| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.63 |
| Score | 0% | 53% |
If angle a = 27° and angle b = 30° what is the length of angle d?
| 150° | |
| 153° | |
| 143° | |
| 136° |
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° - 27° - 30° = 123°
So, d° = 30° + 123° = 153°
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° - 27° = 153°
The endpoints of this line segment are at (-2, 4) and (2, 0). What is the slope-intercept equation for this line?
| y = -x + 2 | |
| y = 2x - 4 | |
| y = 2\(\frac{1}{2}\)x + 2 | |
| y = 1\(\frac{1}{2}\)x + 1 |
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, 0) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(0.0) - (4.0)}{(2) - (-2)} \) = \( \frac{-4}{4} \)Plugging these values into the slope-intercept equation:
y = -x + 2
Solve for b:
5b - 6 > \( \frac{b}{2} \)
| b > -1\(\frac{7}{8}\) | |
| b > -3 | |
| b > 3\(\frac{11}{15}\) | |
| b > 1\(\frac{1}{3}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.
5b - 6 > \( \frac{b}{2} \)
2 x (5b - 6) > b
(2 x 5b) + (2 x -6) > b
10b - 12 > b
10b - 12 - b > 0
10b - b > 12
9b > 12
b > \( \frac{12}{9} \)
b > 1\(\frac{1}{3}\)
Which of the following statements about a parallelogram is not true?
a parallelogram is a quadrilateral |
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the area of a parallelogram is base x height |
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opposite sides and adjacent angles are equal |
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the perimeter of a parallelogram is the sum of the lengths of all sides |
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).
If angle a = 37° and angle b = 23° what is the length of angle c?
| 51° | |
| 131° | |
| 120° | |
| 74° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 37° - 23° = 120°