| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.58 |
| Score | 0% | 72% |
If a = 5, b = 9, c = 4, and d = 1, what is the perimeter of this quadrilateral?
| 20 | |
| 16 | |
| 25 | |
| 19 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 5 + 9 + 4 + 1
p = 19
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
supplementary, vertical |
|
vertical, supplementary |
|
obtuse, acute |
|
acute, obtuse |
Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).
Solve for c:
c2 - c - 35 = -4c + 5
| -3 or -8 | |
| 7 or -2 | |
| 5 or -8 | |
| 8 or 2 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
c2 - c - 35 = -4c + 5
c2 - c - 35 - 5 = -4c
c2 - c + 4c - 40 = 0
c2 + 3c - 40 = 0
Next, factor the quadratic equation:
c2 + 3c - 40 = 0
(c - 5)(c + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 5) or (c + 8) must equal zero:
If (c - 5) = 0, c must equal 5
If (c + 8) = 0, c must equal -8
So the solution is that c = 5 or -8
The dimensions of this cube are height (h) = 7, length (l) = 9, and width (w) = 5. What is the volume?
| 315 | |
| 5 | |
| 144 | |
| 90 |
The volume of a cube is height x length x width:
v = h x l x w
v = 7 x 9 x 5
v = 315
What is 3a - 9a?
| 27a | |
| -6a | |
| -6 | |
| 27a2 |
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 - 9a = -6a