| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
Simplify (7a)(3ab) + (7a2)(7b).
| 140ab2 | |
| -28a2b | |
| 70a2b | |
| 28a2b |
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.
(7a)(3ab) + (7a2)(7b)
(7 x 3)(a x a x b) + (7 x 7)(a2 x b)
(21)(a1+1 x b) + (49)(a2b)
21a2b + 49a2b
70a2b
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
lw x wh + lh |
|
h x l x w |
|
h2 x l2 x w2 |
|
2lw x 2wh + 2lh |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
What is the circumference of a circle with a diameter of 14?
| 14π | |
| 32π | |
| 1π | |
| 5π |
The formula for circumference is circle diameter x π:
c = πd
c = 14π
The dimensions of this cube are height (h) = 7, length (l) = 4, and width (w) = 1. What is the surface area?
| 126 | |
| 78 | |
| 72 | |
| 288 |
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 4 x 1) + (2 x 1 x 7) + (2 x 4 x 7)
sa = (8) + (14) + (56)
sa = 78
Solve for y:
y2 + 14y + 13 = 5y - 1
| 2 or -4 | |
| 4 or -4 | |
| 9 or -1 | |
| -2 or -7 |
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:
y2 + 14y + 13 = 5y - 1
y2 + 14y + 13 + 1 = 5y
y2 + 14y - 5y + 14 = 0
y2 + 9y + 14 = 0
Next, factor the quadratic equation:
y2 + 9y + 14 = 0
(y + 2)(y + 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 2) or (y + 7) must equal zero:
If (y + 2) = 0, y must equal -2
If (y + 7) = 0, y must equal -7
So the solution is that y = -2 or -7