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Math Problems
Algebra 2
Is (x, y) a solution to the system of equations?
Could
10.5
c
m
,
8.0
c
m
10.5 \mathrm{~cm}, 8.0 \mathrm{~cm}
10.5
cm
,
8.0
cm
, and
4.0
c
m
4.0 \mathrm{~cm}
4.0
cm
be the side lengths of a triangle?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Could
10.6
c
m
,
5.6
c
m
10.6 \mathrm{~cm}, 5.6 \mathrm{~cm}
10.6
cm
,
5.6
cm
, and
4.0
c
m
4.0 \mathrm{~cm}
4.0
cm
be the side lengths of a triangle?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Could
7.7
c
m
,
4.0
c
m
7.7 \mathrm{~cm}, 4.0 \mathrm{~cm}
7.7
cm
,
4.0
cm
, and
1.7
c
m
1.7 \mathrm{~cm}
1.7
cm
be the side lengths of a triangle?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Could
10.7
c
m
,
3.2
c
m
10.7 \mathrm{~cm}, 3.2 \mathrm{~cm}
10.7
cm
,
3.2
cm
, and
5.5
c
m
5.5 \mathrm{~cm}
5.5
cm
be the side lengths of a triangle?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Could
13.5
c
m
,
8.0
c
m
13.5 \mathrm{~cm}, 8.0 \mathrm{~cm}
13.5
cm
,
8.0
cm
, and
3.5
c
m
3.5 \mathrm{~cm}
3.5
cm
be the side lengths of a triangle?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
−
8
x
−
3
y=-8 x-3
y
=
−
8
x
−
3
\newline
x
+
y
=
7
x+y=7
x
+
y
=
7
\newline
Is
(
3
,
4
)
(3,4)
(
3
,
4
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
A grocery store charges
$
3.02
\$ 3.02
$3.02
per milk jug and
$
0.10
\$ 0.10
$0.10
per grocery bag. You never buy the bags because you bring your own.
\newline
Is the total price you pay proportional to the number of milk jugs you buy?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Anna does sit-ups to get ready for her first triathlon. When she starts, she does a sit-up every
2
2
2
seconds. But, as she gets tired, each sit-up takes longer and longer to do.
\newline
Is the number of sit-ups Anna does proportional to the time she spends doing them?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Today, Howell has
75
75
75
kiwis. He will eat
2
2
2
of them every day.
\newline
Is the number of kiwis Howell has left proportional to the number of days that pass?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
At the gas station, gas usually costs
$
3
\$ 3
$3
. This month, there's a sale: for every drink you purchase you save
$
0.20
\$ 0.20
$0.20
on gas.
\newline
Assuming your sale savings are less than the cost of your gas, are your total savings on gas proportional to the number of drinks you purchase?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Jimmy receives his first
3
3
3
video games free then pays
$
50
\$ 50
$50
for each game after that.
\newline
Is the amount of money he spends on video games proportional to the number of games he owns?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Apples are on sale for
$
3.12
\$ 3.12
$3.12
per kilogram.
\newline
Is the total cost of the apples proportional to the total mass?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
lim
x
→
π
3
sin
(
x
)
=
?
\lim _{x \rightarrow \frac{\pi}{3}} \sin (x)=?
x
→
3
π
lim
sin
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
\frac{1}{2}
2
1
\newline
(B)
3
2
\frac{\sqrt{3}}{2}
2
3
\newline
(C)
3
\sqrt{3}
3
\newline
(D) The limit doesn't exist.
Get tutor help
lim
x
→
π
cos
(
x
)
=
?
\lim _{x \rightarrow \pi} \cos (x)=?
x
→
π
lim
cos
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
Get tutor help
lim
x
→
π
4
csc
(
x
)
=
?
\lim _{x \rightarrow \frac{\pi}{4}} \csc (x)=?
x
→
4
π
lim
csc
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
\frac{\sqrt{2}}{2}
2
2
\newline
(B)
3
2
\frac{\sqrt{3}}{2}
2
3
\newline
(C)
2
\sqrt{2}
2
\newline
(D) The limit doesn't exist.
Get tutor help
lim
x
→
π
6
sin
(
x
)
=
?
\lim _{x \rightarrow \frac{\pi}{6}} \sin (x)=?
x
→
6
π
lim
sin
(
x
)
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
\frac{1}{2}
2
1
\newline
(B)
2
2
\frac{\sqrt{2}}{2}
2
2
\newline
(C)
2
\sqrt{2}
2
\newline
(D) The limit doesn't exist.
Get tutor help
g
(
x
)
=
15
−
4
x
g(x)=15-4 x
g
(
x
)
=
15
−
4
x
\newline
h
(
x
)
=
3
2
x
+
8
h(x)=\frac{3}{2} x+8
h
(
x
)
=
2
3
x
+
8
\newline
Write
g
(
h
(
x
)
)
g(h(x))
g
(
h
(
x
))
as an expression in terms of
x
x
x
.
\newline
g
(
h
(
x
)
)
=
g(h(x))=
g
(
h
(
x
))
=
Get tutor help
f
(
x
)
=
1
8
x
+
3
f(x)=\frac{1}{8 x+3}
f
(
x
)
=
8
x
+
3
1
\newline
g
(
x
)
=
12
−
5
x
g(x)=12-5 x
g
(
x
)
=
12
−
5
x
\newline
Write
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
as an expression in terms of
x
x
x
.
\newline
f
(
g
(
x
)
)
=
f(g(x))=
f
(
g
(
x
))
=
Get tutor help
E. coli is among the fastest-growing bacteria, with a generation (or doubling) time of
20
20
20
minutes under optimal conditions. After
60
60
60
minutes, the number of bacteria in a culture of
E
E
E
. coli was
400
400
400
. Approximately how many bacteria were in the culture after
30
30
30
minutes?
\newline
Choose
1
1
1
answer:
\newline
(A)
50
50
50
\newline
(B)
142
142
142
\newline
(C)
174
\mathbf{1 7 4}
174
\newline
(D)
200
200
200
Get tutor help
The Shanghai maglev train travels at a speed of
431
431
431
kilometers per hour. Approximately what is the train's speed in miles per hour?
\newline
(
1
1
1
mile
≈
1.61
\approx 1.61
≈
1.61
kilometers)
\newline
Choose
1
1
1
answer:
\newline
(A)
268
268
268
\newline
(B)
370
370
370
\newline
(C)
431
431
431
\newline
(D)
694
694
694
Get tutor help
y
=
2
x
−
1
y=2 x-1
y
=
2
x
−
1
\newline
5
x
−
4
y
=
1
5 x-4 y=1
5
x
−
4
y
=
1
\newline
Is
(
1
,
1
)
(1,1)
(
1
,
1
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
−
4
x
−
5
y=-4 x-5
y
=
−
4
x
−
5
\newline
y
=
3
x
−
2
y=3 x-2
y
=
3
x
−
2
\newline
Is
(
3
,
7
)
(3,7)
(
3
,
7
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
3
x
−
2
y
=
−
1
3 x-2 y=-1
3
x
−
2
y
=
−
1
\newline
y
=
−
x
+
3
y=-x+3
y
=
−
x
+
3
\newline
Is
(
1
,
2
)
(1,2)
(
1
,
2
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
3
x
−
5
y=3 x-5
y
=
3
x
−
5
\newline
y
=
x
−
1
y=x-1
y
=
x
−
1
\newline
Is
(
2
,
1
)
(2,1)
(
2
,
1
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
2
x
+
1
y=2 x+1
y
=
2
x
+
1
\newline
x
−
y
=
−
3
x-y=-3
x
−
y
=
−
3
\newline
Is
(
2
,
5
)
(2,5)
(
2
,
5
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
2
x
+
y
=
4
2 x+y=4
2
x
+
y
=
4
\newline
y
=
3
x
−
1
y=3 x-1
y
=
3
x
−
1
\newline
Is
(
1
,
2
)
(1,2)
(
1
,
2
)
a solution to both equations?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
−
3
x
−
8
y
=
−
8
-3 x-8 y=-8
−
3
x
−
8
y
=
−
8
\newline
y
=
2
−
x
y=2-x
y
=
2
−
x
\newline
Is
(
0
,
1
)
(0,1)
(
0
,
1
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
−
4
x
+
3
y
=
2
-4 x+3 y=2
−
4
x
+
3
y
=
2
\newline
3
x
−
9
y
=
3
3 x-9 y=3
3
x
−
9
y
=
3
\newline
Is
(
4
,
1
)
(4,1)
(
4
,
1
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B)
N
o
\mathrm{No}
No
Get tutor help
If
y
=
x
(
x
−
3
)
(
x
−
2
)
y=x(x-3)(x-2)
y
=
x
(
x
−
3
)
(
x
−
2
)
, what is the value of
y
y
y
when
x
=
3
x=3
x
=
3
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
18
-18
−
18
\newline
(B)
0
0
0
\newline
(C)
3
3
3
\newline
(D)
18
18
18
Get tutor help
8
(
2
2
+
8
)
\sqrt{8}(2 \sqrt{2}+8)
8
(
2
2
+
8
)
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
16
16
16
\newline
(B)
40
40
40
\newline
(C)
8
+
16
2
8+16 \sqrt{2}
8
+
16
2
\newline
(D)
32
+
8
8
32+8 \sqrt{8}
32
+
8
8
Get tutor help
If
2
A
+
B
=
9
2 A+B=9
2
A
+
B
=
9
, which of the following correctly expresses
A
A
A
in terms of
B
B
B
?
\newline
Choose
1
1
1
answer:
\newline
(A)
A
=
9
−
2
B
A=9-2 B
A
=
9
−
2
B
\newline
(B)
A
=
9
−
B
A=9-B
A
=
9
−
B
\newline
(C)
A
=
B
−
9
2
A=\frac{B-9}{2}
A
=
2
B
−
9
\newline
(D)
A
=
9
−
B
2
A=\frac{9-B}{2}
A
=
2
9
−
B
Get tutor help
y
=
5
x
+
2
y=5 x+2
y
=
5
x
+
2
\newline
4
x
−
y
=
0
4 x-y=0
4
x
−
y
=
0
\newline
Is
(
2
,
12
)
(2,12)
(
2
,
12
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
x
−
2
y=x-2
y
=
x
−
2
\newline
y
=
3
x
+
4
y=3 x+4
y
=
3
x
+
4
\newline
Is
(
4
,
2
)
(4,2)
(
4
,
2
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
4
x
−
5
y=4 x-5
y
=
4
x
−
5
\newline
y
=
2
x
+
3
y=2 x+3
y
=
2
x
+
3
\newline
Is
(
4
,
11
)
(4,11)
(
4
,
11
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
2
x
+
7
y
=
1
2 x+7 y=1
2
x
+
7
y
=
1
\newline
y
=
4
x
−
8
y=4 x-8
y
=
4
x
−
8
\newline
Is
(
4
,
8
)
(4,8)
(
4
,
8
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
−
5
x
+
1
y
=
3
x
−
2
\begin{array}{l} y=-5 x+1 \\ y=3 x-2 \end{array}
y
=
−
5
x
+
1
y
=
3
x
−
2
\newline
Is
(
3
,
8
)
(3,8)
(
3
,
8
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
−
8
x
−
3
y=-8 x-3
y
=
−
8
x
−
3
\newline
x
+
y
=
7
x+y=7
x
+
y
=
7
\newline
Is
(
3
,
4
)
(3,4)
(
3
,
4
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
−
5
y
=
−
5
7
x
+
6
y
=
7
\begin{array}{c} -5 y=-5 \\ 7 x+6 y=7 \end{array}
−
5
y
=
−
5
7
x
+
6
y
=
7
\newline
Is
(
5
,
1
)
(5,1)
(
5
,
1
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
2
x
+
3
y=2 x+3
y
=
2
x
+
3
\newline
y
=
4
x
−
3
y=4 x-3
y
=
4
x
−
3
\newline
Is
(
3
,
9
)
(3,9)
(
3
,
9
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
−
x
+
4
y
=
4
-x+4 y=4
−
x
+
4
y
=
4
\newline
−
x
+
3
y
=
1
-x+3 y=1
−
x
+
3
y
=
1
\newline
Is
(
8
,
3
)
(8,3)
(
8
,
3
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
3
x
−
4
y
=
−
5
3 x-4 y=-5
3
x
−
4
y
=
−
5
\newline
y
=
4
x
−
2
y=4 x-2
y
=
4
x
−
2
\newline
Is
(
1
,
2
)
(1,2)
(
1
,
2
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
−
3
x
−
4
y
=
4
−
5
x
+
y
=
2
\begin{array}{r} -3 x-4 y=4 \\ -5 x+y=2 \end{array}
−
3
x
−
4
y
=
4
−
5
x
+
y
=
2
\newline
Is
(
2
,
10
)
(2,10)
(
2
,
10
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
y
=
−
4
x
+
6
y=-4 x+6
y
=
−
4
x
+
6
\newline
3
x
+
4
y
=
−
2
3 x+4 y=-2
3
x
+
4
y
=
−
2
\newline
Is
(
2
,
2
)
(2,2)
(
2
,
2
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
−
x
+
4
y
=
−
9
-x+4 y=-9
−
x
+
4
y
=
−
9
\newline
y
=
−
2
x
+
6
y=-2 x+6
y
=
−
2
x
+
6
\newline
Is
(
2
,
3
)
(2,3)
(
2
,
3
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
2
x
−
3
y
=
−
5
2 x-3 y=-5
2
x
−
3
y
=
−
5
\newline
4
x
−
4
y
=
−
4
4 x-4 y=-4
4
x
−
4
y
=
−
4
\newline
Is
(
2
,
3
)
(2,3)
(
2
,
3
)
a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Lindsay is
5
5
5
years younger than Mark. Seven years ago, the sum of their ages was
31
31
31
.
\newline
Let
l
l
l
be Lindsay's age and let
m
m
m
be Mark's age.
\newline
Which system of equations represents this situation?
\newline
Choose
1
1
1
answer:
\newline
(A)
{
l
=
m
+
5
(
l
−
7
)
+
(
m
−
7
)
=
3
\left\{\begin{array}{l}l=m+5 \\ (l-7)+(m-7)=3\end{array}\right.
{
l
=
m
+
5
(
l
−
7
)
+
(
m
−
7
)
=
3
\newline
(B)
{
l
−
7
=
(
m
−
7
)
−
5
l
+
m
=
31
\left\{\begin{array}{l}l-7=(m-7)-5 \\ l+m=31\end{array}\right.
{
l
−
7
=
(
m
−
7
)
−
5
l
+
m
=
31
\newline
(C)
{
l
=
m
−
5
(
l
−
7
)
+
(
m
−
7
)
=
3
\left\{\begin{array}{l}l=m-5 \\ (l-7)+(m-7)=3\end{array}\right.
{
l
=
m
−
5
(
l
−
7
)
+
(
m
−
7
)
=
3
\newline
(D)
{
l
−
7
=
(
m
−
7
)
+
5
l
+
m
=
31
\left\{\begin{array}{l}l-7=(m-7)+5 \\ l+m=31\end{array}\right.
{
l
−
7
=
(
m
−
7
)
+
5
l
+
m
=
31
Get tutor help
Fred is
4
4
4
times as old as Nathan and is also
27
27
27
years older than Nathan.
\newline
Let
f
f
f
be Fred's age and let
n
n
n
be Nathan's age.
\newline
Which system of equations represents this situation?
\newline
Choose
1
1
1
answer:
\newline
(A)
{
4
f
=
n
f
=
n
+
27
\left\{\begin{array}{l}4 f=n \\ f=n+27\end{array}\right.
{
4
f
=
n
f
=
n
+
27
\newline
(B)
{
f
=
4
n
f
=
n
−
27
\left\{\begin{array}{l}f=4 n \\ f=n-27\end{array}\right.
{
f
=
4
n
f
=
n
−
27
\newline
(C)
{
f
=
4
n
f
=
n
+
27
\left\{\begin{array}{l}f=4 n \\ f=n+27\end{array}\right.
{
f
=
4
n
f
=
n
+
27
\newline
(D)
{
n
=
4
f
n
=
f
+
27
\left\{\begin{array}{l}n=4 f \\ n=f+27\end{array}\right.
{
n
=
4
f
n
=
f
+
27
Get tutor help
12
t
=
4
v
−
3
−
6
t
=
4
v
+
6
\begin{array}{l} 12 t=4 v-3 \\ -6 t=4 v+6 \end{array}
12
t
=
4
v
−
3
−
6
t
=
4
v
+
6
\newline
If
(
t
,
v
)
(t, v)
(
t
,
v
)
is the solution to the system of equations, what is the value of
t
−
v
t-v
t
−
v
?
Get tutor help
Distribute to create an equivalent expression with the fewest symbols possible.
\newline
6
(
a
+
2
b
+
3
c
)
=
6(a+2 b+3 c)=
6
(
a
+
2
b
+
3
c
)
=
Get tutor help
Is
(
1
,
1
)
(1,1)
(
1
,
1
)
a solution to this system of equations?
\newline
4
x
+
10
y
=
14
4x + 10y = 14
4
x
+
10
y
=
14
\newline
x
+
6
y
=
7
x + 6y = 7
x
+
6
y
=
7
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
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