| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.88 |
| Score | 0% | 58% |
Solve for z:
z2 + 12z - 13 = 5z + 5
| -3 or -6 | |
| 3 or -9 | |
| 2 or -9 | |
| 5 or -3 |
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:
z2 + 12z - 13 = 5z + 5
z2 + 12z - 13 - 5 = 5z
z2 + 12z - 5z - 18 = 0
z2 + 7z - 18 = 0
Next, factor the quadratic equation:
z2 + 7z - 18 = 0
(z - 2)(z + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 2) or (z + 9) must equal zero:
If (z - 2) = 0, z must equal 2
If (z + 9) = 0, z must equal -9
So the solution is that z = 2 or -9
If c = 3 and y = 8, what is the value of 8c(c - y)?
| -30 | |
| -120 | |
| 84 | |
| 81 |
To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
8c(c - y)
8(3)(3 - 8)
8(3)(-5)
(24)(-5)
-120
Simplify (3a)(3ab) - (3a2)(9b).
| -18a2b | |
| 36ab2 | |
| 72ab2 | |
| 36a2b |
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.
(3a)(3ab) - (3a2)(9b)
(3 x 3)(a x a x b) - (3 x 9)(a2 x b)
(9)(a1+1 x b) - (27)(a2b)
9a2b - 27a2b
-18a2b
If side a = 4, side b = 3, what is the length of the hypotenuse of this right triangle?
| 5 | |
| \( \sqrt{13} \) | |
| \( \sqrt{162} \) | |
| \( \sqrt{117} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 42 + 32
c2 = 16 + 9
c2 = 25
c = \( \sqrt{25} \)
c = 5
The endpoints of this line segment are at (-2, -1) and (2, 1). What is the slope of this line?
| 1\(\frac{1}{2}\) | |
| 2 | |
| 2\(\frac{1}{2}\) | |
| \(\frac{1}{2}\) |
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, -1) and (2, 1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(1.0) - (-1.0)}{(2) - (-2)} \) = \( \frac{2}{4} \)