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Math Problems
Algebra 2
Is (x, y) a solution to the system of equations?
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.
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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
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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
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−
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
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−
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
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
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
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
=
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
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
=
−
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
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
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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
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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
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
−
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
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
−
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
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