| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.13 |
| Score | 0% | 63% |
If side a = 2, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{17} \) | |
| \( \sqrt{61} \) | |
| \( \sqrt{106} \) | |
| \( \sqrt{53} \) |
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 = \( \sqrt{53} \)
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
vertical, supplementary |
|
supplementary, vertical |
|
acute, obtuse |
|
obtuse, acute |
Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).
Solve for b:
-5b - 9 < \( \frac{b}{6} \)
| b < -\(\frac{25}{26}\) | |
| b < -1\(\frac{23}{31}\) | |
| b < 2\(\frac{10}{11}\) | |
| b < 2\(\frac{8}{11}\) |
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 - 9 < \( \frac{b}{6} \)
6 x (-5b - 9) < b
(6 x -5b) + (6 x -9) < b
-30b - 54 < b
-30b - 54 - b < 0
-30b - b < 54
-31b < 54
b < \( \frac{54}{-31} \)
b < -1\(\frac{23}{31}\)
Simplify 6a x 6b.
| 36\( \frac{b}{a} \) | |
| 36ab | |
| 36a2b2 | |
| 12ab |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
6a x 6b = (6 x 6) (a x b) = 36ab
If the base of this triangle is 7 and the height is 5, what is the area?
| 44 | |
| 78 | |
| 39 | |
| 17\(\frac{1}{2}\) |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 7 x 5 = \( \frac{35}{2} \) = 17\(\frac{1}{2}\)