A construction worker built steps up to a home. The table shows the linear relationship between the height off the ground in inches and the number of steps. What is the rate of change of height off the ground with respect to the number of steps?
Number of Steps Height (inches)
3 20
5 36
7 52
9 68
11 84
Answers:
8 in.per step
16 in.per step
1/8 in.per step
1/16 in.per step
To find the rate of change of height off the ground with respect to the number of steps, we need to calculate the difference in height for each additional step.
The difference in height for each additional step is as follows:
For the first step: 36 - 20 = 16 inches
For the second step: 52 - 36 = 16 inches
For the third step: 68 - 52 = 16 inches
For the fourth step: 84 - 68 = 16 inches
Since the difference in height for each additional step remains constant at 16 inches, the rate of change of height off the ground with respect to the number of steps is 16 inches per step.
Therefore, the correct answer is 16 in.per step.
Solve the equation for y:
2x + 3y = -12
Answers:
y = -2/3 x - 4
y = 2/3 x + 4
y = -3/2 x - 4
y = 3/2 x + 4
To solve the equation for y, we need to isolate y on one side of the equation.
Starting with the equation 2x + 3y = -12, we can rearrange it by subtracting 2x from both sides:
3y = -2x - 12
Next, divide both sides of the equation by 3 to solve for y:
y = (-2/3)x - 4
So, the correct answer is y = -2/3 x - 4.
Which expression is equivalent to -3(2x + 5) + 27 ?
Answers:
-5x - 8
-6x + 12
-2x + 12
-6x - 8
To simplify the expression -3(2x + 5) + 27, we need to distribute the -3 to the terms inside the parentheses and then combine like terms.
Distributing the -3:
-3 * 2x = -6x
-3 * 5 = -15
The expression becomes:
-6x - 15 + 27
Combining like terms, we have:
-6x + 12
So, the correct answer is -6x + 12.
The table represents some points on the graph of a linear function.
x y
-2 -11
2 -17
4 -20
Which function represents this relationship?
Answers:
y = -3/2 x + 4
y = -3/2 x - 14
y = -2/3 x - 9
y = -2/3 x - 1
To find the function that represents the relationship between the x and y values in the table, we need to calculate the slope (rate of change) and the y-intercept.
Using the given points (-2, -11), (2, -17), and (4, -20), we can calculate the slope:
slope = (change in y) / (change in x)
Between (-2, -11) and (2, -17):
slope = (-17 - (-11)) / (2 - (-2)) = (-17 + 11) / (2 + 2) = -6 / 4 = -3/2
Between (2, -17) and (4, -20):
slope = (-20 - (-17)) / (4 - 2) = (-20 + 17) / (4 - 2) = -3 / 2
Since the slope is the same (-3/2) for all the points, we can conclude that the function is a linear function.
Next, we can choose any of the points to find the y-intercept. Using the point (2, -17):
y = mx + b (slope-intercept form of a linear function)
-17 = (-3/2)(2) + b
-17 = -3 + b
b = -14
So, the function that represents this relationship is y = -3/2 x - 14.
Therefore, the correct answer is y = -3/2 x - 14.
Solve: -7 < 2x + 1 < 11
To solve the inequality -7 < 2x + 1 < 11, we need to isolate x.
Starting with -7 < 2x + 1 < 11, let's subtract 1 from all parts of the inequality:
-8 < 2x < 10
Next, divide all parts of the inequality by 2:
-8/2 < 2x/2 < 10/2
This simplifies to:
-4 < x < 5
Therefore, the solution to the inequality is -4 < x < 5.
Which equation is best represented by this graph?
Answers:
y = -7/4 x + 4
y = -7/4 x + 7
y = -4/7 x + 4
y = -4/7 x + 7