| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
If a = c = 3, b = d = 7, what is the area of this rectangle?
| 21 | |
| 25 | |
| 8 | |
| 18 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 3 x 7
a = 21
Solve for x:
-8x + 2 = \( \frac{x}{9} \)
| \(\frac{18}{73}\) | |
| 5\(\frac{1}{3}\) | |
| 1\(\frac{9}{31}\) | |
| -\(\frac{18}{31}\) |
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 equal sign and the answer on the other.
-8x + 2 = \( \frac{x}{9} \)
9 x (-8x + 2) = x
(9 x -8x) + (9 x 2) = x
-72x + 18 = x
-72x + 18 - x = 0
-72x - x = -18
-73x = -18
x = \( \frac{-18}{-73} \)
x = \(\frac{18}{73}\)
For this diagram, the Pythagorean theorem states that b2 = ?
a2 - c2 |
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c2 - a2 |
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c - a |
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c2 + a2 |
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, \(c = \sqrt{a + b}\)
A quadrilateral is a shape with __________ sides.
4 |
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2 |
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3 |
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5 |
A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.
The endpoints of this line segment are at (-2, -6) and (2, 0). What is the slope-intercept equation for this line?
| y = \(\frac{1}{2}\)x + 2 | |
| y = 2\(\frac{1}{2}\)x + 0 | |
| y = 3x + 1 | |
| 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 -3. 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, -6) and (2, 0) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(0.0) - (-6.0)}{(2) - (-2)} \) = \( \frac{6}{4} \)Plugging these values into the slope-intercept equation:
y = 1\(\frac{1}{2}\)x - 3