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WorksheetsDetermining Constraints
Total questions: 15
Worksheet time: 26mins
Constraints are things that _______ options in problems.
limit
expand
all real numbers
12≤n≤52
12≤n≤125
52≤n≤125
An object is in the air for a total of 8 seconds and reaches a maximum height of 24ft before landing on the ground. If h(t) represents the height of the object after t seconds, find the range
0≤y≤8
0≤y≤24
Emma is planning a birthday party and wants balloons and party hats. She has $20 to spend. Each balloon costs $1, and each party hat costs $2. She wants to buy at least 5 balloons. She needs to have enough items so that each of her 12 friends gets either a balloon or a hat. Emma doesn't want to buy more than 15 items in total.
Let x represent the number of balloons and y represent the number of party hats. Select all the inequalities represented by the situation.
x ≤ 0
x ≥ 0
y ≥ 0
y ≤ 0
Which inequality represents "less than 4 ounces"?
x > 4
x < 4
x ≤ 4
x ≥ 4
Which inequality represents "at least 5 people attending"?
x > 5
x < 5
x ≤ 5
x ≥ 5
Janice is working as a babysitter for the Harold Family. They plan to leave for their date at 7:00 pm and be back by 12:00 am. If the equation f(x) = 15x + 20 models the amount that Janice will earn, where x is the number of hours she works, and f(x) is the total money she earns, what is an appropriate range?
any value between 0 and 20
any value between 20 and 125
any value between 20 and 95
any value greater than 0
Greenlings are a group of fish that share common features. The function G(x)=−10x2+100x+44 models the number of greenlings caught, in thousands, in the United States, from 2006 to 2013.
Determine the constraints.
(a) < x < (b)
Greenlings are a group of fish that share common features. The function G(x)=−10x2+100x+44 models the number of greenlings caught, in thousands, in the United States, from 2006 to 2013.
Determine the constraints.
(a) < y < (b)
A photographer was attempting to get the best angle of a building from a helicopter. The height of the helicopter over time is represented by the equation, H(x)=−1(x−40)2+1000 , where 𝑥 is the time (in minutes) and 𝐻 is the height of the helicopter (in feet).
We want to know WHEN the height is the greatest. What key feature do we need?
x-intercept
y-intercept
vertex
domain
A photographer was attempting to get the best angle of a building from a helicopter. The height of the helicopter over time is represented by the equation, H(x)=−1(x−40)2+1000 , where 𝑥 is the time (in minutes) and 𝐻 is the height of the helicopter (in feet).
We want to know WHEN the height is the greatest. Is that going to be the x of the vertex or y?
x-value of the vertex
y-value of the vertex
A photographer was attempting to get the best angle of a building from a helicopter. The height of the helicopter over time is represented by the equation, H(x)=−1(x−40)2+1000 , where 𝑥 is the time (in minutes) and 𝐻 is the height of the helicopter (in feet).
At how many minutes is the height the greatest?
(a)
In 1965, a Ford Mustang cost $2,600. While most cars lose value, a 1965 Mustang in immaculate condition can be worth over $30,000. The function G(x)=20(x−10)2+395 models the price of the 1965 Mustang in the United States since 1965.
In what year is the price the lowest?
(a)
