| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.56 |
| Score | 0% | 71% |
Solve for z:
z2 - 5z - 61 = -4z - 5
| 6 or 3 | |
| -7 or 8 | |
| 8 or 2 | |
| 9 or -1 |
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:
z2 - 5z - 61 = -4z - 5
z2 - 5z - 61 + 5 = -4z
z2 - 5z + 4z - 56 = 0
z2 - z - 56 = 0
Next, factor the quadratic equation:
z2 - z - 56 = 0
(z + 7)(z - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 7) or (z - 8) must equal zero:
If (z + 7) = 0, z must equal -7
If (z - 8) = 0, z must equal 8
So the solution is that z = -7 or 8
What is 4a - 2a?
| 2 | |
| 6 | |
| a2 | |
| 2a |
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.
4a - 2a = 2a
If a = c = 3, b = d = 4, and the blue angle = 60°, what is the area of this parallelogram?
| 6 | |
| 30 | |
| 54 | |
| 12 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 3 x 4
a = 12
If a = 6, b = 4, c = 4, and d = 1, what is the perimeter of this quadrilateral?
| 23 | |
| 15 | |
| 19 | |
| 12 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 6 + 4 + 4 + 1
p = 15
The formula for the area of a circle is which of the following?
a = π r |
|
a = π r2 |
|
a = π d |
|
a = π d2 |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.