| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.82 |
| Score | 0% | 56% |
If the length of AB equals the length of BD, point B __________ this line segment.
midpoints |
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intersects |
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bisects |
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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.
The dimensions of this trapezoid are a = 5, b = 5, c = 8, d = 2, and h = 4. What is the area?
| 14 | |
| 9 | |
| 12 | |
| 7\(\frac{1}{2}\) |
The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:
a = ½(b + d)(h)
a = ½(5 + 2)(4)
a = ½(7)(4)
a = ½(28) = \( \frac{28}{2} \)
a = 14
What is 3a8 - 9a8?
| -6a16 | |
| a816 | |
| 12a16 | |
| -6a8 |
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.
3a8 - 9a8 = -6a8
Simplify (9a)(4ab) + (7a2)(6b).
| -6a2b | |
| 78a2b | |
| -6ab2 | |
| 78ab2 |
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.
(9a)(4ab) + (7a2)(6b)
(9 x 4)(a x a x b) + (7 x 6)(a2 x b)
(36)(a1+1 x b) + (42)(a2b)
36a2b + 42a2b
78a2b
Solve for y:
4y + 4 < \( \frac{y}{8} \)
| y < 3\(\frac{3}{23}\) | |
| y < -1\(\frac{4}{31}\) | |
| y < -1\(\frac{1}{31}\) | |
| y < -\(\frac{15}{22}\) |
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 < sign and the answer on the other.
4y + 4 < \( \frac{y}{8} \)
8 x (4y + 4) < y
(8 x 4y) + (8 x 4) < y
32y + 32 < y
32y + 32 - y < 0
32y - y < -32
31y < -32
y < \( \frac{-32}{31} \)
y < -1\(\frac{1}{31}\)