| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.35 |
| Score | 0% | 67% |
Find the value of b:
-2b + y = -6
3b - 8y = 7
| 2\(\frac{2}{13}\) | |
| 3\(\frac{2}{13}\) | |
| 1 | |
| -3\(\frac{9}{17}\) |
You need to find the value of b so solve the first equation in terms of y:
-2b + y = -6
y = -6 + 2b
then substitute the result (-6 - -2b) into the second equation:
3b - 8(-6 + 2b) = 7
3b + (-8 x -6) + (-8 x 2b) = 7
3b + 48 - 16b = 7
3b - 16b = 7 - 48
-13b = -41
b = \( \frac{-41}{-13} \)
b = 3\(\frac{2}{13}\)
Simplify (6a)(5ab) + (6a2)(3b).
| -12ab2 | |
| 12ab2 | |
| 48a2b | |
| 99ab2 |
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.
(6a)(5ab) + (6a2)(3b)
(6 x 5)(a x a x b) + (6 x 3)(a2 x b)
(30)(a1+1 x b) + (18)(a2b)
30a2b + 18a2b
48a2b
A coordinate grid is composed of which of the following?
y-axis |
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origin |
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all of these |
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x-axis |
The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.
If side a = 3, side b = 3, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{18} \) | |
| \( \sqrt{85} \) | |
| \( \sqrt{2} \) | |
| \( \sqrt{90} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 32 + 32
c2 = 9 + 9
c2 = 18
c = \( \sqrt{18} \)
Order the following types of angle from least number of degrees to most number of degrees.
acute, obtuse, right |
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acute, right, obtuse |
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right, acute, obtuse |
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right, obtuse, acute |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.