| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.42 |
| Score | 0% | 68% |
If angle a = 31° and angle b = 45° what is the length of angle d?
| 149° | |
| 124° | |
| 117° | |
| 111° |
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° - 31° - 45° = 104°
So, d° = 45° + 104° = 149°
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° - 31° = 149°
The dimensions of this trapezoid are a = 4, b = 3, c = 6, d = 2, and h = 3. What is the area?
| 16\(\frac{1}{2}\) | |
| 22 | |
| 7\(\frac{1}{2}\) | |
| 9 |
The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:
a = ½(b + d)(h)
a = ½(3 + 2)(3)
a = ½(5)(3)
a = ½(15) = \( \frac{15}{2} \)
a = 7\(\frac{1}{2}\)
The dimensions of this cube are height (h) = 2, length (l) = 9, and width (w) = 4. What is the volume?
| 72 | |
| 108 | |
| 20 | |
| 105 |
The volume of a cube is height x length x width:
v = h x l x w
v = 2 x 9 x 4
v = 72
Simplify 4a x 2b.
| 8\( \frac{a}{b} \) | |
| 8\( \frac{b}{a} \) | |
| 8a2b2 | |
| 8ab |
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.
4a x 2b = (4 x 2) (a x b) = 8ab
Simplify (9a)(2ab) + (7a2)(3b).
| -3a2b | |
| 39a2b | |
| 39ab2 | |
| 110a2b |
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.
(9a)(2ab) + (7a2)(3b)
(9 x 2)(a x a x b) + (7 x 3)(a2 x b)
(18)(a1+1 x b) + (21)(a2b)
18a2b + 21a2b
39a2b