| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.93 |
| Score | 0% | 59% |
Find the value of c:
-8c + y = -9
9c + 6y = 1
| \(\frac{55}{57}\) | |
| 1\(\frac{1}{12}\) | |
| \(\frac{11}{38}\) | |
| -\(\frac{11}{36}\) |
You need to find the value of c so solve the first equation in terms of y:
-8c + y = -9
y = -9 + 8c
then substitute the result (-9 - -8c) into the second equation:
9c + 6(-9 + 8c) = 1
9c + (6 x -9) + (6 x 8c) = 1
9c - 54 + 48c = 1
9c + 48c = 1 + 54
57c = 55
c = \( \frac{55}{57} \)
c = \(\frac{55}{57}\)
If side a = 5, side b = 2, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{53} \) | |
| \( \sqrt{52} \) | |
| \( \sqrt{45} \) | |
| \( \sqrt{29} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 52 + 22
c2 = 25 + 4
c2 = 29
c = \( \sqrt{29} \)
Order the following types of angle from least number of degrees to most number of degrees.
right, obtuse, acute |
|
right, acute, obtuse |
|
acute, right, obtuse |
|
acute, obtuse, right |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.
For this diagram, the Pythagorean theorem states that b2 = ?
c2 + a2 |
|
c2 - a2 |
|
c - a |
|
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, \(c = \sqrt{a + b}\)
Simplify (y + 7)(y - 9)
| y2 + 16y + 63 | |
| y2 - 16y + 63 | |
| y2 + 2y - 63 | |
| y2 - 2y - 63 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y + 7)(y - 9)
(y x y) + (y x -9) + (7 x y) + (7 x -9)
y2 - 9y + 7y - 63
y2 - 2y - 63