| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
A(n) __________ is two expressions separated by an equal sign.
formula |
|
equation |
|
expression |
|
problem |
An equation is two expressions separated by an equal sign. The key to solving equations is to 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.
If b = 8 and z = 5, what is the value of 5b(b - z)?
| 72 | |
| 160 | |
| 1134 | |
| 120 |
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.)
5b(b - z)
5(8)(8 - 5)
5(8)(3)
(40)(3)
120
If a = 1, b = 2, c = 3, and d = 8, what is the perimeter of this quadrilateral?
| 14 | |
| 19 | |
| 21 | |
| 24 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 1 + 2 + 3 + 8
p = 14
Solve for a:
a2 - 11a + 24 = 0
| 9 or -1 | |
| 8 or 5 | |
| 5 or -4 | |
| 3 or 8 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
a2 - 11a + 24 = 0
(a - 3)(a - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 3) or (a - 8) must equal zero:
If (a - 3) = 0, a must equal 3
If (a - 8) = 0, a must equal 8
So the solution is that a = 3 or 8
The dimensions of this trapezoid are a = 6, b = 4, c = 9, d = 5, and h = 4. What is the area?
| 16\(\frac{1}{2}\) | |
| 18 | |
| 28 | |
| 22 |
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(4 + 5)(4)
a = ½(9)(4)
a = ½(36) = \( \frac{36}{2} \)
a = 18