid-isosceles-then-each-pair-base-angles-is_________?show=239574#a239574Sat, 18 Mar 2017 09:21:15 +0000