| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
The endpoints of this line segment are at (-2, 3) and (2, -9). What is the slope-intercept equation for this line?
| y = -3x - 3 | |
| y = 2x - 3 | |
| y = 2x - 4 | |
| y = \(\frac{1}{2}\)x - 4 |
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, 3) and (2, -9) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-9.0) - (3.0)}{(2) - (-2)} \) = \( \frac{-12}{4} \)Plugging these values into the slope-intercept equation:
y = -3x - 3
What is 2a - 9a?
| 11 | |
| 18a | |
| 11a2 | |
| -7a |
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.
2a - 9a = -7a
The dimensions of this cube are height (h) = 5, length (l) = 8, and width (w) = 7. What is the volume?
| 84 | |
| 96 | |
| 280 | |
| 441 |
The volume of a cube is height x length x width:
v = h x l x w
v = 5 x 8 x 7
v = 280
Find the value of b:
-6b + x = -1
-7b + 8x = 2
| -1\(\frac{32}{45}\) | |
| \(\frac{10}{41}\) | |
| -\(\frac{3}{4}\) | |
| \(\frac{5}{6}\) |
You need to find the value of b so solve the first equation in terms of x:
-6b + x = -1
x = -1 + 6b
then substitute the result (-1 - -6b) into the second equation:
-7b + 8(-1 + 6b) = 2
-7b + (8 x -1) + (8 x 6b) = 2
-7b - 8 + 48b = 2
-7b + 48b = 2 + 8
41b = 10
b = \( \frac{10}{41} \)
b = \(\frac{10}{41}\)
Which of the following is not true about both rectangles and squares?
the area is length x width |
|
the lengths of all sides are equal |
|
the perimeter is the sum of the lengths of all four sides |
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all interior angles are right angles |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).