| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
The dimensions of this trapezoid are a = 5, b = 9, c = 8, d = 2, and h = 3. What is the area?
| 11 | |
| 16 | |
| 16\(\frac{1}{2}\) | |
| 20 |
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(9 + 2)(3)
a = ½(11)(3)
a = ½(33) = \( \frac{33}{2} \)
a = 16\(\frac{1}{2}\)
Solve for b:
9b + 8 = 7 + 5b
| \(\frac{5}{6}\) | |
| 1\(\frac{2}{5}\) | |
| -2\(\frac{2}{3}\) | |
| -\(\frac{1}{4}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
9b + 8 = 7 + 5b
9b = 7 + 5b - 8
9b - 5b = 7 - 8
4b = -1
b = \( \frac{-1}{4} \)
b = -\(\frac{1}{4}\)
Simplify 4a x 5b.
| 20ab | |
| 20a2b2 | |
| 9ab | |
| 20\( \frac{a}{b} \) |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
4a x 5b = (4 x 5) (a x b) = 20ab
For this diagram, the Pythagorean theorem states that b2 = ?
a2 - c2 |
|
c - a |
|
c2 - a2 |
|
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 = 9 and x = 1, what is the value of -8a(a - x)?
| 18 | |
| -80 | |
| -15 | |
| -576 |
To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
-8a(a - x)
-8(9)(9 - 1)
-8(9)(8)
(-72)(8)
-576