Avanti V.

Business Student at UT Austin

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Geometry

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Question:

You have a 3x4 rectangle that is made up of 12 congruent squares. What is the parameter of the rectangle if the area of one square is 81?

Avanti V.

Answer:

So we know that the area of on square is 81. The area of the figure is calculated by length times width we know that L*W = 81. But since this figure is a square we know that the length and the width are the same so it would be L^2 or W^2 = 81. We know that 9^2 is 81 so each side of the square has a length of 9. Now we know that there are 12 squares that make up this rectangle. Since it is a 3x4 we know that the perimeter would be 3L +4W + 3L + 4W. So we just have to plug in 9 for the length and width and solve for the perimeter. So for the length it would be 9x3 = 18 for the length of one side. and there are two sides so the total perimeter of the length would be 18x2 = 36. The width of one side would be 4x9 = 36, multiplied by 2 sides to get a width of 36x2 = 72. Therefore, the perimeter of the rectangle would be 36+72 = 108.

ACT

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Question:

X + 4Y = 11 X +Z = 10 If Z is one less than Y, what is the value of X.

Avanti V.

Answer:

So Z can also be written out at Y-1. So the new equation can be written out as X + (Y-1) = 10. We can now rearrange the equation to solve for Y. The equation would be Y = (10-X) + 1. We would plug This Y into the other equation. (X + 4((10-X)+4) =11). We would expand the 4 into the equations to get X + 40 -4X +4 = 11. We combine like terms to get -3X +44 = 11. Now we would move the 44 to the other side or subtract 44 from both sides to get -3X = -33. Now we would divide both sides by -3 to get X = 11. Therefore, the value of X is 11.

Algebra

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Question:

X+X+X = 30 X+Y+Y = 18 Y-Z = 2 Z+Y x(times) X = ? Solve for ?

Avanti V.

Answer:

So we know that 3X = 30, to solve for x, we must divide both sides by 3. Once we do that we know that X = 10. Now we can plug X into the next equation to get 10+ 2Y = 18. To solve for Y we must first subtract 10 from both sides of move the 10 to the other side. Once we do that we get. 2Y = 8. Now we divide 2 from both sides to get Y = 4 Now that we know what Y is we can plug Y into the next equation to solve for Z. So we now have 4-Z = 2. Lets from add Z to both sides to get 4 = 2+ Z. Next we subtract 2 from both sides or move the 2 over to the other side. We now get that 2 = Z. Since we now have all the values solved we just have to replace them in the equation and solve it. So Z + Y x X becomes 2+4x10. First we need to multiply before we add so we now get 2+40 to solve for ? and get the answer of 42!

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