| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
Simplify (y + 8)(y - 7)
| y2 - 15y + 56 | |
| y2 - y - 56 | |
| y2 + y - 56 | |
| y2 + 15y + 56 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y + 8)(y - 7)
(y x y) + (y x -7) + (8 x y) + (8 x -7)
y2 - 7y + 8y - 56
y2 + y - 56
If b = -3 and y = 1, what is the value of -6b(b - y)?
| 84 | |
| -72 | |
| -210 | |
| -144 |
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(-3)(-3 - 1)
-6(-3)(-4)
(18)(-4)
-72
The endpoints of this line segment are at (-2, 0) and (2, 6). What is the slope of this line?
| -1\(\frac{1}{2}\) | |
| -2\(\frac{1}{2}\) | |
| 1\(\frac{1}{2}\) | |
| 3 |
The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 0) and (2, 6) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(6.0) - (0.0)}{(2) - (-2)} \) = \( \frac{6}{4} \)Solve for x:
-6x + 8 < -7 + 5x
| x < -4\(\frac{1}{2}\) | |
| x < 1\(\frac{4}{11}\) | |
| x < -3 | |
| x < 1\(\frac{4}{5}\) |
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.
-6x + 8 < -7 + 5x
-6x < -7 + 5x - 8
-6x - 5x < -7 - 8
-11x < -15
x < \( \frac{-15}{-11} \)
x < 1\(\frac{4}{11}\)
If side a = 8, side b = 4, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{82} \) | |
| \( \sqrt{68} \) | |
| \( \sqrt{65} \) | |
| \( \sqrt{80} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 82 + 42
c2 = 64 + 16
c2 = 80
c = \( \sqrt{80} \)