| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.15 |
| Score | 0% | 63% |
The dimensions of this cube are height (h) = 5, length (l) = 9, and width (w) = 4. What is the surface area?
| 16 | |
| 48 | |
| 280 | |
| 202 |
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 9 x 4) + (2 x 4 x 5) + (2 x 9 x 5)
sa = (72) + (40) + (90)
sa = 202
What is 9a - 2a?
| 7 | |
| 11 | |
| 7a | |
| 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.
9a - 2a = 7a
The endpoints of this line segment are at (-2, 6) and (2, -2). What is the slope-intercept equation for this line?
| y = x + 2 | |
| y = -2\(\frac{1}{2}\)x + 1 | |
| y = -2x + 2 | |
| y = 3x + 3 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 2. 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, 6) and (2, -2) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-2.0) - (6.0)}{(2) - (-2)} \) = \( \frac{-8}{4} \)Plugging these values into the slope-intercept equation:
y = -2x + 2
Simplify 5a x 3b.
| 15\( \frac{b}{a} \) | |
| 8ab | |
| 15\( \frac{a}{b} \) | |
| 15ab |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
5a x 3b = (5 x 3) (a x b) = 15ab
If angle a = 23° and angle b = 67° what is the length of angle d?
| 149° | |
| 157° | |
| 140° | |
| 150° |
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° - 23° - 67° = 90°
So, d° = 67° + 90° = 157°
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° - 23° = 157°