| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.11 |
| Score | 0% | 62% |
If angle a = 70° and angle b = 63° what is the length of angle c?
| 68° | |
| 114° | |
| 47° | |
| 93° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 70° - 63° = 47°
What is 3a + 2a?
| 5a | |
| a2 | |
| 6a2 | |
| 5 |
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.
3a + 2a = 5a
If angle a = 67° and angle b = 67° what is the length of angle d?
| 143° | |
| 157° | |
| 122° | |
| 113° |
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° - 67° - 67° = 46°
So, d° = 67° + 46° = 113°
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° - 67° = 113°
The dimensions of this cylinder are height (h) = 3 and radius (r) = 5. What is the surface area?
| 80π | |
| 44π | |
| 30π | |
| 234π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(52) + 2π(5 x 3)
sa = 2π(25) + 2π(15)
sa = (2 x 25)π + (2 x 15)π
sa = 50π + 30π
sa = 80π
Factor y2 + 6y + 5
| (y - 1)(y - 5) | |
| (y + 1)(y + 5) | |
| (y + 1)(y - 5) | |
| (y - 1)(y + 5) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 5 as well and sum (Inside, Outside) to equal 6. For this problem, those two numbers are 1 and 5. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 + 6y + 5
y2 + (1 + 5)y + (1 x 5)
(y + 1)(y + 5)