| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.67 |
| Score | 0% | 73% |
For this diagram, the Pythagorean theorem states that b2 = ?
c - a |
|
c2 - a2 |
|
a2 - c2 |
|
c2 + a2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
If a = 5, b = 9, c = 3, and d = 7, what is the perimeter of this quadrilateral?
| 21 | |
| 14 | |
| 24 | |
| 26 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 5 + 9 + 3 + 7
p = 24
What is 3a - 8a?
| 11a2 | |
| a2 | |
| 11 | |
| -5a |
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.
3a - 8a = -5a
If side a = 4, side b = 4, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{52} \) | |
| \( \sqrt{32} \) | |
| \( \sqrt{41} \) | |
| \( \sqrt{145} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 42 + 42
c2 = 16 + 16
c2 = 32
c = \( \sqrt{32} \)
A coordinate grid is composed of which of the following?
x-axis |
|
origin |
|
all of these |
|
y-axis |
The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.