| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.88 |
| Score | 0% | 58% |
If angle a = 61° and angle b = 46° what is the length of angle d?
| 119° | |
| 129° | |
| 158° | |
| 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° - 61° - 46° = 73°
So, d° = 46° + 73° = 119°
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° - 61° = 119°
If side a = 3, side b = 2, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{13} \) | |
| \( \sqrt{145} \) | |
| \( \sqrt{97} \) | |
| 5 |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 32 + 22
c2 = 9 + 4
c2 = 13
c = \( \sqrt{13} \)
What is 4a - 5a?
| 9 | |
| -1a | |
| a2 | |
| 9a2 |
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.
4a - 5a = -1a
For this diagram, the Pythagorean theorem states that b2 = ?
c - a |
|
c2 - a2 |
|
c2 + a2 |
|
a2 - c2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
The endpoints of this line segment are at (-2, 2) and (2, -2). What is the slope-intercept equation for this line?
| y = -2x + 0 | |
| y = -x + 0 | |
| y = x - 2 | |
| y = 3x + 0 |
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 0. 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, -2) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-2.0) - (2.0)}{(2) - (-2)} \) = \( \frac{-4}{4} \)Plugging these values into the slope-intercept equation:
y = -x + 0