| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.76 |
| Score | 0% | 55% |
The dimensions of this cube are height (h) = 3, length (l) = 5, and width (w) = 5. What is the surface area?
| 54 | |
| 236 | |
| 110 | |
| 306 |
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 5 x 5) + (2 x 5 x 3) + (2 x 5 x 3)
sa = (50) + (30) + (30)
sa = 110
The dimensions of this cube are height (h) = 8, length (l) = 9, and width (w) = 9. What is the volume?
| 216 | |
| 648 | |
| 72 | |
| 108 |
The volume of a cube is height x length x width:
v = h x l x w
v = 8 x 9 x 9
v = 648
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
acute, obtuse |
|
obtuse, acute |
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vertical, supplementary |
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supplementary, vertical |
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).
Which of the following statements about parallel lines with a transversal is not correct?
same-side interior angles are complementary and equal each other |
|
all of the angles formed by a transversal are called interior angles |
|
angles in the same position on different parallel lines are called corresponding angles |
|
all acute angles equal each other |
Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).
Solve for y:
y2 + 3y - 11 = y - 3
| 2 or -4 | |
| 3 or -8 | |
| 1 or -3 | |
| 1 or -4 |
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 + 3y - 11 = y - 3
y2 + 3y - 11 + 3 = y
y2 + 3y - y - 8 = 0
y2 + 2y - 8 = 0
Next, factor the quadratic equation:
y2 + 2y - 8 = 0
(y - 2)(y + 4) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 2) or (y + 4) must equal zero:
If (y - 2) = 0, y must equal 2
If (y + 4) = 0, y must equal -4
So the solution is that y = 2 or -4