| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.24 |
| Score | 0% | 45% |
Which of the following is not required to define the slope-intercept equation for a line?
slope |
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x-intercept |
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\({\Delta y \over \Delta x}\) |
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y-intercept |
A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.
The dimensions of this trapezoid are a = 4, b = 7, c = 5, d = 4, and h = 2. What is the area?
| 9 | |
| 10 | |
| 11 | |
| 12 |
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(7 + 4)(2)
a = ½(11)(2)
a = ½(22) = \( \frac{22}{2} \)
a = 11
If a = -5 and y = 7, what is the value of 4a(a - y)?
| 96 | |
| 32 | |
| 240 | |
| 16 |
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.)
4a(a - y)
4(-5)(-5 - 7)
4(-5)(-12)
(-20)(-12)
240
The formula for the area of a circle is which of the following?
c = π r |
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c = π d2 |
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c = π d |
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c = π r2 |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.
The endpoints of this line segment are at (-2, -4) and (2, 8). What is the slope-intercept equation for this line?
| y = -1\(\frac{1}{2}\)x + 0 | |
| y = x - 4 | |
| y = 3x + 2 | |
| y = -x + 0 |
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 2. 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, 8) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(8.0) - (-4.0)}{(2) - (-2)} \) = \( \frac{12}{4} \)Plugging these values into the slope-intercept equation:
y = 3x + 2