| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
What is 4a + 7a?
| 11 | |
| 11a | |
| -3a2 | |
| 11a2 |
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 + 7a = 11a
The dimensions of this cube are height (h) = 6, length (l) = 8, and width (w) = 1. What is the surface area?
| 54 | |
| 292 | |
| 62 | |
| 124 |
The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):
sa = 2lw + 2wh + 2lh
sa = (2 x 8 x 1) + (2 x 1 x 6) + (2 x 8 x 6)
sa = (16) + (12) + (96)
sa = 124
If side a = 3, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{58} \) | |
| \( \sqrt{89} \) | |
| \( \sqrt{113} \) | |
| \( \sqrt{65} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 32 + 72
c2 = 9 + 49
c2 = 58
c = \( \sqrt{58} \)
If b = 5 and z = 1, what is the value of -3b(b - z)?
| 144 | |
| 448 | |
| -60 | |
| 18 |
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.)
-3b(b - z)
-3(5)(5 - 1)
-3(5)(4)
(-15)(4)
-60
Solve for c:
9c + 3 < \( \frac{c}{5} \)
| c < -10\(\frac{2}{7}\) | |
| c < -\(\frac{3}{4}\) | |
| c < -\(\frac{15}{44}\) | |
| c < -3\(\frac{9}{11}\) |
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.
9c + 3 < \( \frac{c}{5} \)
5 x (9c + 3) < c
(5 x 9c) + (5 x 3) < c
45c + 15 < c
45c + 15 - c < 0
45c - c < -15
44c < -15
c < \( \frac{-15}{44} \)
c < -\(\frac{15}{44}\)