Graph the inequalities that represent this scenario

Graph the inequalities that represent this scenario on the set of axes below.
Kai says that the point (6,2) is a solution to this system. Determine if he is correct and explain
your reasoning.
y
x
Zx
y
14
Xty
8
Zx
Lx
7
ys8
A
d
s
ol
ol
l
ol
t
it
y
x

35 An airplane leaves New York City and heads toward Los Angeles. As it climbs, the plane gradually
increases its speed until it reaches cruising altitude, at which time it maintains a constant speed
for several hours as long as it stays at cruising altitude. After flying for 32 minutes, the plane
reaches cruising altitude and has flown 192 miles. After flying for a total of 92 minutes, the plane
has flown a total of 762 miles.
Determine the speed of the plane, at cruising altitude, in miles per minute.
Write an equation to represent the number of miles the plane has flown, y , during x minutes at
cruising altitude, only.
Assuming that the plane maintains its speed at cruising altitude, determine the total number of
miles the plane has flown 2 hours into the flight.
32
minutes
92
minutes
bominutes
192
miles
762
miles
570
mile
cruising
speed
570
mph
or
9.5
miles
per
minute
g
9.5
Algebra I (Common Core) – June ’16
[18]
9
9.5188
120 32 88
9
836
1028
miles
after
2 hours
836
192
1028

36 On the set of axes below, graph
g ( x ) x 1
and
f ( x )
How many values of x satisfy the equation f ( x ) g ( x )? Explain your answer, using evidence from
your graphs.
y
x
2 1, 1
2 , 1
2
x x
x x
≤
>





1
2
Algebra I (Common Core) – June ’16
[19] [OVER]
o
o
oo
L
One value because the functions intersect on the graph
once

37 Franco and Caryl went to a bakery to buy desserts. Franco bought 3 packages of cupcakes and
2 packages of brownies for $19. Caryl bought 2 packages of cupcakes and 4 packages of brownies
for $24. Let x equal the price of one package of cupcakes and y equal the price of one package
of brownies.
Write a system of equations that describes the given situation.
On the set of axes below, graph the system of equations.
Determine the exact cost of one package of cupcakes and the exact cost of one package of
brownies in dollars and cents. Justify your solution.
y
x
Algebra I (Common Core) – June ’16
[20]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate
the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
Utilize the information provided to determine your answer. Note that diagrams are not
necessarily drawn to scale. A correct numerical answer with no work shown will receive only
1 credit. All answers should be written in pen, except for graphs and drawings, which should
be done in pencil. [
6
]
3
29
19
3
25
19
2
49
24
3k
2y
l9
3
2
4
49
24
9
9.5
3 1
2k
T
4y 2 24
oo
I
FF
3
3
1
y
x
r
3.50 cupcakes
21
6
32
9.50
4 25 brownies
µ
substitute
for
x
Ix 21
3.50
1
3
5
6 4.25
2
3
4.25 4.25
11
3.500