| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.26 |
| Score | 0% | 65% |
The dimensions of this cube are height (h) = 2, length (l) = 2, and width (w) = 1. What is the surface area?
| 70 | |
| 16 | |
| 76 | |
| 26 |
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 2 x 1) + (2 x 1 x 2) + (2 x 2 x 2)
sa = (4) + (4) + (8)
sa = 16
Solve for a:
a2 - 15a + 29 = -3a + 2
| 3 or 9 | |
| -1 or -3 | |
| 6 or -7 | |
| -3 or -5 |
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:
a2 - 15a + 29 = -3a + 2
a2 - 15a + 29 - 2 = -3a
a2 - 15a + 3a + 27 = 0
a2 - 12a + 27 = 0
Next, factor the quadratic equation:
a2 - 12a + 27 = 0
(a - 3)(a - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 3) or (a - 9) must equal zero:
If (a - 3) = 0, a must equal 3
If (a - 9) = 0, a must equal 9
So the solution is that a = 3 or 9
If side x = 7cm, side y = 11cm, and side z = 14cm what is the perimeter of this triangle?
| 31cm | |
| 32cm | |
| 30cm | |
| 36cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 7cm + 11cm + 14cm = 32cm
Simplify 9a x 9b.
| 81\( \frac{b}{a} \) | |
| 18ab | |
| 81ab | |
| 81a2b2 |
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 x 9b = (9 x 9) (a x b) = 81ab
Which types of triangles will always have at least two sides of equal length?
isosceles and right |
|
equilateral and right |
|
equilateral, isosceles and right |
|
equilateral and isosceles |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.