| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.64 |
| Score | 0% | 53% |
Solve for b:
b2 + 8b + 12 = 2b + 3
| 4 or -2 | |
| 4 or -8 | |
| -3 or -7 | |
| -3 |
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:
b2 + 8b + 12 = 2b + 3
b2 + 8b + 12 - 3 = 2b
b2 + 8b - 2b + 9 = 0
b2 + 6b + 9 = 0
Next, factor the quadratic equation:
b2 + 6b + 9 = 0
(b + 3)(b + 3) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, (b + 3) must equal zero:
If (b + 3) = 0, b must equal -3
So the solution is that b = -3
The dimensions of this cylinder are height (h) = 3 and radius (r) = 2. What is the surface area?
| 104π | |
| 324π | |
| 20π | |
| 10π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(22) + 2π(2 x 3)
sa = 2π(4) + 2π(6)
sa = (2 x 4)π + (2 x 6)π
sa = 8π + 12π
sa = 20π
Which types of triangles will always have at least two sides of equal length?
isosceles and right |
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equilateral and right |
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equilateral, isosceles and right |
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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.
For this diagram, the Pythagorean theorem states that b2 = ?
c2 + a2 |
|
a2 - c2 |
|
c2 - a2 |
|
c - a |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
If a = c = 9, b = d = 8, and the blue angle = 79°, what is the area of this parallelogram?
| 54 | |
| 72 | |
| 18 | |
| 5 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 9 x 8
a = 72