| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.97 |
| Score | 0% | 59% |
Solve for z:
z2 + 18z + 67 = z - 5
| 8 or -9 | |
| 9 or 2 | |
| -8 or -9 | |
| -4 or -5 |
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 + 18z + 67 = z - 5
z2 + 18z + 67 + 5 = z
z2 + 18z - z + 72 = 0
z2 + 17z + 72 = 0
Next, factor the quadratic equation:
z2 + 17z + 72 = 0
(z + 8)(z + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 8) or (z + 9) must equal zero:
If (z + 8) = 0, z must equal -8
If (z + 9) = 0, z must equal -9
So the solution is that z = -8 or -9
If a = 2 and z = 5, what is the value of -a(a - z)?
| 6 | |
| -60 | |
| 96 | |
| -16 |
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.)
-a(a - z)
-1(2)(2 - 5)
-1(2)(-3)
(-2)(-3)
6
The dimensions of this cylinder are height (h) = 5 and radius (r) = 5. What is the volume?
| 27π | |
| 125π | |
| 128π | |
| 45π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(52 x 5)
v = 125π
If the length of AB equals the length of BD, point B __________ this line segment.
bisects |
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trisects |
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intersects |
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midpoints |
A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.
Which of the following statements about math operations is incorrect?
you can subtract monomials that have the same variable and the same exponent |
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you can multiply monomials that have different variables and different exponents |
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all of these statements are correct |
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you can add monomials that have the same variable and the same exponent |
You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a2 - a2 = 3a2 but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.