| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
Which of the following statements about math operations is incorrect?
all of these statements are correct |
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you can multiply monomials that have different variables and different exponents |
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you can add monomials that have the same variable and the same exponent |
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you can subtract 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.
Solve for a:
a2 - 18a + 53 = -4a + 5
| 1 or -6 | |
| 3 or -4 | |
| 8 or 7 | |
| 6 or 8 |
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:
a2 - 18a + 53 = -4a + 5
a2 - 18a + 53 - 5 = -4a
a2 - 18a + 4a + 48 = 0
a2 - 14a + 48 = 0
Next, factor the quadratic equation:
a2 - 14a + 48 = 0
(a - 6)(a - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 6) or (a - 8) must equal zero:
If (a - 6) = 0, a must equal 6
If (a - 8) = 0, a must equal 8
So the solution is that a = 6 or 8
A(n) __________ is two expressions separated by an equal sign.
expression |
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formula |
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equation |
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problem |
An equation is two expressions separated by an equal sign. The key to solving equations is to 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.
If the length of AB equals the length of BD, point B __________ this line segment.
midpoints |
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bisects |
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intersects |
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trisects |
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.
Solve for c:
c2 - 4 = 0
| 1 or -4 | |
| 3 or 1 | |
| 2 or -2 | |
| 9 or -7 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
c2 - 4 = 0
(c - 2)(c + 2) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c + 2) must equal zero:
If (c - 2) = 0, c must equal 2
If (c + 2) = 0, c must equal -2
So the solution is that c = 2 or -2