| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.77 |
| Score | 0% | 55% |
If angle a = 44° and angle b = 62° what is the length of angle d?
| 131° | |
| 136° | |
| 141° | |
| 143° |
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° - 44° - 62° = 74°
So, d° = 62° + 74° = 136°
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° - 44° = 136°
On this circle, line segment CD is the:
radius |
|
diameter |
|
circumference |
|
chord |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).
If side a = 2, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{53} \) | |
| \( \sqrt{89} \) | |
| \( \sqrt{40} \) | |
| \( \sqrt{145} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 22 + 72
c2 = 4 + 49
c2 = 53
c = \( \sqrt{53} \)
Solve for c:
7c + 6 < \( \frac{c}{-5} \)
| c < 9\(\frac{1}{7}\) | |
| c < 1\(\frac{17}{23}\) | |
| c < -\(\frac{5}{6}\) | |
| c < -2\(\frac{5}{29}\) |
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.
7c + 6 < \( \frac{c}{-5} \)
-5 x (7c + 6) < c
(-5 x 7c) + (-5 x 6) < c
-35c - 30 < c
-35c - 30 - c < 0
-35c - c < 30
-36c < 30
c < \( \frac{30}{-36} \)
c < -\(\frac{5}{6}\)
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
2lw x 2wh + 2lh |
|
h2 x l2 x w2 |
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h x l x w |
|
lw x wh + lh |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.