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Math Problems
Algebra 1
Solve rational equations
Consider the equation:
\newline
z
4
=
16
z^{4}=16
z
4
=
16
\newline
One solution is
z
=
2
z=2
z
=
2
, another is
−
2
-2
−
2
, and there are
2
2
2
more distinct complex solutions.
\newline
What are those solutions?
\newline
Choose
2
\mathbf{2}
2
answers:
\newline
A
z
=
4
i
z=4 i
z
=
4
i
\newline
B
z
=
2
i
z=2 i
z
=
2
i
\newline
c.
z
=
−
4
i
z=-4 i
z
=
−
4
i
\newline
D
z
=
−
2
i
z=-2 i
z
=
−
2
i
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Consider the equation:
\newline
z
4
=
81
z^{4}=81
z
4
=
81
\newline
One solution is
z
=
3
z=3
z
=
3
, another is
−
3
-3
−
3
, and there are
2
2
2
more distinct complex solutions.
\newline
What are those solutions?
\newline
Choose
2
2
2
answers:
\newline
A)
z
=
3
i
z=3 i
z
=
3
i
\newline
B)
z
=
27
i
z=27 i
z
=
27
i
\newline
C)
z
=
−
3
i
z=-3 i
z
=
−
3
i
\newline
D)
z
=
−
27
i
z=-27 i
z
=
−
27
i
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A
=
T
T
+
E
+
M
+
I
A=\frac{T}{T+E+M+I}
A
=
T
+
E
+
M
+
I
T
\newline
A musical software company uses the formula to rate the accuracy rate
A
A
A
of their software in transcribing the pitches in a music recording, where the recorded music has
T
T
T
total notes, and the transcription includes
E
E
E
extra notes,
M
M
M
missed notes, and
I
I
I
incorrect notes. Which of the following equations best shows the number of incorrect notes in terms of the number of total notes, extra notes, and missed notes?
\newline
Choose
1
1
1
answer:
\newline
(A)
I
=
−
E
−
M
I=-E-M
I
=
−
E
−
M
\newline
(B)
I
=
1
A
−
1
−
E
−
M
I=\frac{1}{A}-1-E-M
I
=
A
1
−
1
−
E
−
M
\newline
(C)
I
=
T
A
−
T
+
E
+
M
I=\frac{T}{A}-T+E+M
I
=
A
T
−
T
+
E
+
M
\newline
(D)
I
=
T
A
−
T
−
E
−
M
I=\frac{T}{A}-T-E-M
I
=
A
T
−
T
−
E
−
M
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4
p
−
2
t
=
6
4 p-2 t=6
4
p
−
2
t
=
6
\newline
8
p
+
6
t
=
12
+
2
t
8 p+6 t=12+2 t
8
p
+
6
t
=
12
+
2
t
\newline
Which of the following accurately describes all solutions to the system of equations shown?
\newline
Choose
1
1
1
answer:
\newline
(A)
p
=
3
2
p=\frac{3}{2}
p
=
2
3
and
t
=
0
t=0
t
=
0
\newline
(B)
p
=
3
p=3
p
=
3
and
t
=
3
t=3
t
=
3
\newline
(C) There are infinite solutions to the system.
\newline
(D) There are no solutions to the system.
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4
y
−
3
x
=
40
4 y-3 x=40
4
y
−
3
x
=
40
\newline
4
y
=
3
x
−
30
4 y=3 x-30
4
y
=
3
x
−
30
\newline
Which of the following accurately describes all solutions to the system of equations shown?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
=
0
x=0
x
=
0
and
y
=
0
y=0
y
=
0
\newline
(B)
x
=
5
3
x=\frac{5}{3}
x
=
3
5
and
y
=
45
4
y=\frac{45}{4}
y
=
4
45
\newline
(C) There are infinite solutions to the system.
\newline
D There are no solutions to the system.
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4
x
−
6
−
2
y
=
4
y
+
8
x
+
2
4 x-6-2 y=4 y+8 x+2
4
x
−
6
−
2
y
=
4
y
+
8
x
+
2
\newline
2
x
+
3
=
11
2 x+3=11
2
x
+
3
=
11
\newline
Consider the given system of equations. If
(
x
,
y
)
(x, y)
(
x
,
y
)
is the solution to the system, then what is the value of
x
+
y
x+y
x
+
y
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
8
-8
−
8
\newline
(B)
0
0
0
\newline
(C)
8
8
8
\newline
D There are no solutions to this system of equations.
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3
z
−
4
y
=
2
z
−
4.5
3 z-4 y=2 z-4.5
3
z
−
4
y
=
2
z
−
4.5
\newline
8
y
=
2
z
+
5
8 y=2 z+5
8
y
=
2
z
+
5
\newline
Consider the system of equations. If
(
y
,
z
)
(y, z)
(
y
,
z
)
is the solution to the system, then what is the value of
y
−
z
y-z
y
−
z
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
8
-\frac{1}{8}
−
8
1
\newline
(B)
1
8
\frac{1}{8}
8
1
\newline
(C)
1
1
1
\newline
(D) There are no solutions to this system of equations.
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7.99
C
+
9.50
M
=
S
7.99 C+9.50 M=S
7.99
C
+
9.50
M
=
S
\newline
The given equation represents the total Anais spends,
S
S
S
, in dollars, if she purchases
C
C
C
pounds of candy and
M
M
M
movie tickets. According to the equation, how much does each movie ticket cost?
\newline
Choose
1
1
1
answer:
\newline
(A)
$
5.26
\$ 5.26
$5.26
\newline
(B)
$
6.26
\$ 6.26
$6.26
\newline
(C)
$
7.99
\$ 7.99
$7.99
\newline
(D)
$
9.50
\$ 9.50
$9.50
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Each student in Mr. Ricardo's class has one camera that holds
320
320
320
pictures. He asks each student to delete
1
4
\frac{1}{4}
4
1
of the pictures and turn in the rest. Which of the following functions best represents the number of pictures,
p
p
p
, that
M
r
\mathrm{Mr}
Mr
. Ricardo will collect depending on the number of cameras,
c
c
c
, that his students have?
\newline
Choose
1
1
1
answer:
\newline
(A)
p
=
80
c
p=80 c
p
=
80
c
\newline
(B)
p
=
160
c
p=160 c
p
=
160
c
\newline
(C)
p
=
240
c
p=240 c
p
=
240
c
\newline
(D)
p
=
320
c
p=320 c
p
=
320
c
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0.5
(
8
w
+
2
v
)
=
3
0.5(8 w+2 v)=3
0.5
(
8
w
+
2
v
)
=
3
\newline
8
w
=
2
−
v
+
4
w
8 w=2-v+4 w
8
w
=
2
−
v
+
4
w
\newline
Which of the following accurately describes all solutions to the system of equations shown?
\newline
Choose
1
1
1
answer:
\newline
(A)
v
=
1
v=1
v
=
1
and
w
=
1
4
w=\frac{1}{4}
w
=
4
1
\newline
(B)
v
=
4
v=4
v
=
4
and
w
=
−
1
4
w=-\frac{1}{4}
w
=
−
4
1
\newline
(C) There are infinite solutions to the system.
\newline
(D) There are no solutions to the system.
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