| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
For this diagram, the Pythagorean theorem states that b2 = ?
a2 - c2 |
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c2 - a2 |
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c2 + a2 |
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c - a |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
The endpoints of this line segment are at (-2, 4) and (2, -4). What is the slope-intercept equation for this line?
| y = -1\(\frac{1}{2}\)x - 2 | |
| y = -2\(\frac{1}{2}\)x + 4 | |
| y = -2x + 0 | |
| y = -1\(\frac{1}{2}\)x - 3 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 0. 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, 4) and (2, -4) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-4.0) - (4.0)}{(2) - (-2)} \) = \( \frac{-8}{4} \)Plugging these values into the slope-intercept equation:
y = -2x + 0
A(n) __________ is two expressions separated by an equal sign.
problem |
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equation |
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expression |
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formula |
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.
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
lw x wh + lh |
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h x l x w |
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2lw x 2wh + 2lh |
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h2 x l2 x w2 |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
If a = -3 and z = -7, what is the value of 5a(a - z)?
| -6 | |
| 520 | |
| -60 | |
| -180 |
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.)
5a(a - z)
5(-3)(-3 + 7)
5(-3)(4)
(-15)(4)
-60