| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.13 |
| Score | 0% | 63% |
If a = -7 and x = 2, what is the value of -4a(a - x)?
| 336 | |
| -252 | |
| -144 | |
| -12 |
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.)
-4a(a - x)
-4(-7)(-7 - 2)
-4(-7)(-9)
(28)(-9)
-252
If a = c = 2, b = d = 3, and the blue angle = 52°, what is the area of this parallelogram?
| 63 | |
| 28 | |
| 6 | |
| 64 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 2 x 3
a = 6
If angle a = 62° and angle b = 54° what is the length of angle d?
| 157° | |
| 121° | |
| 118° | |
| 119° |
An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:
d° = b° + c°
To find angle c, remember that the sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 62° - 54° = 64°
So, d° = 54° + 64° = 118°
A shortcut to get this answer is to remember that angles around a line add up to 180°:
a° + d° = 180°
d° = 180° - a°
d° = 180° - 62° = 118°
What is 9a5 - 3a5?
| 27a10 | |
| 12a10 | |
| 12 | |
| 6a5 |
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.
9a5 - 3a5 = 6a5
Solve for z:
z2 + z - 19 = 4z - 1
| -4 or -6 | |
| -3 or 6 | |
| 4 or -4 | |
| 6 or -9 |
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 + z - 19 = 4z - 1
z2 + z - 19 + 1 = 4z
z2 + z - 4z - 18 = 0
z2 - 3z - 18 = 0
Next, factor the quadratic equation:
z2 - 3z - 18 = 0
(z + 3)(z - 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 3) or (z - 6) must equal zero:
If (z + 3) = 0, z must equal -3
If (z - 6) = 0, z must equal 6
So the solution is that z = -3 or 6