| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.80 |
| Score | 0% | 56% |
Solve for c:
c2 + 8c + 17 = -3c - 1
| -1 or -6 | |
| 4 or -4 | |
| 4 or 2 | |
| -2 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:
c2 + 8c + 17 = -3c - 1
c2 + 8c + 17 + 1 = -3c
c2 + 8c + 3c + 18 = 0
c2 + 11c + 18 = 0
Next, factor the quadratic equation:
c2 + 11c + 18 = 0
(c + 2)(c + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 2) or (c + 9) must equal zero:
If (c + 2) = 0, c must equal -2
If (c + 9) = 0, c must equal -9
So the solution is that c = -2 or -9
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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same-side interior angles are complementary and equal each other |
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all of the angles formed by a transversal are called interior angles |
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°).
Simplify (y + 2)(y - 1)
| y2 + y - 2 | |
| y2 + 3y + 2 | |
| y2 - 3y + 2 | |
| y2 - y - 2 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y + 2)(y - 1)
(y x y) + (y x -1) + (2 x y) + (2 x -1)
y2 - y + 2y - 2
y2 + y - 2
If angle a = 34° and angle b = 37° what is the length of angle d?
| 146° | |
| 144° | |
| 116° | |
| 132° |
An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:
d° = b° + c°
To find angle c, remember that the sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 34° - 37° = 109°
So, d° = 37° + 109° = 146°
A shortcut to get this answer is to remember that angles around a line add up to 180°:
a° + d° = 180°
d° = 180° - a°
d° = 180° - 34° = 146°
What is 2a2 - 4a2?
| -2a4 | |
| -2 | |
| -2a2 | |
| a24 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
2a2 - 4a2 = -2a2