Math Homework Answers - Recent questions and answers in Algebra 2 Answers
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Powered by Question2AnswerAnswered: how long it take him to walk home?
https://www.mathhomeworkanswers.org/40237/how-long-it-take-him-to-walk-home?show=253182#a253182
<p style="text-align: justify;">Since since distance=speed times time we can write s=20t1=10t2 where s is the distance to school and t1 and t2 the travelling times to and from school. Also t1+t2=1 hour.</p>
<p style="text-align: justify;">So 2t1=t2 and t1+t2=t1+2t1=1, so 3t1=60 mins, and t1=20 mins, t2=40 mins.</p>
<p style="text-align: justify;">So it takes Jose 40 minutes to walk home.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/40237/how-long-it-take-him-to-walk-home?show=253182#a253182Fri, 20 Jul 2018 11:27:48 +0000Answered: ABCD is an isoceles trapezoid with a height of 4 and bases a + 2 and a + 4. Find the area of the trapezoid.
https://www.mathhomeworkanswers.org/253114/abcd-isoceles-trapezoid-with-height-bases-find-area-trapezoid?show=253119#a253119
<p style="text-align:justify">The trapezoid is made up of a rectangle and 2 congruent right triangles.</p>
<p style="text-align:justify">Area of rectangle=4(a+2) sq units</p>
<p style="text-align:justify">Combined area of triangles=4 sq units</p>
<p style="text-align:justify">Total area=4a+8+4=4a+12 sq units</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=16400290454556987221" style="height:258px; width:350px"></p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253114/abcd-isoceles-trapezoid-with-height-bases-find-area-trapezoid?show=253119#a253119Tue, 17 Jul 2018 12:08:18 +0000Answered: Please help solve for x: x-(x-1)/2=3
https://www.mathhomeworkanswers.org/253097/please-help-solve-for-x-x-x-1-2-3?show=253099#a253099
<p style="text-align:justify">Following through with your idea, you should have multiplied x by 2:</p>
<p style="text-align:justify">2x-(x-1)=6</p>
<p style="text-align:justify">Remember that minus outside a bracket changes the signs within the bracket:</p>
<p style="text-align:justify">2x-x+1=6, x+1=6, x=5.</p>
<p style="text-align:justify">Always check your answer by going back to the original equation and substituting for x:</p>
<p style="text-align:justify">5-(5-1)/2=5-2=3 which is correct!</p>
<p style="text-align:justify">I’m pleased that you want to work out these problems for yourself. So many students just want someone to do the problems for them, over and over again. That’s no fun. You’ll get a kick out of solving them yourself.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253097/please-help-solve-for-x-x-x-1-2-3?show=253099#a253099Mon, 16 Jul 2018 10:20:21 +0000Answered: Write this in a algebraic expression. 50 less than the product of eight and a number
https://www.mathhomeworkanswers.org/253085/write-algebraic-expression-less-than-product-eight-number?show=253087#a253087
<p style="text-align:justify">8x-50 where x is the number.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253085/write-algebraic-expression-less-than-product-eight-number?show=253087#a253087Sat, 14 Jul 2018 23:40:50 +0000Answered: A bakery sells 9 types of sandwiches. Here are their calorie amounts: 548,564,580,596,607,615,622,632,932. Which measure should be used to summarize the data ?
https://www.mathhomeworkanswers.org/252957/bakery-sandwiches-calorie-amounts-measure-should-summarize?show=252971#a252971
<p style="text-align:justify">You could use the mean (average), mode (most common), median (central value of the ordered set) as a single figure to represent the data. The mean is found by adding the calorific values and dividing by the number of data=9. I think that, without analysing the data more closely, in this case the mean would be best, because there is no mode, since each value is unique. If we work out the mean and median we may find they have similar values.</p>
<p style="text-align:justify">The data is already ordered and the median is the 5th value=607. The value 932 is an “outsider” (outlier) which will make the mean higher than 607. Nevertheless we can calculate the mean and compare it with the median.</p>
<p style="text-align:justify">The mean is 632.9 which is a lot higher than 607, and is actually higher than the penultimate value 632, and if presented as a general single value, it may mislead customers into thinking that the sandwiches have a high calorific value. We don’t know how many sandwiches of different types there are, and there may only be a few with high values. <strong>So I would use the median 607 as a typical value for the number of calories.</strong></p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252957/bakery-sandwiches-calorie-amounts-measure-should-summarize?show=252971#a252971Tue, 10 Jul 2018 07:59:03 +0000Answered: prove by induction that 1/1(2)+1/2(3)+1/3(4)+... + 1/n(n+1)=n/(n+1)
https://www.mathhomeworkanswers.org/81212/prove-by-induction-that-1-1-2-1-2-3-1-3-4-1-n-n-1-n-n-1?show=252809#a252809
<ol>
<li style="text-align: justify;">Base case: n=1, S₁=1/(1×2)=1/2=1/(1+1). So base case is true.</li>
<li style="text-align: justify;">If a[k]=1/(k(k+1)) represents the kth term, and we assume the sum to the kth term is S[k]=k/(k+1), then S[k+1]=S[k]+a[k+1]=k/(k+1)+1/((k+1)(k+2))=(k(k+2)+1)/((k+1)(k+2)).</li>
<li style="text-align: justify;">So we get (k²+2k+1)/((k+1)(k+2)) = (k+1)²/((k+1)(k+2)) = (k+1)/(k+2)=S[k+1]. This proves by induction that S[n]=n/(n+1).</li>
</ol>Algebra 2 Answershttps://www.mathhomeworkanswers.org/81212/prove-by-induction-that-1-1-2-1-2-3-1-3-4-1-n-n-1-n-n-1?show=252809#a252809Wed, 27 Jun 2018 12:43:36 +0000Answered: If f = { ( 2 , -1 ) , ( − 4 , − 3 ) , ( 1 , 1/4 ) , ( π , − 3 ) } g={(3,1),(-3,-1),(2/3,-1),(π,-2)} and g ={(3,1)(-3,-1),(2/3,-1)} find each of the following values of f and g .
https://www.mathhomeworkanswers.org/252756/if-%CF%80-2-and-g-3-1-3-1-2-3-1-find-each-of-the-following-values-of-f-and-g?show=252762#a252762
<p style="text-align: justify;">The paired values in the curly brackets (sets) are really saying: when x=2, f(x)=-1; when x=-4, f(x)=-3, etc.</p>
<p style="text-align: justify;">Or f(2)=-1, f(-4)=-3, etc.</p>
<p style="text-align: justify;">So (a) is f(2)=-1. We just look for a pair with 2 in the first position.</p>
<p style="text-align: justify;">(b) g(3)=1</p>
<p style="text-align: justify;">(c) -1</p>
<p style="text-align: justify;">(d) 1/4</p>
<p style="text-align: justify;">(e) -1</p>
<p style="text-align: justify;">(f) -3</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252756/if-%CF%80-2-and-g-3-1-3-1-2-3-1-find-each-of-the-following-values-of-f-and-g?show=252762#a252762Sun, 24 Jun 2018 10:50:22 +0000Answered: For the function f ( x ) = 1/4 x + 4 , find the value of x for which f ( x ) = x
https://www.mathhomeworkanswers.org/252758/for-the-function-f-x-1-4-x-4-find-the-value-of-x-for-which-f-x-x?show=252760#a252760
<p style="text-align: justify;">It may be easier to think of this as y=¼x+4 and y=x as two simultaneous equations.</p>
<p style="text-align: justify;">To solve, we equate the y values: x=¼x+4. ¾x=4, so x=16/3.</p>
<p style="text-align: justify;">f(16/3)=4/3+4=4/3+12/3=16/3, so f(x)=x.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252758/for-the-function-f-x-1-4-x-4-find-the-value-of-x-for-which-f-x-x?show=252760#a252760Sun, 24 Jun 2018 10:35:28 +0000Answered: 4(2-x)+1=2x+2-5(1-4x)
https://www.mathhomeworkanswers.org/252711/4-2-x-1-2x-2-5-1-4x?show=252712#a252712
<p><a href="https://www.mathhomeworkanswers.org/252711/4-2-x-1-2x-2-5-1-4x" rel="nofollow" style="background-color: transparent; box-sizing: border-box; color: rgb(51, 122, 183); font-family: &quot;Open Sans&quot;,sans-serif; font-size: 29px; font-style: normal; font-variant: normal; font-weight: 500; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">4(2-x)+1=2x+2-5(1-4x) </a></p>
<p>Let's expand both sides of the equation.</p>
<p>8 - 4x + 1 = 2x + 2 - 5 + 20x</p>
<p>Put all the unknown values on one side and all the constant values on the other.</p>
<p>- 4x - 2x - 20x = -8 - 1 + 2 - 5</p>
<p>Comnbine all the terms on both sides.</p>
<p>-26x = -12</p>
<p>x = 12/26 = <span style="text-decoration: underline;">6/13</span></p>
<p><span style="text-decoration: underline;"><strong>Answer: x = 6/13</strong></span></p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252711/4-2-x-1-2x-2-5-1-4x?show=252712#a252712Wed, 20 Jun 2018 17:43:25 +0000Answered: how do you find a 180 degree rotation of f(x)=3x^(4)-2x^(3)+x^(2)-4x-5 ?
https://www.mathhomeworkanswers.org/69080/how-do-you-find-a-180-degree-rotation-of-f-x-3x-4-2x-3-x-2-4x-5?show=252665#a252665
<p style="text-align:justify">Replace x with -x: 3x⁴+2x³+x²+4x-5 then negating the whole expression: -3x⁴-2x³-x²-4x+5.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/69080/how-do-you-find-a-180-degree-rotation-of-f-x-3x-4-2x-3-x-2-4x-5?show=252665#a252665Fri, 15 Jun 2018 17:31:20 +0000Answered: Complex Number
https://www.mathhomeworkanswers.org/252592/complex-number?show=252629#a252629
<p style="text-align:justify">We can write 2=e^(ln(2)) and we can write z=a+ib.</p>
<p style="text-align:justify">So 2^z=</p>
<p style="text-align:justify">(e^(ln(2)))^z=</p>
<p style="text-align:justify">e^(zln(2))=</p>
<p style="text-align:justify">e^(ln(2)(a+ib))=</p>
<p style="text-align:justify">e^(aln(2))×e^(ibln(2)). Let r=e^(aln(2)).</p>
<p style="text-align:justify">But e^(ibln(2)) can be expressed as cosθ+isinθ where θ=bln(2).</p>
<p style="text-align:justify">So we have re^iθ to replace the original 2^z, where r is the modulus |2^z|.</p>
<p style="text-align:justify">So r=1=e^(aln(2)) making a=0. Since a is the real part of z, Re(z)=0, answer A.</p>
<p style="text-align:justify"> </p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252592/complex-number?show=252629#a252629Wed, 13 Jun 2018 17:10:16 +0000Answered: A line that passes midway between and is parallel to both x - y = 6 and x - y = -6.
https://www.mathhomeworkanswers.org/252593/line-that-passes-midway-between-and-is-parallel-to-both-and-x?show=252606#a252606
<p style="text-align: justify;">The line passes midway between the x and y intercepts. These are x=-6 and +6 and y=-6 and +6.</p>
<p style="text-align: justify;">Therefore the line passes through the origin (0,0) and has the same slope so y=x is the equation.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252593/line-that-passes-midway-between-and-is-parallel-to-both-and-x?show=252606#a252606Tue, 12 Jun 2018 23:29:38 +0000Answered: Limit of a function
https://www.mathhomeworkanswers.org/252591/limit-of-a-function?show=252604#a252604
<p style="text-align: justify;">sin(1/x) becomes indeterminate (between +1 and -1) as x➝0. However sinx➝0 as x➝0 and any value multiplied by 0 is also 0. So the limit appears to be 0, answer A.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252591/limit-of-a-function?show=252604#a252604Tue, 12 Jun 2018 23:02:36 +0000Answered: If log4096 is converted to log(base4) A, find the value of A.
https://www.mathhomeworkanswers.org/78847/if-log4096-is-converted-to-log-base4-a-find-the-value-of-a?show=252560#a252560
<p style="text-align: justify;">4⁶=4096, so log₄4006=6. Therefore A=6.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/78847/if-log4096-is-converted-to-log-base4-a-find-the-value-of-a?show=252560#a252560Mon, 11 Jun 2018 16:48:16 +0000Answered: 3x+2y=13; 2x-y=8
https://www.mathhomeworkanswers.org/252536/3x-2y-13-2x-y-8?show=252537#a252537
<p style="text-align: justify;">Double the second equation then add it to the first: 3x+2y+4x-2y=13+16=29. So 7x=29 and x=29/7.</p>
<p style="text-align: justify;">y=2x-8=58/7-8=(58-56)/7=2/7.</p>
<p style="text-align: justify;">So x=29/7 and y=2/7.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252536/3x-2y-13-2x-y-8?show=252537#a252537Sun, 10 Jun 2018 18:14:48 +0000Answered: how to find three rational and three irrational numbers between the following :
https://www.mathhomeworkanswers.org/252519/three-rational-three-irrational-numbers-between-following?show=252528#a252528
<p style="text-align:justify">a) First, the rational numbers. Average of 6.5 and 7.8=(6.5+7.8)/2=7.15. Now take two more averages: (6.5+7.15)/2=6.825 and (7.15+7.8)/2=7.475. So 3 rational numbers could be 6.825, 7.15 and 7.475.</p>
<p style="text-align:justify">Now the irrationals. Square both numbers: 42.25 and 60.84. If we take any three numbers between these limits (excluding perfect squares) and then take the square root of the numbers we will get 3 irrational numbers. Lets’s pick 43, 51 and 59. The square roots are √43, √51 and √59. These all lie between 6.5 and 7.8.</p>
<p style="text-align:justify">b) Using the techniques from (a), we have rationals: 2.75, 2.525, 2.975. And irrationals √6, √10, √7.</p>
<p style="text-align:justify">c) Rationals: 3/14, 5/28, 1/4; irrationals: (√3)/10, (√5)/10, (√7)/10. (1/7)²=1/49=0.02 approx, (2/7)²=4/49=0.08 approx. The numbers 0.03=3/100, 0.05=5/100, 0.07=7/100 lie between these squares. So the square roots must be n the range 1/7 to 2/7: (√3)/10, (√5)/10, (√7)/10.</p>
<p style="text-align:justify">d) We need 3 rationals whose square lies between 1.5 and 2.5. Multiply these by 100: 150 and 250. Now it’s easier to find perfect squares between these: 169=13², 196=14², 225=15². Divide each of these candidates by 10 and we get 1.3, 1.4 and 1.5. These are rational examples that can also be expressed as fractions: 13/10, 7/5, 3/2. Right between 3/2 and 5/2 lies 4/2=2, so √2 lies between √(3/2) and √5/2). We need two more irrationals. √(3/2)=√(6/4)=(√6)/2 and √(5/2)=√(10/4)=(√10)/2. Can we pick an integer between 6 and 10? We can’t pick 8 or 9 because we end up with √2 (which we’ve already chosen) and 9 is a perfect square. But √7/2 we can pick. The average of the two square roots is also irrational, so we have ((√6)/2+(√10)/2)/2=((√6)+(√10))/4 as our third irrational.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252519/three-rational-three-irrational-numbers-between-following?show=252528#a252528Sat, 09 Jun 2018 13:37:50 +0000Answered: how to represent a rational number in the form p/q
https://www.mathhomeworkanswers.org/252508/how-to-represent-a-rational-number-in-the-form-p-q?show=252513#a252513
<p style="text-align:justify">a) Multiply by 100 to get <a href="denied:tel:123.7777" rel="nofollow">123.7777</a>... This separates the recurring part of the decimal from the rest of the number. Now we take the recurring digit(s). There’s only, that’s 7, so we divide by as many 9s, so we need only one to give us 7/9 as a fraction. What we have now is 123 and 7/9. Convert to an improper fraction: 1114/9 (1114=9×123+7). But remember we multiplied by 100 so we now have to divide by that: 1114/900=557/450. That is the fraction in its most reduced form.</p>
<p style="text-align:justify">b) I guess that 8 should be 7 to make the recurring part 745. Follow the rules in (a) and we get 745/999 as the fraction. This doesn’t reduce further so work out the improper fraction: 3+745/999=3742/999.</p>
<p style="text-align:justify">c) Multiply by 100: 823.2727.... 27/99=3/11. So we have 823+3/11=9056/11. Now divide by 100: 9056/1100=2264/275.</p>
<p style="text-align:justify">d) Multiply by 10: 32.3838.... 38/99 is the fraction. So 32+38/99 is 3206/99. Now divide by 10: 3206/990=1603/495.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252508/how-to-represent-a-rational-number-in-the-form-p-q?show=252513#a252513Fri, 08 Jun 2018 19:17:58 +0000Answered: How is the graph of y = csc(x6) transformed from its parent function?
https://www.mathhomeworkanswers.org/252448/how-the-graph-of-csc-x6-transformed-from-its-parent-function?show=252456#a252456
<p style="text-align: justify;">Assuming the parent function is csc(x), it consists of U-shaped curves (upright or inverted) with asymptotes at regular intervals which are for x equal to multiples of π. For odd multiples of π/2, we have vertices at y=1 and y=-1 for upright and inverted curves respectively. csc(x) is not symmetrical about the y axis.</p>
<p style="text-align: justify;">The transformation for csc(x⁶) is to make the U curves very narrow so that the asymptotes are much close together. The vertices are still at y=1 and -1, but, like the asymptotes, are closer together. Unlike the parent function, csc(x⁶) is reflected in the y axis, so is symmetrical about the y axis. Like the parent function, the curves alternate between upright and inverted.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252448/how-the-graph-of-csc-x6-transformed-from-its-parent-function?show=252456#a252456Tue, 05 Jun 2018 13:36:22 +0000Answered: Use the formula to evaluate the series -3+6-12+24-...a^7
https://www.mathhomeworkanswers.org/252403/use-the-formula-to-evaluate-the-series-3-6-12-24-a-7?show=252416#a252416
<p style="text-align:justify">This is a geometric series with starting value a=-3, ratio r=-2.</p>
<p style="text-align:justify">The sum to n terms is a(r^n - 1)/(r-1).</p>
<p style="text-align:justify">Therefore substituting a=-3 and r=-2, this is -3((-2)^n - 1)/-3=(-2)^n - 1.</p>
<p style="text-align:justify">For example S₇=-128-1=-129.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252403/use-the-formula-to-evaluate-the-series-3-6-12-24-a-7?show=252416#a252416Sat, 02 Jun 2018 19:27:05 +0000Answered: Rual has 5 boxes of golf balls each box contains y golf balls his farther gives him antheor 8 golf balls
https://www.mathhomeworkanswers.org/252389/rual-boxes-balls-contains-balls-farther-gives-antheor-balls?show=252395#a252395
1 box contains y balls so 5 boxes contain 5y balls. Plus 8 given to him makes 5y+8.<br />
<br />
When y=4 the total number of golf balls is 5×4+8=28.Algebra 2 Answershttps://www.mathhomeworkanswers.org/252389/rual-boxes-balls-contains-balls-farther-gives-antheor-balls?show=252395#a252395Fri, 01 Jun 2018 12:41:41 +0000Answered: Help with inequalities problems
https://www.mathhomeworkanswers.org/25201/help-with-inequalities-problems?show=252277#a252277
Assuming x= corn, y=tomatoes<br />
<br />
x+y less than equal to 20<br />
<br />
y greater than equal to 5<br />
<br />
x greater than equal to 2y<br />
<br />
Idk the second one but the system is aboveAlgebra 2 Answershttps://www.mathhomeworkanswers.org/25201/help-with-inequalities-problems?show=252277#a252277Thu, 24 May 2018 02:18:10 +0000Answered: The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3)
https://www.mathhomeworkanswers.org/73142/the-ellipse-with-foci-at-4-0-and-4-0-y-intercepts-0-3-and-0-3?show=252272#a252272
<p style="text-align:justify">The ellipse has its centre at the origin (0,0) because of the symmetry of its foci and vertices.</p>
<p style="text-align:justify">The foci lie on the x axis so it’s a horizontal ellipse with standard equation x²/a²+y²/b²=1 where a and b are the lengths of the semi major and semi minor axes respectively. The y intercepts are when x=0 so y²/b²=1 and b²=y²=9 because 3 and -3 squared are both 9. c²=a²-b² where c is the distance of each focus from the centre. We know this distance is 4, so 16=a²-9, and a²=25. So the equation is x²/25+y²/9=1.</p>
<p style="text-align:justify">This can be written 9x²+25y²=225.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/73142/the-ellipse-with-foci-at-4-0-and-4-0-y-intercepts-0-3-and-0-3?show=252272#a252272Wed, 23 May 2018 17:19:01 +0000Answered: What is the equation of the ellipse with foci (0, 3), (0, -3) and co-vertices (1, 0), (-1, 0)?
https://www.mathhomeworkanswers.org/252247/what-is-the-equation-of-the-ellipse-with-foci-and-co-vertices?show=252263#a252263
<p style="text-align: justify;">The centre of the ellipse is at the origin because the foci are equidistant from the origin and lie on the y axis.</p>
<p style="text-align: justify;">The general equation of such an ellipse is x²/a²+y²/b²=1 or x²/b²+y²/a²=1. The ellipse is vertical because the foci are on the y axis. That means we take the second standard form of the ellipse, where a is the length of the semi major axis and b the length of the semi minor axis. The co-vertices are on the x axis and lie on the ellipse itself. We can plug in the coords: 1/b²=1 so b=1. c²=a²-b² where c is the distance of either focus from the centre of the ellipse, which in this case is (0,0). Therefore, since c=3, 9=a²-b²=a²-1, and a²=10.</p>
<p style="text-align: justify;">The equation of the ellipse is x²+y²/10=1. This looks better if we multiply through by 10: 10x²+y²=10.</p>
<p style="text-align: justify;"> </p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252247/what-is-the-equation-of-the-ellipse-with-foci-and-co-vertices?show=252263#a252263Wed, 23 May 2018 09:13:06 +0000Answered: On a rectanle hyperbola, if one point is (2,3) and y is inversely to x, find y when x is 6
https://www.mathhomeworkanswers.org/252248/rectanle-hyperbola-if-one-point-is-and-inversely-find-when-is?show=252261#a252261
<p style="text-align: justify;">y=k/x is the type of equation we’re looking for, where k is constant.</p>
<p style="text-align: justify;">Plug in the given values: 3=k/2 so k=6 and y=6/x. When x=6, y=1.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252248/rectanle-hyperbola-if-one-point-is-and-inversely-find-when-is?show=252261#a252261Wed, 23 May 2018 08:38:58 +0000Answered: Fifteen mothers were asked how many months old their babies we're when they cut their first tooth 8,8,6,8,9,10,5,7,9,5,9,7,6,8,7
https://www.mathhomeworkanswers.org/252222/fifteen-mothers-asked-months-their-babies-their-first-tooth?show=252223#a252223
<p style="text-align: justify;">First, order the data:</p>
<p style="text-align: justify;">5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10.</p>
<p style="text-align: justify;">The median (Q2) is the 8th datum: 8.</p>
<p style="text-align: justify;">We now have a dataset split into two halves: 5, 5, 6, 6, 7, 7, 7 and 8, 8, 8, 9, 9, 9, 10.</p>
<p style="text-align: justify;">Now take the central datum of each half: 6 (Q1) and 9 (Q3).</p>
<p style="text-align: justify;">The IQR is 9-6=3.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252222/fifteen-mothers-asked-months-their-babies-their-first-tooth?show=252223#a252223Mon, 21 May 2018 16:59:45 +0000Answered: The absolute value function is horizontally stretched by a factor of 5, shifted 3 units right, and 4 units down
https://www.mathhomeworkanswers.org/252174/absolute-function-horizontally-stretched-factor-shifted?show=252182#a252182
<p style="text-align:justify">If the function is f(x)=|x| the graph is like a V where the vertex of the V is at the origin. The slope for x>0 is 1 and for x<0 the slope is -1. If we stretch the graph horizontal by a factor of 5, it means that instead of f(1)=1 we want to make the new f(5)=1 so x➝x/5. This makes the slope shallower because of the stretch.</p>
<p style="text-align:justify">We need to displace the vertex, which was at the origin, 3 units right. That means we want f(x) to be zero when x=3. So now we have x/5➝(x-3)/5 because the vertex is now (3,0) instead of (0,0). When x=8, f(8)=1 so the graph is displaced 3 units to the right. Finally, the vertical displacement downwards is achieved by subtracting 4 outside the absolute function: f(x)=|(x-3)/5|-4. The constant -4 is outside because the whole graph is shifted downwards for all x. The vertex is now at (3,-4) and f(8)=-3.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=5952076082065402972" style="height:250px; width:400px"></p>
<p style="text-align:justify">The picture shows in steps how the transformation takes place. The black line is the original function. The red line is the stretch. The blue is the shift to the right. The green line is the shift down, the final transformation.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252174/absolute-function-horizontally-stretched-factor-shifted?show=252182#a252182Thu, 17 May 2018 23:51:58 +0000Answered: Which equation correctly describes the available planting area for the vegetable garden?
https://www.mathhomeworkanswers.org/252116/equation-correctly-describes-available-planting-vegetable?show=252118#a252118
<p style="text-align: justify;">The total garden including the border has dimension 3x by x where x is the width in inches.</p>
<p style="text-align: justify;">The dimensions of the growing area are reduced by 6 inches (3 inches on each side) so its dimensions are 3x-6 by x-6 and the equation for the area is 180=(3x-6)(x-6)=3x²-24x+36, answer option 2.</p>
<p style="text-align: justify;">(Although the question doesn’t ask for it we get the equation 3x²-24x-144=0, which reduces to x²-8x-48=0=(x-12)(x+4), so x=12 inches and the dimensions are 12 by 36 inches, with the growing area 6 by 30 inches.)</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252116/equation-correctly-describes-available-planting-vegetable?show=252118#a252118Mon, 14 May 2018 21:47:05 +0000Answered: P(all three six-sided dice show the same number)
https://www.mathhomeworkanswers.org/252080/p-all-three-six-sided-dice-show-the-same-number?show=252085#a252085
<p style="text-align: justify;">There are 216 possible outcomes for throwing 3 dice. 6 of these outcomes are throwing the same number for all three throws. 6/216=1/36 as the probability.</p>
<p style="text-align: justify;">Another way is to consider just one die. The chances of the other two having the same number are (1/6)²=1/36.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252080/p-all-three-six-sided-dice-show-the-same-number?show=252085#a252085Mon, 14 May 2018 00:08:48 +0000Answered: You are designing a rectangular swimming pool that is above the ground. The width of the pool is 3 feet more than the depth and
https://www.mathhomeworkanswers.org/252051/designing-rectangular-swimming-above-ground-width-than-depth?show=252052#a252052
<p style="text-align:justify">Width=d+3 and length=d+43 where d is the depth. The volume is d(d+3)(d+43) cu ft.</p>
<p style="text-align:justify">The volume can be written d³+46d²+129d.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252051/designing-rectangular-swimming-above-ground-width-than-depth?show=252052#a252052Fri, 11 May 2018 15:20:29 +0000Answered: y varies directly as x, and y = 30 when x = -6
https://www.mathhomeworkanswers.org/252039/y-varies-directly-as-x-and-y-30-when-x-6?show=252047#a252047
<p style="text-align: justify;">y=kx is the equation of proportionality where k is the constant.</p>
<p style="text-align: justify;">Plug in values: 30=-6k, so k=-5.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252039/y-varies-directly-as-x-and-y-30-when-x-6?show=252047#a252047Fri, 11 May 2018 09:39:43 +0000Answered: If y varies directly as x and y=20 when x=5 then what is y when x is 8?
https://www.mathhomeworkanswers.org/251972/if-y-varies-directly-as-x-and-y-20-when-x-5-then-what-is-when-x-is-8?show=251995#a251995
<p style="text-align: justify;">If x is 5 when y is 20, then y=4 when x is 1. So when x=8, y=32.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251972/if-y-varies-directly-as-x-and-y-20-when-x-5-then-what-is-when-x-is-8?show=251995#a251995Wed, 09 May 2018 09:06:41 +0000Answered: (45^50-9)/44
https://www.mathhomeworkanswers.org/251935/45-50-9-44?show=251967#a251967
<p style="text-align:justify">45⁵⁰ is a huge number so subtracting 9 from it is pointless since the number is well out of range for a calculator. But an estimate can be given for the whole expression: it’s approximately 1 followed by 81 zeroes!</p>
<p style="text-align:justify">But it is possible to find the remainder which is always 36.</p>
<p style="text-align:justify">45-9=36 so when we divide by 44 the remainder is 36.</p>
<p style="text-align:justify">Now take 45⁵-9=184528116 and divide by 44=x+36/44, where x is an integer.</p>
<p style="text-align:justify">In fact all powers of 45 when divided by 44 have a remainder of 1. This is because 45=44+1. 45ⁿ=(44+1)ⁿ.</p>
<p style="text-align:justify">If we expand the binomial we get a series of terms which, apart from the last term, contain some multiple of 44. The last term is 1 no matter what n is. So when we divide by 44, we are always left with 1.</p>
<p style="text-align:justify">We can write the original expression as 45⁵⁰/44 - (44-35)/44. So we have in terms of remainders 1+35=36.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251935/45-50-9-44?show=251967#a251967Tue, 08 May 2018 13:36:41 +0000Answered: Find the sum of the first 50 terms. -6,-2,2,6,
https://www.mathhomeworkanswers.org/251942/find-the-sum-of-the-first-50-terms-6-2-2-6?show=251956#a251956
<p style="text-align: justify;">The common difference is 4. The terms in the series can be written, -6, -6+4, -6+2*4, -6+3*4, ...</p>
<p style="text-align: justify;">When we add the first 50 terms we get 50(-6)=-300 to start and then 4(0+1+2+3+...+49).</p>
<p style="text-align: justify;">The sum of the terms in brackets we can write as (0+49)+(1+48)+(2+47)+...+(24+25)=49+49+49+... 25 times.</p>
<p style="text-align: justify;">So that’s 25*49=1225. So the sum of the first 50 terms is -300+4*1225=-300+4900=4600.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251942/find-the-sum-of-the-first-50-terms-6-2-2-6?show=251956#a251956Tue, 08 May 2018 09:58:52 +0000Answered: Solve quadratic equations
https://www.mathhomeworkanswers.org/251949/solve-quadratic-equations?show=251955#a251955
<p style="text-align: justify;">Let the width be W then the length is 2W-1. The area is 10=W(2W-1)=2W²-W.</p>
<p style="text-align: justify;">So we get the quadratic 2W²-W-10=0=(2W-5)(W+2). We reject negative values for W so 2W-5=0, W=5/2=2.5 feet is the solution: the width is 2½ feet and the length is 4 feet.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251949/solve-quadratic-equations?show=251955#a251955Tue, 08 May 2018 09:45:24 +0000Answered: Solve by completing the square 2x^2+3x-4=0
https://www.mathhomeworkanswers.org/251904/solve-by-completing-the-square-2x-2-3x-4-0?show=251905#a251905
<p style="text-align:justify">First, divide through by 2 so that we have x² instead of 2x²:</p>
<p style="text-align:justify">x²+3x/2-2=0.</p>
<p style="text-align:justify">Now, halve the x coefficient and square it: (3/4)²=9/16. We can write this as:</p>
<p style="text-align:justify">x²+3x/2+9/16 - (9/16+2)=0; (x+3/4)²=41/16.</p>
<p style="text-align:justify">Take the square root of each side:</p>
<p style="text-align:justify">x+3/4=±√41/4, x=-3/4±√41/4=0.85078 and -2.35078 approx.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251904/solve-by-completing-the-square-2x-2-3x-4-0?show=251905#a251905Sat, 05 May 2018 16:35:08 +0000Answered: solve by complex ting the square 2x^2+3x-4=0
https://www.mathhomeworkanswers.org/251891/solve-by-complex-ting-the-square-2x-2-3x-4-0?show=251894#a251894
<p><em>solve by complex ting the square 2x^2+3x-4=0</em></p>
<p>In questions like this, you should note that the coefficient of thr x^2 term should be a square number also. So multilpy the whole expression by 2. This gives us,</p>
<p>4x^2 + 6x - 8 = 0</p>
<p>We are looking for an expression of the form: ax^2 + 2abx + b^2, which equals (ax + b)^2</p>
<p>we've got the <span style="text-decoration: underline;">a = 4</span>, so now we need 2abx = 6x.</p>
<p>This gives <span style="text-decoration: underline;">b = 3/2</span>, Hence b^2 = 9/4.</p>
<p>rearranging, we get</p>
<p>4x^2 + 6x - 8 = 0</p>
<p>4x^2 + 2*(3/2)*x + 9/14 - 9/4 - 8 = 0</p>
<p>(2x + 3/2)^2 - 9/4 - 32/4 = 0</p>
<p>(2x + 3/2)^2 = 41/4</p>
<p>2x + 3/2 = ±√(41)/2</p>
<p>x + 3/4 = ±√(41)/4</p>
<p><span style="text-decoration: underline;"><strong>x = (-3 ± √(41)) / 4</strong></span></p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251891/solve-by-complex-ting-the-square-2x-2-3x-4-0?show=251894#a251894Sat, 05 May 2018 06:21:30 +0000Answered: al can change the oil and rotate a car's tire in 25 minutes. Together Al and Joe can do the same job in 15 minutes. How long would it take for joe to do the job working by himself?
https://www.mathhomeworkanswers.org/251873/change-rotate-minutes-together-minutes-would-working-himself?show=251881#a251881
<p style="text-align:justify">Al’s job rate is 1 job in 25 minutes or 1/25.</p>
<p style="text-align:justify">Joe’s job rate is 1 job in J minutes or 1/J.</p>
<p style="text-align:justify">Together their rate is 1/25+1/J=one job in 15 minutes=1/15.</p>
<p style="text-align:justify">So the equation is 1/25+1/J=1/15.</p>
<p style="text-align:justify">Multiply through by 75J:</p>
<p style="text-align:justify">3J+75=5J so 2J=75 and J=37.5 minutes, if Joe did the job on his own.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251873/change-rotate-minutes-together-minutes-would-working-himself?show=251881#a251881Fri, 04 May 2018 11:28:07 +0000Answered: a ball thrown from the top row of seats. the function h(t)=16t^2+80t+96 give the hight in feet, of the ball t seconds after it is thrown. how long does it take before the ball hits the ground?
https://www.mathhomeworkanswers.org/251875/thrown-seats-function-hight-seconds-after-thrown-before-ground?show=251878#a251878
<p style="text-align:justify">When h(t)=0 the ball reaches the ground, so 16(t²+5t+6)=0, so t²+5t+6=0=(t+3)(t+2) which gives us negative values for t, so I suspect that 16t² should be -16t².</p>
<p style="text-align:justify">So we would have -t²+5t+6=0, that is, t²-5t-6=0=(t-6)(t+1) and t=6 seconds is the time the ball takes to reach the ground. We ignore t=-1 as meaningless (time before the ball was thrown).</p>
<p style="text-align:justify">The constant 96 feet is the height of the top row of seats. -16t² is the negative effect of gravity on the ball and 80 feet per second is the vertical component of the speed the ball was thrown. This is how h(t) was constructed.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251875/thrown-seats-function-hight-seconds-after-thrown-before-ground?show=251878#a251878Fri, 04 May 2018 11:08:17 +0000Answered: find the least common multiple of 15a and 6n^2
https://www.mathhomeworkanswers.org/251859/find-the-least-common-multiple-of-15a-and-6n-2?show=251864#a251864
<p style="text-align: justify;">15=3*5 and 6=3*2, LCM of 15 and 6=30, so LCM of expressions is 30an².</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251859/find-the-least-common-multiple-of-15a-and-6n-2?show=251864#a251864Thu, 03 May 2018 16:44:53 +0000Answered: how to solve mid-segment theorem math problems?
https://www.mathhomeworkanswers.org/251827/how-to-solve-mid-segment-theorem-math-problems?show=251835#a251835
<p style="text-align: justify;">If you’re given the coords of the endpoints of a line segment, the midway point can be found easily by averaging the x and y coords. So if the endpoints were (a,b) and (c,d) the midpoint is ((a+c)/2,(b+d)/2).</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251827/how-to-solve-mid-segment-theorem-math-problems?show=251835#a251835Wed, 02 May 2018 16:37:57 +0000Answered: F(x)=x^3 is scaled by -2, so what happens to the graph?
https://www.mathhomeworkanswers.org/251800/f-x-x-3-is-scaled-by-2-so-what-happens-to-the-graph?show=251802#a251802
<p style="text-align:justify">It’s assumed that by scaled you mean x➝-2x and y➝-8x³.</p>
<p style="text-align:justify">The minus sign inverts or reflects the graph in the x-axis. The factor 2 makes the curve narrower or elongated. For example, when x=1, the original curve passes through (1,1), but after the transformation this point becomes (1,-8). When x=2, (2,8)➝(2,-64). When x=½, (½,⅛)➝(½,-1). The origin is unaffected.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=14674740467229536986" style="height:774px; width:400px"></p>
<p style="text-align:justify">The red curve is the original and the blue curve is its transformation after scaling. Note that the saddle point at the origin becomes quite narrow.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251800/f-x-x-3-is-scaled-by-2-so-what-happens-to-the-graph?show=251802#a251802Tue, 01 May 2018 15:06:56 +0000Answered: i need help with this
https://www.mathhomeworkanswers.org/251798/i-need-help-with-this?show=251801#a251801
<p style="text-align: justify;">3y≥2x-12, y≥2x/3-4 so slope is 2/3 and y-intercept is -4. Since this is an inequality not an equation, the slope and y-intercept are properties of the lower boundary of the graph.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251798/i-need-help-with-this?show=251801#a251801Tue, 01 May 2018 14:47:14 +0000Answered: A concrete mix has the ratio 1 part cement, 2 parts water, and 3 parts sand. How much water can be used if 78 kg of sand and 21 kg of cement are available? How much concrete can be made?
https://www.mathhomeworkanswers.org/251777/concrete-cement-water-parts-water-cement-available-concrete?show=251789#a251789
<p><em>A concrete mix has the ratio 1 part cement, 2 parts water, and 3 parts sand. How much water can be used if 78 kg of sand and 21 kg of cement are available? How much concrete can be made?</em></p>
<p>Ratio of cement:water:sand = 1:2:3</p>
<p>We have 78 kg sand and 21 kg cement</p>
<p>But, ratio of cement:sand is 1:3 = 21:63</p>
<p>i.e. for 21 kg cement we only need to use 63 kg sand (the remaining 15 kg sand is not used - perhaps next time!)</p>
<p>Ratio of cement:water is 1:2 = 21:42</p>
<p><span style="text-decoration: underline;"><strong>Therefore we should use 42 kg water.</strong></span></p>
<p>Total mix is 21 + 42 + 63 = 126 kg</p>
<p><span style="text-decoration: underline;"><strong>Amount of concrete made is 126 kg</strong></span></p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251777/concrete-cement-water-parts-water-cement-available-concrete?show=251789#a251789Tue, 01 May 2018 05:55:55 +0000Answered: Write the quadratic equation whose roots are -4 and -6, and whose leading coefficient is 1
https://www.mathhomeworkanswers.org/251781/write-quadratic-equation-whose-whose-leading-coefficient?show=251784#a251784
<p><em>Write the quadratic equation whose roots are -4 and -6, and whose leading coefficient is 1</em></p>
<p>the roots are -4 and -6</p>
<p>Therefore two factors are (x + 4) and (x + 6).</p>
<p>The equation from which these two factores are derived can be given be the product of the two factors, viz.</p>
<p><span style="text-decoration: underline;">(x + 4)(x + 6) = 0 </span></p>
<p>Any constant multiple of the above product is also a possible solution, i.e.</p>
<p>C*(x + 4)(x + 6) = 0</p>
<p>Multiplying out gives,</p>
<p>C*(x*2 + 10x + 24) = 0</p>
<p>If we set C = 1, then this quadratic would have a leading coefficient of 1.</p>
<p><span style="text-decoration: underline;"><strong>The quadratic then is: x^2 + 10x + 24 = 0</strong></span></p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251781/write-quadratic-equation-whose-whose-leading-coefficient?show=251784#a251784Tue, 01 May 2018 05:17:23 +0000Answered: What is ABC?
https://www.mathhomeworkanswers.org/251739/what-is-abc?show=251741#a251741
<p style="text-align: justify;">B=3A+26 and C=A+49.</p>
<p style="text-align: justify;">Also, A+B+C=180 so A+3A+26+A+49=180.</p>
<p style="text-align: justify;">Therefore, 5A+75=180, A+15=36 (dividing through by common factor 5).</p>
<p style="text-align: justify;">So, A=36-15=21. We can work out B=3*21+26=89, C=21+49=70.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251739/what-is-abc?show=251741#a251741Sun, 29 Apr 2018 20:58:02 +0000Answered: -1,1/2,1/3
https://www.mathhomeworkanswers.org/251691/1-1-2-1-3?show=251694#a251694
<p style="text-align: justify;">My guess is that the next two terms will be 1/4 and -1/5.</p>
<p style="text-align: justify;">The generator for each term is (-1)ⁿ(1/n).</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251691/1-1-2-1-3?show=251694#a251694Fri, 27 Apr 2018 14:16:52 +0000Which equation BEST represents the line of best fit for the scatterplot? A) y = x B) y = -x C) y = x + 1 D) y = x - 1
https://www.mathhomeworkanswers.org/251676/which-equation-best-represents-line-best-for-the-scatterplot
<p> </p>
<table border="0" cellpadding="0" cellspacing="0" style="color:rgb(83, 83, 83); font-family:ptsansregular,arial,helvetica,sans-serif; font-size:14px; margin-top:10px; width:100%">
<tbody>
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<td style="border-color:black">
<p>Which equation BEST represents the line of best fit for the scatterplot?</p>
</td>
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</table>
<table border="0" cellpadding="5" cellspacing="0" class="answer_table" id="answer_table_1783" style="width:660px">
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<td style="border-color:black">A)</td>
<td style="border-color:black">y = x</td>
<td style="border-color:black; width:70px"> </td>
</tr>
<tr>
<td style="border-color:black"> </td>
<td style="border-color:black">B)</td>
<td style="border-color:black">y = -x</td>
<td style="border-color:black; width:70px"> </td>
</tr>
<tr>
<td style="border-color:black"> </td>
<td style="border-color:black">C)</td>
<td style="border-color:black">y = x + 1</td>
<td style="border-color:black; width:70px"> </td>
</tr>
<tr>
<td style="border-color:black"> </td>
<td style="border-color:black">D)</td>
<td style="border-color:black">y = x - 1</td>
</tr>
</tbody>
</table>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251676/which-equation-best-represents-line-best-for-the-scatterplotThu, 26 Apr 2018 22:10:22 +0000Answered: g(x) when f(x)= /x/ +3 translated horizontally 6 units to the left and reflected across the y axis
https://www.mathhomeworkanswers.org/7102/when-translated-horizontally-units-reflected-across-axis?show=251592#a251592
<p style="text-align:justify">The horizontal translation produces |x+6|+3 moving the vertex from (0,3) to (-6,3). The y intercept is 9. (It was 3 for f(x).)</p>
<p style="text-align:justify">The reflection in the y axis translates the vertex to (6,3), which is a shift of 12 to the right. The y intercept remains at 9.</p>
<p style="text-align:justify">The equation is g(x)=|x-6|+3.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/7102/when-translated-horizontally-units-reflected-across-axis?show=251592#a251592Fri, 20 Apr 2018 20:59:12 +0000Answered: why are x is greater than or equal to 0 and y is greater than or equal to 0 part of the constraints in many linear programs?
https://www.mathhomeworkanswers.org/247827/greater-equal-greater-than-equal-constraints-linear-programs?show=251590#a251590
<p style="text-align: justify;">The usual reason is that negative values would have no meaning in the context for which the linear model was designed. This is particularly true in the field of economics, marketing, trends, etc. The equations used usually have the capability of processing negative amounts and producing negative results, but such values would have no meaning when applied practically.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/247827/greater-equal-greater-than-equal-constraints-linear-programs?show=251590#a251590Fri, 20 Apr 2018 12:29:52 +0000Answered: A triangle is reflected across line l and them m. If the lines intersect,what type of isometry is this composition of reflections
https://www.mathhomeworkanswers.org/251528/triangle-reflected-intersect-isometry-composition-reflections?show=251570#a251570
<p style="text-align:justify">Since the two reflections have the same aspect, the isometry is rotation and translation.</p>
<p style="text-align:justify">(The degree of rotation is twice the angle between l and m.)</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/251528/triangle-reflected-intersect-isometry-composition-reflections?show=251570#a251570Thu, 19 Apr 2018 11:40:42 +0000