| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.52 |
| Score | 0% | 50% |
What is 7a5 + 4a5?
| 28a5 | |
| a510 | |
| 11a5 | |
| 11 |
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.
7a5 + 4a5 = 11a5
Find the value of c:
-2c + x = -5
4c - x = -6
| -\(\frac{1}{3}\) | |
| -5\(\frac{1}{2}\) | |
| \(\frac{9}{28}\) | |
| -\(\frac{6}{13}\) |
You need to find the value of c so solve the first equation in terms of x:
-2c + x = -5
x = -5 + 2c
then substitute the result (-5 - -2c) into the second equation:
4c - 1(-5 + 2c) = -6
4c + (-1 x -5) + (-1 x 2c) = -6
4c + 5 - 2c = -6
4c - 2c = -6 - 5
2c = -11
c = \( \frac{-11}{2} \)
c = -5\(\frac{1}{2}\)
Which of the following statements about parallel lines with a transversal is not correct?
all acute angles equal each other |
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same-side interior angles are complementary and 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 |
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°).
If angle a = 60° and angle b = 66° what is the length of angle d?
| 120° | |
| 135° | |
| 158° | |
| 124° |
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° - 60° - 66° = 54°
So, d° = 66° + 54° = 120°
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° - 60° = 120°
The endpoints of this line segment are at (-2, -4) and (2, 8). What is the slope-intercept equation for this line?
| y = -2\(\frac{1}{2}\)x - 2 | |
| y = -x + 4 | |
| y = \(\frac{1}{2}\)x - 4 | |
| y = 3x + 2 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 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, -4) and (2, 8) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(8.0) - (-4.0)}{(2) - (-2)} \) = \( \frac{12}{4} \)Plugging these values into the slope-intercept equation:
y = 3x + 2