| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
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Solve for y:
4y - 4 = \( \frac{y}{4} \)
| -\(\frac{64}{73}\) | |
| 1\(\frac{1}{15}\) | |
| -1\(\frac{2}{7}\) | |
| \(\frac{14}{27}\) |
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 equal sign and the answer on the other.
4y - 4 = \( \frac{y}{4} \)
4 x (4y - 4) = y
(4 x 4y) + (4 x -4) = y
16y - 16 = y
16y - 16 - y = 0
16y - y = 16
15y = 16
y = \( \frac{16}{15} \)
y = 1\(\frac{1}{15}\)
Solve for c:
c2 - 6c - 29 = -3c - 1
| 3 or 1 | |
| 9 or 5 | |
| -4 or 7 | |
| -3 or -6 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
c2 - 6c - 29 = -3c - 1
c2 - 6c - 29 + 1 = -3c
c2 - 6c + 3c - 28 = 0
c2 - 3c - 28 = 0
Next, factor the quadratic equation:
c2 - 3c - 28 = 0
(c + 4)(c - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 4) or (c - 7) must equal zero:
If (c + 4) = 0, c must equal -4
If (c - 7) = 0, c must equal 7
So the solution is that c = -4 or 7
A(n) __________ is to a parallelogram as a square is to a rectangle.
trapezoid |
|
triangle |
|
rhombus |
|
quadrilateral |
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
Simplify 5a x 3b.
| 15a2b2 | |
| 15ab | |
| 8ab | |
| 15\( \frac{a}{b} \) |
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.
5a x 3b = (5 x 3) (a x b) = 15ab
The endpoints of this line segment are at (-2, -3) and (2, -5). What is the slope of this line?
| 1 | |
| -2\(\frac{1}{2}\) | |
| -\(\frac{1}{2}\) | |
| 3 |
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, -3) and (2, -5) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-5.0) - (-3.0)}{(2) - (-2)} \) = \( \frac{-2}{4} \)