Question 1

a bicycle manufacturing company makes a particular type of bike. each child bike requires 4 hours to build and 4 hours to test. each adult bike requires 6 hours to build and 4 hours to test. with the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. if c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week.

no, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
no, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

question 2

solve the following systems of inequalities and select the correct graph:

2x − y > 4
x + y < −1

in each graph, the area for f(x) is shaded and labeled a, the area for g(x) is shaded and labeled b, and the area where they have shading in common is labeled ab.

a dashed line g of x rising left to right that is shaded below and a dashed line f of x that is falling left to right that is shaded above
a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above
a dashed line g of x rising left to right that is shaded above and a dashed line f of x that is falling left to right that is shaded below
a dashed line g of x rising left to right that is shaded below and a dashed line f of x that is falling left to right that is shaded below

question 3

in the graph, the area below f(x) is shaded and labeled a, the area below g(x) is shaded and labeled b, and the area where f(x) and g(x) have shading in common is labeled ab.

graph of two intersecting lines. one line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded above the line. the other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded in below the line.

the graph represents which system of inequalities?

y ≤ −3x − 1
y ≤ −x − 4
y ≥ −3x + 1
y ≤ −x − 4
y ≤ 3x − 1
y ≤ −x + 4
y ≤ 3x − 1
y ≥ −x + 4

question 4

which of the following points lie in the solution set to the following system of inequalities?

y < −3x + 3
y < x + 2

(1, −5)
(1, 5)
(5, 1)
(−1, 5)

question 5

a summer camp cookout is planned for the campers and their families. there is room for 200 people. each adult costs $4, and each camper costs $3. there is a maximum budget of $750. write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers.

x + y ≤ 200
4x + 3y ≤ 750
x + y ≤ 750
4x + 3y ≤ 200
x + y ≤ 200
3x + 4y ≤ 750
x + y ≤ 750
3x + 4y ≤ 200

question 6

in the graph, the area above f(x) is shaded and labeled a, the area below g(x) is shaded and labeled b, and the area where f(x) and g(x) have shading in common is labeled ab.

graph of two intersecting lines. the line g of x is solid, and goes through the points 0, negative 2 and 1, 0 and is shaded in below the line. the other line f of x is dashed, and goes through the points 0, 3, 3, 0 and is shaded in above the line.

the graph represents which system of inequalities?

y > 2x − 3
y > −x − 3
y < 2x − 2
y < −x + 3
y ≤ 2x − 2
y > −x + 3
none of the above