| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.15 |
| Score | 0% | 63% |
If side a = 4, side b = 6, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{80} \) | |
| \( \sqrt{85} \) | |
| \( \sqrt{52} \) | |
| \( \sqrt{58} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 42 + 62
c2 = 16 + 36
c2 = 52
c = \( \sqrt{52} \)
The dimensions of this trapezoid are a = 6, b = 5, c = 9, d = 8, and h = 4. What is the area?
| 11 | |
| 21 | |
| 26 | |
| 18 |
The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:
a = ½(b + d)(h)
a = ½(5 + 8)(4)
a = ½(13)(4)
a = ½(52) = \( \frac{52}{2} \)
a = 26
Which of the following statements about a triangle is not true?
area = ½bh |
|
exterior angle = sum of two adjacent interior angles |
|
perimeter = sum of side lengths |
|
sum of interior angles = 180° |
A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.
A coordinate grid is composed of which of the following?
all of these |
|
y-axis |
|
origin |
|
x-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.
Solve for b:
b2 - 17b + 62 = -b - 1
| 8 or 3 | |
| 7 or 9 | |
| 8 or 8 | |
| 4 or -3 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
b2 - 17b + 62 = -b - 1
b2 - 17b + 62 + 1 = -b
b2 - 17b + b + 63 = 0
b2 - 16b + 63 = 0
Next, factor the quadratic equation:
b2 - 16b + 63 = 0
(b - 7)(b - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 7) or (b - 9) must equal zero:
If (b - 7) = 0, b must equal 7
If (b - 9) = 0, b must equal 9
So the solution is that b = 7 or 9