| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
If the area of this square is 1, what is the length of one of the diagonals?
| \( \sqrt{2} \) | |
| 8\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| 7\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{1} \) = 1
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 12 + 12
c2 = 2
c = \( \sqrt{2} \)
If side a = 3, side b = 1, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{85} \) | |
| \( \sqrt{65} \) | |
| \( \sqrt{10} \) | |
| \( \sqrt{106} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 32 + 12
c2 = 9 + 1
c2 = 10
c = \( \sqrt{10} \)
What is 2a - 9a?
| 18a | |
| 11 | |
| -7a | |
| -7 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
2a - 9a = -7a
A(n) __________ is to a parallelogram as a square is to a rectangle.
trapezoid |
|
quadrilateral |
|
triangle |
|
rhombus |
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
The endpoints of this line segment are at (-2, -1) and (2, -7). What is the slope of this line?
| -1\(\frac{1}{2}\) | |
| -3 | |
| -2 | |
| 1\(\frac{1}{2}\) |
The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -1) and (2, -7) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-7.0) - (-1.0)}{(2) - (-2)} \) = \( \frac{-6}{4} \)