| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.26 |
| Score | 0% | 65% |
The endpoints of this line segment are at (-2, 6) and (2, -6). What is the slope of this line?
| -1 | |
| -3 | |
| -\(\frac{1}{2}\) | |
| -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, 6) and (2, -6) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-6.0) - (6.0)}{(2) - (-2)} \) = \( \frac{-12}{4} \)If a = 5, b = 2, c = 1, and d = 4, what is the perimeter of this quadrilateral?
| 14 | |
| 23 | |
| 12 | |
| 18 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 5 + 2 + 1 + 4
p = 12
A(n) __________ is to a parallelogram as a square is to a rectangle.
triangle |
|
quadrilateral |
|
trapezoid |
|
rhombus |
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
What is 2a8 + 8a8?
| -6 | |
| 10a8 | |
| -6a16 | |
| 10 |
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.
2a8 + 8a8 = 10a8
If the area of this square is 49, what is the length of one of the diagonals?
| 7\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) | |
| 8\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7
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 = 72 + 72
c2 = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)