| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.32 |
| Score | 0% | 46% |
Factor y2 - 16y + 63
| (y + 9)(y - 7) | |
| (y - 9)(y + 7) | |
| (y + 9)(y + 7) | |
| (y - 9)(y - 7) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 63 as well and sum (Inside, Outside) to equal -16. For this problem, those two numbers are -9 and -7. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 16y + 63
y2 + (-9 - 7)y + (-9 x -7)
(y - 9)(y - 7)
For this diagram, the Pythagorean theorem states that b2 = ?
c - a |
|
a2 - c2 |
|
c2 + a2 |
|
c2 - a2 |
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, \(c = \sqrt{a + b}\)
Find the value of c:
-3c + z = 8
-5c + 4z = 3
| -\(\frac{35}{59}\) | |
| -\(\frac{16}{43}\) | |
| -1\(\frac{1}{10}\) | |
| -4\(\frac{1}{7}\) |
You need to find the value of c so solve the first equation in terms of z:
-3c + z = 8
z = 8 + 3c
then substitute the result (8 - -3c) into the second equation:
-5c + 4(8 + 3c) = 3
-5c + (4 x 8) + (4 x 3c) = 3
-5c + 32 + 12c = 3
-5c + 12c = 3 - 32
7c = -29
c = \( \frac{-29}{7} \)
c = -4\(\frac{1}{7}\)
The formula for the area of a circle is which of the following?
c = π d2 |
|
c = π r |
|
c = π d |
|
c = π r2 |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.
If a = c = 4, b = d = 5, and the blue angle = 63°, what is the area of this parallelogram?
| 6 | |
| 20 | |
| 15 | |
| 10 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 4 x 5
a = 20