Math Homework Answers - Recent questions and answers in Algebra 2 Answers
https://www.mathhomeworkanswers.org/qa/algebra-2-answers
Powered by Question2AnswerAnswered: Through the origin with slope -5
https://www.mathhomeworkanswers.org/254386/through-the-origin-with-slope-5?show=254395#a254395
<p style="text-align: justify;">Because the line goes through the origin, there are no intercepts so y=-5x is the line.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/254386/through-the-origin-with-slope-5?show=254395#a254395Thu, 20 Sep 2018 09:14:08 +0000Answered: set all inequalities that model this solution
https://www.mathhomeworkanswers.org/254384/set-all-inequalities-that-model-this-solution?show=254385#a254385
<p style="text-align: justify;">x+y≥25, x>10 or x≥11, x≥25-y, y≥25-x</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/254384/set-all-inequalities-that-model-this-solution?show=254385#a254385Wed, 19 Sep 2018 21:38:51 +0000Answered: Story problem equation
https://www.mathhomeworkanswers.org/254368/story-problem-equation?show=254372#a254372
<p style="text-align:justify">Let x be the first child’s enrolment fee per day, which is 5x for 5 days, then the second child’s is 5x-50 for 5 days.</p>
<p style="text-align:justify">Total fee is 5x+5x-50=200.</p>
<p style="text-align:justify">10x=250, x=$25. </p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/254368/story-problem-equation?show=254372#a254372Wed, 19 Sep 2018 07:28:22 +0000Answered: 144 = (x+4)(3x+6)
https://www.mathhomeworkanswers.org/254285/144-x-4-3x-6?show=254286#a254286
<p style="text-align:justify">144=3x²+18x+24, divide through by 3: 48=x²+6x+8, x²+6x-40=0=(x+10)(x-4).</p>
<p style="text-align:justify">So x=-10 or 4.</p>
<p style="text-align:justify">OR</p>
<p style="text-align:justify">Divide the original equation by 3:</p>
<p style="text-align:justify">48=(x+4)(x+2)=x²+6x+8, ...</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/254285/144-x-4-3x-6?show=254286#a254286Sun, 16 Sep 2018 08:22:57 +0000Answered: Write the equation of the line passing through given points
https://www.mathhomeworkanswers.org/254265/write-the-equation-of-the-line-passing-through-given-points?show=254267#a254267
<p style="text-align: justify;">Slope=(-2-(-3))/(-6-(-4))=-1/2.</p>
<p style="text-align: justify;">If we start with y=mx+b where m=slope=-1/2 and b is the y intercept, we can derive the form required.</p>
<p style="text-align: justify;">y=-x/2+b, plug in a point (-4,-3): -3=2+b, b=-5.</p>
<p style="text-align: justify;">So y+x/2=-5 which can be written: 2y+x=-10.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/254265/write-the-equation-of-the-line-passing-through-given-points?show=254267#a254267Fri, 14 Sep 2018 20:17:05 +0000Answered: Find an equation of the line through (3,8) and parallel to y=4x-8. write the equation using function notation.
https://www.mathhomeworkanswers.org/254261/equation-through-parallel-equation-using-function-notation?show=254262#a254262
<p style="text-align:justify">Parallel lines have the same slope so we can write the equation of the required line as y=4x+b where b is the y intercept. Plug in (3,8): 8=4×3+b, 8=12+b, b=-4, so y=4x-4, that is, f(x)=4x-4 or f:x➝4x-4.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/254261/equation-through-parallel-equation-using-function-notation?show=254262#a254262Fri, 14 Sep 2018 18:32:50 +0000Answered: Solve inequality and graph
https://www.mathhomeworkanswers.org/254205/solve-inequality-and-graph?show=254213#a254213
<p style="text-align:justify">You haven’t submitted a question, so I guess you want some general ideas.</p>
<p style="text-align:justify">Start with a number line. Let’s mark a point on the line, say, at 5.</p>
<p style="text-align:justify">The line to the left of 5, but not including 5 itself, is all the numbers less than 5, and we can represent these by writing x<5. When we include 5 itself, we get x≤5, all numbers less than or equal to 5.</p>
<p style="text-align:justify">The line to the right of 5 is represented by x>5 or x≥5, depending on whether 5 is excluded or included.</p>
<p style="text-align:justify">I guess you already understand this, so let’s move on.</p>
<p style="text-align:justify">What does y<x+5 mean? To represent this we can’t use just one number line, but we use two at right angles, one for x (horizontal) and one for y (vertical). Where they cross is the origin (0,0) where both number lines have their zero.</p>
<p style="text-align:justify">The graph of y<x+5 is a straight line which crosses the x number line (x axis) at -5 and crosses the y number line (y axis) at 5. The line slopes to the right at 45°. The whole area below the line represents y<x+5, but excludes points on the line itself, whereas y≤x+5 includes points on the line. So when we switched from a single number line to two number lines, we went from left and right to lower than (or below) to higher than (or above). Remember L=left=lower=less. y>x+5 and y≥x+5 represent combinations of x and y above the line, excluding or including points on the line itself. </p>
<p style="text-align:justify">Similarly, we use the same reasoning and representation for, say, y<3x+4, but the line is steeper. Above and below still represent the same things. And no matter what equation we have to relate x and y the same rules apply using above and below (higher and lower).</p>
<p style="text-align:justify">To solve inequalities we apply the same rules as for solving an equation but take care to preserve the inequality sign. If we have y<2x+7 we can express x in terms of y:</p>
<p style="text-align:justify">y<2x+7; subtract 7 from both sides: y-7<2x. Now divide through by 2: ½(y-7)<x. Note that the “wide” part of the inequality sign faces x, so if we switch the left and right sides of the inequality we also switch the sign itself: x>½(y-7), and note that the wide part of the sign still faces x.</p>
<p style="text-align:justify">I hope this helps you.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/254205/solve-inequality-and-graph?show=254213#a254213Wed, 12 Sep 2018 09:31:32 +0000Answered: P plus 3-18
https://www.mathhomeworkanswers.org/254129/p-plus-3-18?show=254146#a254146
<p style="text-align: justify;">Do you want two numbers that add up to 3 and multiply to be -18?</p>
<p style="text-align: justify;">If so we can call the numbers a and b, so a+b=3 and ab=-18.</p>
<p style="text-align: justify;">b=3-a so ab=a(3-a)=-18. 3a-a²=-18, a²-3a-18=0=(a-6)(a+3).</p>
<p style="text-align: justify;">So the two numbers are 6 and -3.</p>
<p style="text-align: justify;"> </p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/254129/p-plus-3-18?show=254146#a254146Fri, 07 Sep 2018 13:57:25 +0000Answered: find P(5) by synthetic division if P(x)=2x^4 -x^2 +3x -1.
https://www.mathhomeworkanswers.org/254064/find-p-5-by-synthetic-division-if-p-x-2x-4-x-2-3x-1?show=254074#a254074
<p style="text-align: justify;">P(5)=2×5⁴-5²+3×5-1=1250-25+15-1=1239.</p>
<p style="text-align: justify;">Synthetic division is usually applied when factorising given a known or estimated zero.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/254064/find-p-5-by-synthetic-division-if-p-x-2x-4-x-2-3x-1?show=254074#a254074Wed, 05 Sep 2018 07:47:56 +0000Answered: what is the hcf of 77,143 and 91
https://www.mathhomeworkanswers.org/60631/what-is-the-hcf-of-77-143-and-91?show=254061#a254061
GFC = 1 :)Algebra 2 Answershttps://www.mathhomeworkanswers.org/60631/what-is-the-hcf-of-77-143-and-91?show=254061#a254061Tue, 04 Sep 2018 13:00:07 +0000Answered: What is set of natural numbers less than 10?
https://www.mathhomeworkanswers.org/37377/what-is-set-of-natural-numbers-less-than-10?show=254060#a254060
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16Algebra 2 Answershttps://www.mathhomeworkanswers.org/37377/what-is-set-of-natural-numbers-less-than-10?show=254060#a254060Tue, 04 Sep 2018 12:15:43 +0000Answered: Find the perimeter of the triangle with the vertices at (2, 2), (-3, 5), and (-2, -6).
https://www.mathhomeworkanswers.org/253924/find-the-perimeter-of-the-triangle-with-the-vertices-at-and-2?show=253932#a253932
<p style="text-align:justify">Let these three points be A, B and C the vertices of the triangle.</p>
<p style="text-align:justify">Use Pythagoras Theorem for each pair of coordinates, the root of the sum of the squares of the differences between the x and y coords:</p>
<p style="text-align:justify">AB=√((2-(-3))²+(2-5)²)=√(5²+(-3)²)=√(25+9)=√34 (x-coord diff=2-(-3)=2+3=5, y-coord diff=2-5=-3)</p>
<p style="text-align:justify">BC=√((-3-(-2))²+(5-(-6))²)=√((-1)²+11²)=√(1+121)=√122</p>
<p style="text-align:justify">CA=√((-2-2)²+(-6-2)²)=√((-4)²+(-8)²)=√(16+64)=√80</p>
<p style="text-align:justify">The perimeter=AB+BC+CA=√34+√122+√80=25.8206 approx.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=15610955156772962125" style="height:684px; width:400px"></p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253924/find-the-perimeter-of-the-triangle-with-the-vertices-at-and-2?show=253932#a253932Wed, 29 Aug 2018 08:40:23 +0000Answered: (y^3+1)-[(y^2+1)+(3y-7)]
https://www.mathhomeworkanswers.org/253891/y-3-1-y-2-1-3y-7?show=253892#a253892
<p style="text-align:justify">y³+1-[(y²+1)+(3y-7)]=</p>
<p style="text-align:justify">y³+1-(y²+1)-(3y-7)=</p>
<p style="text-align:justify">y³+1-y²-1-3y+7=</p>
<p style="text-align:justify">y³-y²-3y+7, which is the result in standard polynomial form. The expression doesn’t simplify any further.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253891/y-3-1-y-2-1-3y-7?show=253892#a253892Sun, 26 Aug 2018 08:39:07 +0000Answered: Write the equation of the line if m=-3/2 and b=16
https://www.mathhomeworkanswers.org/253721/write-the-equation-of-the-line-if-m-3-2-and-b-16?show=253722#a253722
<p style="text-align: justify;">y=mx+b so y=-3x/2+16.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253721/write-the-equation-of-the-line-if-m-3-2-and-b-16?show=253722#a253722Mon, 20 Aug 2018 22:32:45 +0000Answered: working alone,Maria can pick forty bushels of apples in 10 hours.Kathryn can pick the same amount in 13 hours.Find how long it would take them if they worked together
https://www.mathhomeworkanswers.org/253581/working-maria-bushels-apples-kathryn-amount-worked-together?show=253590#a253590
<p style="text-align:justify">Maria works at the rate of 40 bushels per 10 hours=40/10=4 bushels per hour.</p>
<p style="text-align:justify">Kathryn’s rate is 40/13 bushels per hour.</p>
<p style="text-align:justify">Combined rate is 4+40/13=92/13 bushels per hour. This is the same as 13/92 hours per bushel.</p>
<p style="text-align:justify">So, for 40 bushels the time it takes is 40×13÷92=10×13/23=130/23=5.65 hours.</p>
<p style="text-align:justify">Another way to do this is to divide the 40 bushels in the ratio of their rates of working. Since they are both timed on how long it takes to pick 40 bushels, the ratio is 10:13. That means the quantity is split as 10/(10+13)=10/23 and 13/(10+13)=13/23. So 40 bushels is split as 10/23×40=400/23 bushels and 13/23×40=520/23 bushels.</p>
<p style="text-align:justify">The faster worker is given the larger portion. Maria is faster than Kathryn and her rate is 40/10=4 bushels per hour. The time it takes Maria to pick 520/23 (the larger portion) is quantity/rate=520/23÷4=130/23=5.65hrs approx. The time it takes Kathryn to pick 400/23 bushels at the rate of 40/13 bushels per hour is 400/23÷(40/13)=400/23×13/40=130/23=5.65hrs, the same time Maria takes to pick her portion.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253581/working-maria-bushels-apples-kathryn-amount-worked-together?show=253590#a253590Wed, 15 Aug 2018 09:01:05 +0000Answered: Find the value that completes the square and rewrite as a perfect square.
https://www.mathhomeworkanswers.org/253504/find-the-value-that-completes-square-rewrite-perfect-square?show=253506#a253506
<p style="text-align: justify;">Halve the central coefficient and square it: (15/2)²=225/4.</p>
<p style="text-align: justify;">So x²+15x+225/4=(x+15/2)².</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253504/find-the-value-that-completes-square-rewrite-perfect-square?show=253506#a253506Tue, 07 Aug 2018 16:50:33 +0000Answered: Solve each equation by taking the square roots
https://www.mathhomeworkanswers.org/253503/solve-each-equation-by-taking-the-square-roots?show=253505#a253505
<p style="text-align: justify;">17b²-6=-227, 17b²=-221, b²=-13, so the solution is a complex number.</p>
<p style="text-align: justify;">b=±i√13 where i is the imaginary √-1. Therefore b=±3.6056i approx.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253503/solve-each-equation-by-taking-the-square-roots?show=253505#a253505Tue, 07 Aug 2018 16:34:54 +0000Answered: X+15%=76.77
https://www.mathhomeworkanswers.org/253337/x-15%25-76-77?show=253352#a253352
<p style="text-align:justify">15% is 0.15 decimal.</p>
<p style="text-align:justify">Assuming this means x plus 15% of x then x+0.15x=1.15x=76.77, making x=76.77/1.15=66.76 approx.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253337/x-15%25-76-77?show=253352#a253352Sat, 28 Jul 2018 13:08:38 +0000Answered: How do you solve, x+15%=76.77
https://www.mathhomeworkanswers.org/253338/how-do-you-solve-x-15%25-76-77?show=253344#a253344
<p style="text-align:justify">x+15% is probably the same as x+(15% of x), that is, x+0.15x or x(1+0.15)=1.15x, making the equation 1.15x=76.77.</p>
<p style="text-align:justify">So x=76.77/1.15=66.76 approx.</p>
<p style="text-align:justify">The only other interpretation is to convert 15% into a decimal 0.15: x+0.15=76.77 so x=76.62, but I don’t think that’s how the question should be interpreted because it has no practical meaning.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253338/how-do-you-solve-x-15%25-76-77?show=253344#a253344Sat, 28 Jul 2018 08:46:55 +0000Answered: Can you please help me solving the problem?
https://www.mathhomeworkanswers.org/253266/can-you-please-help-me-solving-the-problem?show=253267#a253267
<p style="text-align: justify;">5p=q/2, so 10p=q or q=10p.</p>
<p style="text-align: justify;">This means that, if p=1, q=10; if p=2, q=20, and so on. It also means, if p=½, q=5. So when we know p we can find q; and when we know q we can find p.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/253266/can-you-please-help-me-solving-the-problem?show=253267#a253267Tue, 24 Jul 2018 14:49:02 +0000Answered: 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 +0000