| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
If a = c = 7, b = d = 4, what is the area of this rectangle?
| 8 | |
| 18 | |
| 16 | |
| 28 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 7 x 4
a = 28
Solve for z:
-3z + 7 = -8 + 2z
| -\(\frac{8}{9}\) | |
| 3 | |
| -\(\frac{1}{3}\) | |
| -1 |
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.
-3z + 7 = -8 + 2z
-3z = -8 + 2z - 7
-3z - 2z = -8 - 7
-5z = -15
z = \( \frac{-15}{-5} \)
z = 3
If b = 1 and y = -9, what is the value of 6b(b - y)?
| 105 | |
| 0 | |
| -54 | |
| 60 |
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.)
6b(b - y)
6(1)(1 + 9)
6(1)(10)
(6)(10)
60
Solve for y:
y2 + 2y + 11 = -4y + 3
| 3 or -2 | |
| 6 or 1 | |
| -2 or -4 | |
| 1 or -2 |
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:
y2 + 2y + 11 = -4y + 3
y2 + 2y + 11 - 3 = -4y
y2 + 2y + 4y + 8 = 0
y2 + 6y + 8 = 0
Next, factor the quadratic equation:
y2 + 6y + 8 = 0
(y + 2)(y + 4) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 2) or (y + 4) must equal zero:
If (y + 2) = 0, y must equal -2
If (y + 4) = 0, y must equal -4
So the solution is that y = -2 or -4
Solve for c:
-2c - 9 > 1 - 3c
| c > 10 | |
| c > \(\frac{4}{7}\) | |
| c > \(\frac{4}{9}\) | |
| c > -3 |
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 > sign and the answer on the other.
-2c - 9 > 1 - 3c
-2c > 1 - 3c + 9
-2c + 3c > 1 + 9
c > 10