| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.82 |
| Score | 0% | 56% |
Solve for a:
a2 - 2a - 5 = -5a + 5
| 2 or -5 | |
| 7 or -7 | |
| 3 or -1 | |
| 9 or -9 |
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 - 2a - 5 = -5a + 5
a2 - 2a - 5 - 5 = -5a
a2 - 2a + 5a - 10 = 0
a2 + 3a - 10 = 0
Next, factor the quadratic equation:
a2 + 3a - 10 = 0
(a - 2)(a + 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 2) or (a + 5) must equal zero:
If (a - 2) = 0, a must equal 2
If (a + 5) = 0, a must equal -5
So the solution is that a = 2 or -5
Which of the following statements about parallel lines with a transversal is not correct?
all acute angles equal each other |
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angles in the same position on different parallel lines are called corresponding angles |
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all of the angles formed by a transversal are called interior angles |
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same-side interior angles are complementary and 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°).
The endpoints of this line segment are at (-2, 2) and (2, -4). What is the slope of this line?
| -2 | |
| 1\(\frac{1}{2}\) | |
| 3 | |
| -1\(\frac{1}{2}\) |
The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 2) and (2, -4) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-4.0) - (2.0)}{(2) - (-2)} \) = \( \frac{-6}{4} \)If b = 7 and x = -7, what is the value of 4b(b - x)?
| 42 | |
| 450 | |
| 392 | |
| 330 |
To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
4b(b - x)
4(7)(7 + 7)
4(7)(14)
(28)(14)
392
If side x = 6cm, side y = 7cm, and side z = 9cm what is the perimeter of this triangle?
| 20cm | |
| 23cm | |
| 31cm | |
| 22cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 6cm + 7cm + 9cm = 22cm