The coefficient of the expression is -22.
The monthly depreciation value of the gadget is represented by the coefficient. Therefore, the correct answer is: The monthly depreciation value of the gadget.
Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future; however, its value depreciates monthly. The expression shows the depreciated sales value of the gadget:
2,020 − 22m
What does the coefficient of the expression represent?
The number of months Megan will wait to sell the gadget
The monthly depreciation value of the gadget
The amount of money Megan will get when she sells the gadget
The original value of the gadget
17 answers
The equation the quantity x plus 33 end quantity over 4 equals 3 times x models the workload of a class project, where x is the number of hours each student must contribute. How many hours does each student work on the project?
2 hours
3 hours
7 hours
11 hours
2 hours
3 hours
7 hours
11 hours
To solve the equation, we can cross-multiply:
(3)(x) = (x + 33)/4
12x = x + 33
11x = 33
x = 3
Therefore, each student works on the project for 3 hours.
(3)(x) = (x + 33)/4
12x = x + 33
11x = 33
x = 3
Therefore, each student works on the project for 3 hours.
Which equation is equivalent to the formula r = st?
t equals s over r
t = rs
s equals r over t
s = rt
t equals s over r
t = rs
s equals r over t
s = rt
The equation that is equivalent to the formula r = st is s = rt.
A pilot was scheduled to depart at 4:00 p.m., but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination.
In the original flight plan, the pilot calculated that it will take her x minutes to arrive at her destination.
However, with the new flight plan, she will arrive four times faster. This means it will take her x/4 minutes to arrive at her destination.
Since her departure was delayed by 16 minutes, we need to add this delay to the time it takes her to arrive with the new flight plan.
Therefore, the equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination is:
(4:00 p.m. + 16 minutes) + x/4 minutes = 4:00 p.m. + (16 + x/4) minutes
However, with the new flight plan, she will arrive four times faster. This means it will take her x/4 minutes to arrive at her destination.
Since her departure was delayed by 16 minutes, we need to add this delay to the time it takes her to arrive with the new flight plan.
Therefore, the equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination is:
(4:00 p.m. + 16 minutes) + x/4 minutes = 4:00 p.m. + (16 + x/4) minutes
A pilot was scheduled to depart at 4:00 p.m., but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination.
y equals one fourth times x minus 16
y = 4x − 16
y equals one fourth times x plus 16
y = 4x + 16
y equals one fourth times x minus 16
y = 4x − 16
y equals one fourth times x plus 16
y = 4x + 16
Since the pilot's departure was delayed by 16 minutes, the time of her original flight will be the time it takes to arrive at her destination (y) minus the delay (16 minutes).
The new flight plan allows her to arrive four times faster than her original plan, so the time it takes to arrive at her destination will be x/4 minutes.
Therefore, the equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination is:
y = (x/4) - 16
The new flight plan allows her to arrive four times faster than her original plan, so the time it takes to arrive at her destination will be x/4 minutes.
Therefore, the equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination is:
y = (x/4) - 16
Graph g(x) = −4x + 8 and identify its x-intercept.
(0, 2)
(0, 8)
(2, 0)
(8, 0)
(0, 2)
(0, 8)
(2, 0)
(8, 0)
To find the x-intercept of the graph, we set y (or g(x)) equal to zero and solve for x.
0 = -4x + 8
Rearranging the equation:
4x = 8
Dividing both sides by 4:
x = 2
Therefore, the graph of g(x) = -4x + 8 has an x-intercept of (2, 0).
0 = -4x + 8
Rearranging the equation:
4x = 8
Dividing both sides by 4:
x = 2
Therefore, the graph of g(x) = -4x + 8 has an x-intercept of (2, 0).
What are the vertex and range of y = |2x + 4| + 5?
(0, 5); −∞ < y < ∞
(0, 5); 5 ≤ y < ∞
(−2, 5); −∞ < y < ∞
(−2, 5); 5 ≤ y < ∞
(0, 5); −∞ < y < ∞
(0, 5); 5 ≤ y < ∞
(−2, 5); −∞ < y < ∞
(−2, 5); 5 ≤ y < ∞
To find the vertex of the given equation, we need to find the values of x and y that correspond to the minimum point of the graph.
The vertex of the absolute value function y = |2x + 4| + 5 occurs when the expression inside the absolute value, 2x + 4, is equal to zero.
2x + 4 = 0
Solving for x:
2x = -4
x = -2
Substituting this value of x back into the original equation, we can find the y-coordinate of the vertex:
y = |2(-2) + 4| + 5
y = |-4 + 4| + 5
y = |0| + 5
y = 5
Therefore, the vertex of the graph is (-2, 5).
To find the range, we note that the absolute value function will always result in a value greater than or equal to zero. Adding 5 to this result will shift the range upward.
Therefore, the range of y = |2x + 4| + 5 is 5 ≤ y < ∞.
Hence, the correct answer is (−2, 5); 5 ≤ y < ∞.
The vertex of the absolute value function y = |2x + 4| + 5 occurs when the expression inside the absolute value, 2x + 4, is equal to zero.
2x + 4 = 0
Solving for x:
2x = -4
x = -2
Substituting this value of x back into the original equation, we can find the y-coordinate of the vertex:
y = |2(-2) + 4| + 5
y = |-4 + 4| + 5
y = |0| + 5
y = 5
Therefore, the vertex of the graph is (-2, 5).
To find the range, we note that the absolute value function will always result in a value greater than or equal to zero. Adding 5 to this result will shift the range upward.
Therefore, the range of y = |2x + 4| + 5 is 5 ≤ y < ∞.
Hence, the correct answer is (−2, 5); 5 ≤ y < ∞.
Choose the graph that correctly corresponds to the equation x = −4.
graph of a horizontal line through the point 0, 4
graph of a vertical line through the point 4, 0
graph a horizontal line through the point 0, negative 4
graph of a vertical line through the point negative 4, 0
graph of a horizontal line through the point 0, 4
graph of a vertical line through the point 4, 0
graph a horizontal line through the point 0, negative 4
graph of a vertical line through the point negative 4, 0
The equation x = -4 represents a vertical line because the value of x is constant (-4) for all y-values.
Therefore, the correct graph would be the graph of a vertical line through the point (-4, 0).
Therefore, the correct graph would be the graph of a vertical line through the point (-4, 0).
A contractor can spend at most $350 a day on operating costs and payroll. It costs $75 each day to operate the forklift and $55 a day for each crew member. Write an inequality to represent the contractor's budget for the day.
75 + 55x ≥ 350
75 + 55x ≤ 350
75x + 55 ≥ 350
75x + 55 ≤ 350
75 + 55x ≥ 350
75 + 55x ≤ 350
75x + 55 ≥ 350
75x + 55 ≤ 350
The cost of operating the forklift is $75, and the cost for each crew member is $55. Therefore, the total cost for the day can be represented by the expression 75 + 55x, where x represents the number of crew members.
The contractor can spend at most $350, so we can write the inequality:
75 + 55x ≤ 350
Therefore, the correct inequality to represent the contractor's budget for the day is 75 + 55x ≤ 350.
The contractor can spend at most $350, so we can write the inequality:
75 + 55x ≤ 350
Therefore, the correct inequality to represent the contractor's budget for the day is 75 + 55x ≤ 350.