| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.85 |
| Score | 0% | 57% |
If angle a = 60° and angle b = 34° what is the length of angle d?
| 156° | |
| 118° | |
| 136° | |
| 120° |
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° - 60° - 34° = 86°
So, d° = 34° + 86° = 120°
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° - 60° = 120°
The endpoints of this line segment are at (-2, 3) and (2, -3). What is the slope-intercept equation for this line?
| y = -1\(\frac{1}{2}\)x + 0 | |
| y = \(\frac{1}{2}\)x + 3 | |
| y = -1\(\frac{1}{2}\)x - 1 | |
| y = -\(\frac{1}{2}\)x - 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 0. 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, 3) and (2, -3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-3.0) - (3.0)}{(2) - (-2)} \) = \( \frac{-6}{4} \)Plugging these values into the slope-intercept equation:
y = -1\(\frac{1}{2}\)x + 0
What is the circumference of a circle with a radius of 17?
| 34π | |
| 3π | |
| 30π | |
| 5π |
The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:
c = πd
c = π(2 * r)
c = π(2 * 17)
c = 34π
A cylinder with a radius (r) and a height (h) has a surface area of:
2(π r2) + 2π rh |
|
π r2h2 |
|
π r2h |
|
4π r2 |
A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r2h and the surface area is 2(π r2) + 2π rh.
Simplify (3a)(2ab) + (9a2)(5b).
| 70ab2 | |
| 51a2b | |
| 39a2b | |
| 51ab2 |
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.
(3a)(2ab) + (9a2)(5b)
(3 x 2)(a x a x b) + (9 x 5)(a2 x b)
(6)(a1+1 x b) + (45)(a2b)
6a2b + 45a2b
51a2b