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Solve -7a - 3a = -8a - 5y + 1 for a in terms of y.
| -1\(\frac{1}{8}\)y + \(\frac{3}{8}\) | |
| -\(\frac{2}{5}\)y + \(\frac{2}{15}\) | |
| 4y + \(\frac{1}{4}\) | |
| -2y + 1 |
To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.
-7a - 3y = -8a - 5y + 1
-7a = -8a - 5y + 1 + 3y
-7a + 8a = -5y + 1 + 3y
a = -2y + 1
The endpoints of this line segment are at (-2, -9) and (2, 3). What is the slope of this line?
| \(\frac{1}{2}\) | |
| 3 | |
| -1 | |
| -2\(\frac{1}{2}\) |
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, -9) and (2, 3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(3.0) - (-9.0)}{(2) - (-2)} \) = \( \frac{12}{4} \)What is 4a2 + 4a2?
| 0 | |
| 16a2 | |
| 8a2 | |
| 8 |
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.
4a2 + 4a2 = 8a2
The dimensions of this cube are height (h) = 4, length (l) = 3, and width (w) = 1. What is the volume?
| 14 | |
| 12 | |
| 189 | |
| 126 |
The volume of a cube is height x length x width:
v = h x l x w
v = 4 x 3 x 1
v = 12
Solve for c:
c2 - 14c + 9 = -5c - 5
| 6 or -7 | |
| 9 or -8 | |
| 4 or -8 | |
| 2 or 7 |
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 - 14c + 9 = -5c - 5
c2 - 14c + 9 + 5 = -5c
c2 - 14c + 5c + 14 = 0
c2 - 9c + 14 = 0
Next, factor the quadratic equation:
c2 - 9c + 14 = 0
(c - 2)(c - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c - 7) must equal zero:
If (c - 2) = 0, c must equal 2
If (c - 7) = 0, c must equal 7
So the solution is that c = 2 or 7