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Math Problems
Algebra 2
Ratio and Quadratic equation
The scatterplot shows average
2014
2014
2014
Major League
\newline
Baseball (MLB) salaries,
y
y
y
, in millions of dollars, for players
x
x
x
years of age. Which of the following quadratic equations best models the relationship between a MLB player's age and his salary?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
0.1
(
x
−
23.1
)
2
+
0.78
y=0.1(x-23.1)^{2}+0.78
y
=
0.1
(
x
−
23.1
)
2
+
0.78
\newline
(B)
y
=
0.1
(
x
+
23.1
)
2
+
0.78
y=0.1(x+23.1)^{2}+0.78
y
=
0.1
(
x
+
23.1
)
2
+
0.78
\newline
(c)
y
=
2
(
x
−
23.1
)
2
+
0.78
y=2(x-23.1)^{2}+0.78
y
=
2
(
x
−
23.1
)
2
+
0.78
\newline
(D)
y
=
2
(
x
+
23.1
)
2
+
0.78
y=2(x+23.1)^{2}+0.78
y
=
2
(
x
+
23.1
)
2
+
0.78
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An isosceles triangle has a height of
12.5
m
12.5 \mathrm{~m}
12.5
m
and two equal angles that measure
5
5
∘
55^{\circ}
5
5
∘
. Determine the area of the triangle.
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15
15
15
.
\newline
The price value,
V
V
V
, of a car that is
t
t
t
years old is given by
V
=
f
(
t
)
=
17000
−
3100
t
V=f(t)=17000-3100 t
V
=
f
(
t
)
=
17000
−
3100
t
. Find thr domain and range of
f
(
t
)
f(t)
f
(
t
)
.
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A copper cube that is
15
c
m
15 \mathrm{~cm}
15
cm
on each side is suspended from a spring scale and then placed in water? How much will the cube
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A
300
300
300
-room hotel collects
$
75
\$75
$75
per occupied room and does not collect any money for vacant rooms. Which of the following functions best represents how many dollars,
d
d
d
, the hotel generates if there are
v
v
v
vacant rooms in the hotel?
\newline
Choose
1
1
1
answer:
\newline
(A)
d
=
75
(
300
−
v
)
d=75(300-v)
d
=
75
(
300
−
v
)
\newline
(B)
d
=
75
(
300
+
v
)
d=75(300+v)
d
=
75
(
300
+
v
)
\newline
(C)
d
=
300
(
75
−
v
)
d=300(75-v)
d
=
300
(
75
−
v
)
\newline
(D)
d
=
300
(
75
+
v
)
d=300(75+v)
d
=
300
(
75
+
v
)
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48
48
48
\newline
A right square pyramid is shown.
\newline
The height is
10
10
10
centimeters and the side length of the base is
16
16
16
centimeters.
\newline
What is the length, in centimeters
(
c
m
)
(\mathrm{cm})
(
cm
)
, of
s
s
s
?
\newline
s
=
s=
s
=
\newline
c
m
\mathrm{cm}
cm
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Region I and II are squares. If region I has an area of
16
16
16
and region II has an area of
64
64
64
, what is the area of region III?
\newline
A.
16
16
16
\newline
B.
50
50
50
\newline
C.
80
80
80
\newline
D.
512
512
512
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An object is launched from a platform.
\newline
Its height (in meters),
x
x
x
seconds after the launch, is modeled by
\newline
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
h(x)=-5(x+1)(x-9)
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
\newline
How many seconds after launch will the object hit the ground?
\newline
□
\square
□
seconds
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Simon has
160
160
160
meters of fencing to build a rectangular garden.
\newline
The garden's area (in square meters) as a function of the garden's width
x
x
x
(in meters) is modeled by
\newline
A
(
x
)
=
−
x
(
x
−
80
)
A(x)=-x(x-80)
A
(
x
)
=
−
x
(
x
−
80
)
\newline
What is the maximum area possible?
\newline
□
\square
□
square meters
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The power generated by an electrical circuit (in watts) as a function of its current
\newline
x
x
x
(in amperes) is modeled by
\newline
P
(
x
)
=
−
15
x
(
x
−
8
)
P(x)=-15 x(x-8)
P
(
x
)
=
−
15
x
(
x
−
8
)
\newline
What current will produce the maximum power?
\newline
□
\square
□
amperes
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The area of a rectangular window is
(
4
x
2
−
21
x
−
18
)
\left(4 x^{2}-21 x-18\right)
(
4
x
2
−
21
x
−
18
)
. Both the length and width are polynomials with integer coefficients. What are the dimensions?
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The derivative of a function
g
g
g
is given by
\newline
g
′
(
x
)
=
x
3
−
2
x
2
−
3
x
+
4.
g^{\prime}(x)=x^{3}-2 x^{2}-3 x+4 .
g
′
(
x
)
=
x
3
−
2
x
2
−
3
x
+
4.
\newline
On which intervals is the graph of
g
g
g
increasing?
\newline
Use a graphing calculator.
\newline
Choose
1
1
1
answer:
\newline
(A)
x
≤
−
1.562
x \leq-1.562
x
≤
−
1.562
and
\newline
1
≤
x
≤
2.562
1 \leq x \leq 2.562
1
≤
x
≤
2.562
\newline
(B)
−
1.562
≤
x
≤
1
-1.562 \leq x \leq 1
−
1.562
≤
x
≤
1
and
x
≥
2.562
x \geq 2.562
x
≥
2.562
\newline
(C)
x
≤
−
0.535
x \leq-0.535
x
≤
−
0.535
and
x
≥
1.869
x \geq 1.869
x
≥
1.869
\newline
(D)
−
0.535
≤
x
≤
1.869
-0.535 \leq x \leq 1.869
−
0.535
≤
x
≤
1.869
\newline
(E) All real numbers
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The radius of the base of a cylinder is increasing at a rate of
7
7
7
millimeters per hour.
\newline
The height of the cylinder is fixed at
1
1
1
.
5
5
5
millimeters.
\newline
At a certain instant, the radius is
12
12
12
millimeters.
\newline
What is the rate of change of the volume of the cylinder at that instant (in cubic millimeters per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
216
π
216 \pi
216
π
\newline
(B)
1512
π
1512 \pi
1512
π
\newline
(C)
126
π
126 \pi
126
π
\newline
(D)
252
π
252 \pi
252
π
\newline
The volume of a cylinder with radius
r
r
r
and height
h
h
h
is
π
r
2
h
\pi r^{2} h
π
r
2
h
.
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The radius of the base of a cylinder is increasing at a rate of
7
7
7
millimeters per hour.
\newline
The height of the cylinder is fixed at
1
1
1
.
5
5
5
millimeters.
\newline
At a certain instant, the radius is
12
12
12
millimeters.
\newline
What is the rate of change of the volume of the cylinder at that instant (in cubic millimeters per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
252
π
252 \pi
252
π
\newline
(B)
216
π
216 \pi
216
π
\newline
(C)
1512
π
1512 \pi
1512
π
\newline
(D)
126
π
126 \pi
126
π
\newline
The volume of a cylinder with radius
r
r
r
and height
h
h
h
is
π
r
2
h
\pi r^{2} h
π
r
2
h
.
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R
=
206.835
−
1.015
W
−
84.6
S
R=206.835-1.015 W-84.6 S
R
=
206.835
−
1.015
W
−
84.6
S
\newline
The formula gives the Flesch Reading Ease score
R
R
R
for a passage of text with an average of
W
W
W
words per sentence and an average of
S
S
S
syllables per word. Which of the following equations correctly shows the average number of syllables per word in terms of the average number of words per sentence and the Flesch Reading Ease score?
\newline
Choose
1
1
1
answer:
\newline
(A)
S
=
R
84.6
+
206.835
−
1.015
W
S=\frac{R}{84.6}+206.835-1.015 W
S
=
84.6
R
+
206.835
−
1.015
W
\newline
(B)
S
=
R
−
84.6
−
206.835
+
1.015
W
S=\frac{R}{-84.6}-206.835+1.015 W
S
=
−
84.6
R
−
206.835
+
1.015
W
\newline
(C)
S
=
R
84.6
−
206.835
+
1.015
W
S=\frac{R}{84.6-206.835+1.015 W}
S
=
84.6
−
206.835
+
1.015
W
R
\newline
(D)
S
=
R
−
206.835
+
1.015
W
−
84.6
S=\frac{R-206.835+1.015 W}{-84.6}
S
=
−
84.6
R
−
206.835
+
1.015
W
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An object is launched from a platform.
\newline
Its height (in meters),
x
x
x
seconds after the launch, is modeled by
\newline
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
h(x)=-5(x+1)(x-9)
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
\newline
What is the height of the object at the time of launch?
\newline
□
\square
□
meters
\text{meters}
meters
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Ana dives into a pool off of a springboard high dive.
\newline
Her height (in meters above the water),
x
x
x
seconds after diving, is modeled by
\newline
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
3
)
h(x)=-5(x+1)(x-3)
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
3
)
\newline
How many seconds after diving will Ana hit the water?
\newline
□
\square
□
seconds
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A
+
b
+
c
=
220
A+b+c=220
A
+
b
+
c
=
220
and
a
+
d
=
200
a+d=200
a
+
d
=
200
and
b
+
c
=
140
b+c=140
b
+
c
=
140
and
c
+
d
=
160
c+d=160
c
+
d
=
160
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Guillermo is a professional deep water free diver.
\newline
His altitude (in meters relative to sea level),
x
x
x
seconds after diving, is modeled by
\newline
g
(
x
)
=
1
20
x
(
x
−
100
)
g(x)=\frac{1}{20} x(x-100)
g
(
x
)
=
20
1
x
(
x
−
100
)
\newline
How many seconds after diving will Guillermo reach his lowest altitude?
\newline
□
\square
□
seconds
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Elsie has a plastic box she uses for send art design boxes
10
10
10
inches. The width is
7
7
7
inches
5
5
5
inches solve equation so you can find the volume of the sand and cubic inches.
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PRACTICE Area of Sectors and
\newline
Question
14
14
14
, *
0
0
0
.
6
6
6
.
5
5
5
\newline
HW Score:
20.83
%
20.83 \%
20.83%
\newline
Points:
0
0
0
of
1
1
1
\newline
Some farmers use a circular irrigation method. An irrigation arm acts as the radius of an irrigation circle. How much land is covered with an irrigation arm of
370
f
t
370 \mathrm{ft}
370
ft
?
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In San Diego, the number of daylight hours is dependent on the day of the year. The number of daylight hours
D
D
D
can be modeled by the sinusoidal function
D
(
t
)
=
2.4
sin
(
0.017
(
t
−
81
)
)
+
12
D(t)=2.4 \sin (0.017(t-81))+12
D
(
t
)
=
2.4
sin
(
0.017
(
t
−
81
))
+
12
, where
t
t
t
is the day of the year from
t
=
1
t=1
t
=
1
to
t
=
365
t=365
t
=
365
. Based on this model, which of the following statements is correct?
\newline
(A) The minimum number of daylight hours in San Diego is
12
12
12
hours.
\newline
(B) The maximum number of daylight hours in San Diego is
12
12
12
hours.
\newline
(C) The minimum number of daylight hours in San Diego is
9
9
9
.
6
6
6
hours.
\newline
(D) The maximum number of daylight hours in San Diego is
9
9
9
.
6
6
6
hours.
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Our school bought
300
300
300
Pencils for
$
75
\$75
$75
. They came in boxes of
12
12
12
Pencils. How much did each box cost?
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Simon has
160
160
160
meters of fencing to build a rectangular garden.
\newline
The garden's area (in square meters) as a function of the garden's width
x
x
x
(in meters) is modeled by
\newline
A
(
x
)
=
−
x
(
x
−
80
)
A(x)=-x(x-80)
A
(
x
)
=
−
x
(
x
−
80
)
\newline
What width will produce the maximum garden area?
\newline
□
\square
□
meters
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Δ
P
=
6.2
×
(
600
(
450000
)
1
/
3
)
1.1
\Delta P=6.2\times(600(450000)^{1/3})^{1.1}
Δ
P
=
6.2
×
(
600
(
450000
)
1/3
)
1.1
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Mr. Kirby's physics class went to the football field to launch a rocket into the air. The rocket's height in feet,
f
(
x
)
f(x)
f
(
x
)
, depends on the number of seconds,
x
x
x
, that have elapsed since launch.
\newline
What does
f
(
8
)
=
0
f(8) = 0
f
(
8
)
=
0
tell you?
\newline
Choices:
\newline
(A)The rocket starts its launch
8
8
8
feet above the ground.
\newline
(B)After
8
8
8
seconds, the rocket has already landed on the field.
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If a bank has
222
222
222
million dollars in expenses and an efficiency ratio of
75
75
75
, what is its revenue in millions of dollars?
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Marquise has
200
200
200
meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width (in meters) is modeled by:
A
(
x
)
=
−
x
2
+
100
x
A(x)=-x^2+100x
A
(
x
)
=
−
x
2
+
100
x
What is the maximum area possible?
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Jason used a discount coupon for
5
%
5 \%
5%
off at his favorite clothing store. He bought
9
9
9
pairs of shoes for
x
x
x
dollars each and
7
7
7
coats for
y
y
y
dollars each. Which expression represents the total amount Jason paid after the coupon was applied?
\newline
5
(
9
x
+
7
y
)
5(9 x+7 y)
5
(
9
x
+
7
y
)
\newline
0.05
(
9
x
+
7
y
)
+
(
9
x
+
7
y
)
0.05(9 x+7 y)+(9 x+7 y)
0.05
(
9
x
+
7
y
)
+
(
9
x
+
7
y
)
\newline
0.95
(
9
x
+
7
y
)
0.95(9 x+7 y)
0.95
(
9
x
+
7
y
)
\newline
(
9
x
+
7
y
)
−
0.95
(
9
x
+
7
y
)
(9 x+7 y)-0.95(9 x+7 y)
(
9
x
+
7
y
)
−
0.95
(
9
x
+
7
y
)
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Magan bought
f
f
f
folders that cost
$
0.30
\$ 0.30
$0.30
each and
m
m
m
markers that cost
$
0.65
\$ 0.65
$0.65
each. Sales tax is
8.25
%
8.25 \%
8.25%
. Which expression represents the total amount Magan paid, including tax?
\newline
0.3
(
0.0825
f
)
+
0.65
(
0.0825
m
)
0.3(0.0825 f)+0.65(0.0825 m)
0.3
(
0.0825
f
)
+
0.65
(
0.0825
m
)
\newline
(
0.3
+
0.65
)
+
0.0825
(
0.3
+
0.65
)
(0.3+0.65)+0.0825(0.3+0.65)
(
0.3
+
0.65
)
+
0.0825
(
0.3
+
0.65
)
\newline
(
0.3
f
+
0.65
m
)
+
0.0825
(
0.3
f
+
0.65
m
)
(0.3 f+0.65 m)+0.0825(0.3 f+0.65 m)
(
0.3
f
+
0.65
m
)
+
0.0825
(
0.3
f
+
0.65
m
)
\newline
1.0825
(
f
+
m
)
1.0825(f+m)
1.0825
(
f
+
m
)
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Guillermo is a professional deep water free diver.
\newline
His altitude (in meters relative to sea level),
x
x
x
seconds after diving, is nodeled by
\newline
g
(
x
)
=
1
20
x
(
x
−
100
)
g(x)=\frac{1}{20} x(x-100)
g
(
x
)
=
20
1
x
(
x
−
100
)
\newline
How many seconds after diving will Guillermo reach his lowest altitude?
\newline
seconds
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R
(
q
)
=
−
0.31
(
q
−
260
)
2
+
9
,
500
R(q)=-0.31(q-260)^{2}+9,500
R
(
q
)
=
−
0.31
(
q
−
260
)
2
+
9
,
500
\newline
A shoe manufacturer determines that its monthly revenue,
R
(
q
)
R(q)
R
(
q
)
, in dollars is given by the function, where
q
q
q
is the number of pairs of shoes sold each month. What is the maximum value of the company's monthly revenue in dollars?
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The average amount of water in
4
4
4
similar tanks is
k
k
k
litres.
\newline
(a) Express the total amount of water in the tanks in terms of
k
k
k
.
\newline
(b) If
k
=
15
k=15
k
=
15
, find the total amount of water in the
4
4
4
tanks.
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A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by:
P
(
x
)
=
−
3
(
x
−
5
)
2
+
12
P(x)=-3(x-5)^2+12
P
(
x
)
=
−
3
(
x
−
5
)
2
+
12
What sock price should the company set to earn a maximum profit?
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Uche pumps gasoline at a rate of
18
L
min
\frac{18\,\text{L}}{\text{min}}
min
18
L
. What is Uche's pumping rate in
mL
s
\frac{\text{mL}}{\text{s}}
s
mL
?
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A sheet of glass has a density of
2.5
g
cm
3
\frac{2.5\,\text{g}}{\text{cm}^3}
cm
3
2.5
g
. What is the density of the glass in
kg
m
3
\frac{\text{kg}}{\text{m}^3}
m
3
kg
?
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Consider the reaction between
N
a
2
C
O
3
(
a
q
)
\mathrm{Na_2CO_3(aq)}
N
a
2
C
O
3
(
aq
)
and
H
3
P
O
4
(
a
q
)
\mathrm{H_3PO_4(aq)}
H
3
P
O
4
(
aq
)
as shown in the following balanced equation:
\newline
3
N
a
2
C
O
3
(
a
q
)
+
2
H
3
P
O
4
(
a
q
)
→
2
N
a
3
P
O
4
(
a
q
)
+
3
H
2
O
(
l
)
+
3
C
O
2
(
g
)
3\mathrm{Na_2CO_3(aq)} + 2\mathrm{H_3PO_4(aq)} \rightarrow 2\mathrm{Na_3PO_4(aq)} + 3\mathrm{H_2O(l)} + 3\mathrm{CO_2(g)}
3
N
a
2
C
O
3
(
aq
)
+
2
H
3
P
O
4
(
aq
)
→
2
N
a
3
P
O
4
(
aq
)
+
3
H
2
O
(
l
)
+
3
C
O
2
(
g
)
\newline
\begin{array}{ll}
\newline
\text{Chemical} & \text{MW} (\newline\)\mathrm{Na_2CO_3} &
105
105
105
.
991
991
991
(\newline\)\mathrm{H_3PO_4} &
97
97
97
.
9977
9977
9977
(\newline\)\mathrm{Na_3PO_4} &
163
163
163
.
944
944
944
(\newline\)\mathrm{H_2O} &
18
18
18
.
0158
0158
0158
(\newline\)\mathrm{CO_2} &
44
44
44
.
011
011
011
(\newline\)\end{array}
\newline
What is the concentration of the phosphoric acid solution if
199.2
m
L
199.2\,\mathrm{mL}
199.2
mL
of it generates
345.4
m
L
345.4\,\mathrm{mL}
345.4
mL
of a
1.23
M
1.23\,\mathrm{M}
1.23
M
sodium phosphate for complete reaction?
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A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by:
p
(
x
)
=
−
3
(
x
−
5
)
2
+
12
p(x)=-3(x-5)^2+12
p
(
x
)
=
−
3
(
x
−
5
)
2
+
12
\newline
What is the maximum profit that the company can earn?
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A town has a population of
5.56
×
1
0
4
5.56 \times 10^{4}
5.56
×
1
0
4
and grows at a rate of
4
%
4 \%
4%
every year. Which equation represents the town's population after
7
7
7
years?
\newline
P
=
(
5.56
×
1
0
4
)
(
1
+
0.04
)
7
P=\left(5.56 \times 10^{4}\right)(1+0.04)^{7}
P
=
(
5.56
×
1
0
4
)
(
1
+
0.04
)
7
\newline
P
=
(
5.56
×
1
0
4
)
(
1
+
0.04
)
(
1
+
0.04
)
(
1
+
0.04
)
(
1
+
0.04
)
P=\left(5.56 \times 10^{4}\right)(1+0.04)(1+0.04)(1+0.04)(1+0.04)
P
=
(
5.56
×
1
0
4
)
(
1
+
0.04
)
(
1
+
0.04
)
(
1
+
0.04
)
(
1
+
0.04
)
\newline
P
=
(
5.56
×
1
0
4
)
(
0.04
)
7
P=\left(5.56 \times 10^{4}\right)(0.04)^{7}
P
=
(
5.56
×
1
0
4
)
(
0.04
)
7
\newline
P
=
(
5.56
×
1
0
4
)
(
1
−
0.04
)
7
P=\left(5.56 \times 10^{4}\right)(1-0.04)^{7}
P
=
(
5.56
×
1
0
4
)
(
1
−
0.04
)
7
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T
=
277
+
4
s
T=277+4s
T
=
277
+
4
s
\newline
The temperature in kelvin,
T
T
T
, of a resistor in a circuit
s
s
s
seconds after connecting a battery is given by the equation. For how many seconds does the battery need to be connected for the temperature to increase by
1
1
1
kelvin?
\newline
Choose
1
1
1
answer:
\newline
(A)
0.25
0.25
0.25
\newline
(B)
4
4
4
\newline
(C)
69
69
69
\newline
(D)
277
277
277
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Consumer surplus is the amount of money that consumers save because they are able to buy a product at a price lower than the highest price they would be willing to pay.
\newline
The consumer surplus for a certain product increases at a rate of
900
(
x
+
13
)
−
35
\frac{900}{(x+13)}-35
(
x
+
13
)
900
−
35
dollars per thousand units of the product sold (where
x
x
x
is the number of thousands of units sold).
\newline
By how many dollars does the surplus increase between
x
=
7
x=7
x
=
7
and
x
=
12
x=12
x
=
12
?
\newline
Choose
1
1
1
answer:
\newline
(A)
900
ln
(
0.8
)
−
35
900 \ln (0.8)-35
900
ln
(
0.8
)
−
35
\newline
(B)
900
ln
(
1.25
)
−
35
900 \ln (1.25)-35
900
ln
(
1.25
)
−
35
\newline
(C)
900
ln
(
0.8
)
−
175
900 \ln (0.8)-175
900
ln
(
0.8
)
−
175
\newline
(D)
900
ln
(
1.25
)
−
175
900 \ln (1.25)-175
900
ln
(
1.25
)
−
175
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