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Avanti V.
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Geometry
TutorMe
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.

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
TutorMe
Question:

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

Avanti V.

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
TutorMe
Question:

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

Avanti V.

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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