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Math Problems
Algebra 2
Find trigonometric functions using a calculator
Solve for
h
h
h
. Give an exact answer.
\newline
3
h
=
7
(
2
7
−
3
7
h
)
−
10
3h=7\left(\frac{2}{7}-\frac{3}{7}h\right)-10
3
h
=
7
(
7
2
−
7
3
h
)
−
10
\newline
h
=
h=
h
=
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Which sign makes the statement true?
\newline
−
1
100
?
−
0.01
-\frac{1}{100} ? -0.01
−
100
1
?
−
0.01
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
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In
0.7
0.7
0.7
, in which place is the
7
7
7
?
\newline
Choices:
\newline
(A) ones
\newline
(B) tenths
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Simplify
\newline
(
−
6
x
−
6
)
(
6
x
−
3
)
(-6x-6)(6x-3)
(
−
6
x
−
6
)
(
6
x
−
3
)
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u
⃗
=
(
−
9
,
3
)
\vec{u} = (-9,3)
u
=
(
−
9
,
3
)
\newline
Find the direction angle of
u
⃗
\vec{u}
u
.
\newline
Enter your answer as an angle in degrees between
0
∘
0^{\circ}
0
∘
and
36
0
∘
360^{\circ}
36
0
∘
rounded to the nearest hundredth.
\newline
θ
=
\theta=
θ
=
□
∘
\square^{\circ}
□
∘
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The length of the day in Lagos, Nigeria (in minutes),
t
t
t
days since the beginning of the year can be estimated by this formula:
\newline
L
(
t
)
=
727
+
22
sin
(
2
π
(
t
−
80.75
)
365
)
.
L(t)=727+22 \sin \left(\frac{2 \pi(t-80.75)}{365}\right) .
L
(
t
)
=
727
+
22
sin
(
365
2
π
(
t
−
80.75
)
)
.
\newline
When is the longest day of the year? Give an exact answer.
\newline
□
\square
□
days since the beginning of the year
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Find the rate of interest.
\newline
115.00
=
100
(
1
+
r
4
)
4
⋅
1
115.00=100\left(1+\frac{r}{4}\right)^{4 \cdot 1}
115.00
=
100
(
1
+
4
r
)
4
⋅
1
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Calculate.
\newline
Δ
P
=
6.2
×
(
45000
0
1
3
120
)
1.1
\Delta P = 6.2 \times \left(\frac{450000^{\frac{1}{3}}}{120}\right)^{1.1}
Δ
P
=
6.2
×
(
120
45000
0
3
1
)
1.1
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Simplify.
\newline
5
×
1
0
2
3
×
1
0
8
\frac{5 \times 10^{2}}{3 \times 10^{8}}
3
×
1
0
8
5
×
1
0
2
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Solve for
x
x
x
to the nearest
10
10
10
th.
\newline
3000
=
6680
(
0.985
)
x
−
1200
3000=6680(0.985)^{x}-1200
3000
=
6680
(
0.985
)
x
−
1200
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A list of numbers ordered from least value to greatest value is shown. One number is missing.
\newline
18
5
,
3.71
,
_
_
_
_
_
,
17
\frac{18}{5}, 3.71, \_\_\_\_\_, \sqrt{17}
5
18
,
3.71
,
_____
,
17
\newline
Which number could be the missing number?
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The angle of elevation to a nearby tree from a point on the ground is measured to be
6
4
∘
64^{\circ}
6
4
∘
. How tall is the tree if the point on the ground is
49
49
49
feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.
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The following are all angle measures (in radians, rounded to the nearest hundredth) whose cosine is
−
0.26
\mathbf{- 0 . 2 6}
−
0.26
.
\newline
Which is the principal value of
cos
−
1
(
−
0.26
)
\cos ^{-1}(-0.26)
cos
−
1
(
−
0.26
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
17
-17
−
17
.
02
02
02
\newline
(B)
−
10
-10
−
10
.
73
73
73
\newline
(C)
−
4
-4
−
4
.
45
45
45
\newline
(D)
1
1
1
.
83
83
83
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Find
z
α
/
2
z_{\alpha / 2}
z
α
/2
for
α
=
0.13
\alpha=0.13
α
=
0.13
.
\newline
z
α
/
2
=
□
\mathrm{z}_{\alpha / 2}=\square
z
α
/2
=
□
(Round to two decimal places as needed.)
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1.6
(
y
2
+
5
)
=
13.4
y
1.6\left(y^{2}+5\right)=13.4 y
1.6
(
y
2
+
5
)
=
13.4
y
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(
x
+
55
)
2
+
(
y
−
11.5
)
2
=
121
(x+55)^2+(y-11.5)^2=121
(
x
+
55
)
2
+
(
y
−
11.5
)
2
=
121
what is the diameter
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In
△
F
G
H
,
g
=
170
c
m
,
f
=
960
c
m
\triangle \mathrm{FGH}, g=170 \mathrm{~cm}, f=960 \mathrm{~cm}
△
FGH
,
g
=
170
cm
,
f
=
960
cm
and
∠
F
=
1
9
∘
\angle \mathrm{F}=19^{\circ}
∠
F
=
1
9
∘
. Find all possible values of
∠
G
\angle \mathrm{G}
∠
G
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
△
F
G
H
,
g
=
190
c
m
,
f
=
900
c
m
\triangle \mathrm{FGH}, g=190 \mathrm{~cm}, f=900 \mathrm{~cm}
△
FGH
,
g
=
190
cm
,
f
=
900
cm
and
∠
F
=
2
7
∘
\angle \mathrm{F}=27^{\circ}
∠
F
=
2
7
∘
. Find all possible values of
∠
G
\angle \mathrm{G}
∠
G
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
△
H
I
J
,
j
=
8.6
c
m
,
i
=
4.6
c
m
\triangle \mathrm{HIJ}, j=8.6 \mathrm{~cm}, i=4.6 \mathrm{~cm}
△
HIJ
,
j
=
8.6
cm
,
i
=
4.6
cm
and
∠
I
=
15
8
∘
\angle \mathrm{I}=158^{\circ}
∠
I
=
15
8
∘
. Find all possible values of
∠
J
\angle \mathrm{J}
∠
J
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
△
N
O
P
,
p
=
760
\triangle \mathrm{NOP}, p=760
△
NOP
,
p
=
760
inches,
o
=
710
o=710
o
=
710
inches and
∠
O
=
12
4
∘
\angle \mathrm{O}=124^{\circ}
∠
O
=
12
4
∘
. Find all possible values of
∠
P
\angle \mathrm{P}
∠
P
, to the nearest degree.
\newline
Answer:
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In
△
O
P
Q
,
p
=
39
\triangle \mathrm{OPQ}, p=39
△
OPQ
,
p
=
39
inches,
o
=
66
o=66
o
=
66
inches and
∠
O
=
8
1
∘
\angle \mathrm{O}=81^{\circ}
∠
O
=
8
1
∘
. Find all possible values of
∠
P
\angle \mathrm{P}
∠
P
, to the nearest degree.
\newline
Answer:
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In
△
D
E
F
,
e
=
840
\triangle \mathrm{DEF}, e=840
△
DEF
,
e
=
840
inches,
d
=
760
d=760
d
=
760
inches and
∠
D
=
13
4
∘
\angle \mathrm{D}=134^{\circ}
∠
D
=
13
4
∘
. Find all possible values of
∠
E
\angle \mathrm{E}
∠
E
, to the nearest degree.
\newline
Answer:
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In
△
T
U
V
,
u
=
8.4
c
m
,
t
=
8
c
m
\triangle \mathrm{TUV}, u=8.4 \mathrm{~cm}, t=8 \mathrm{~cm}
△
TUV
,
u
=
8.4
cm
,
t
=
8
cm
and
∠
T
=
7
2
∘
\angle \mathrm{T}=72^{\circ}
∠
T
=
7
2
∘
. Find all possible values of
∠
U
\angle \mathrm{U}
∠
U
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
Δ
M
N
O
,
o
=
870
\Delta \mathrm{MNO}, o=870
Δ
MNO
,
o
=
870
inches,
n
=
550
n=550
n
=
550
inches and
∠
N
=
1
8
∘
\angle \mathrm{N}=18^{\circ}
∠
N
=
1
8
∘
. Find all possible values of
∠
O
\angle \mathrm{O}
∠
O
, to the nearest degree.
\newline
Answer:
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In
△
M
N
O
,
n
=
57
\triangle \mathrm{MNO}, n=57
△
MNO
,
n
=
57
inches,
m
=
69
m=69
m
=
69
inches and
∠
M
=
5
8
∘
\angle \mathrm{M}=58^{\circ}
∠
M
=
5
8
∘
. Find all possible values of
∠
N
\angle \mathrm{N}
∠
N
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
△
N
O
P
,
n
=
300
c
m
,
p
=
100
c
m
\triangle \mathrm{NOP}, n=300 \mathrm{~cm}, p=100 \mathrm{~cm}
△
NOP
,
n
=
300
cm
,
p
=
100
cm
and
∠
P
=
4
5
∘
\angle \mathrm{P}=45^{\circ}
∠
P
=
4
5
∘
. Find all possible values of
∠
N
\angle \mathrm{N}
∠
N
, to the nearest degree.
\newline
Answer:
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In
Δ
S
T
U
,
t
=
77
\Delta \mathrm{STU}, t=77
Δ
STU
,
t
=
77
inches,
s
=
22
s=22
s
=
22
inches and
∠
S
=
16
1
∘
\angle \mathrm{S}=161^{\circ}
∠
S
=
16
1
∘
. Find all possible values of
∠
T
\angle \mathrm{T}
∠
T
, to the nearest degree.
\newline
Answer:
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In
△
V
W
X
,
w
=
510
\triangle \mathrm{VWX}, w=510
△
VWX
,
w
=
510
inches,
v
=
890
v=890
v
=
890
inches and
∠
V
=
13
7
∘
\angle \mathrm{V}=137^{\circ}
∠
V
=
13
7
∘
. Find all possible values of
∠
W
\angle \mathrm{W}
∠
W
, to the nearest degree.
\newline
Answer:
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In
△
W
X
Y
,
x
=
450
\triangle \mathrm{WXY}, x=450
△
WXY
,
x
=
450
inches,
w
=
220
w=220
w
=
220
inches and
∠
W
=
15
7
∘
\angle \mathrm{W}=157^{\circ}
∠
W
=
15
7
∘
. Find all possible values of
∠
X
\angle \mathrm{X}
∠
X
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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Carter measures a line to be
3.19
c
m
3.19 \mathrm{~cm}
3.19
cm
long. If the actual measurement is
3
c
m
3 \mathrm{~cm}
3
cm
, find Carter's relative error to the nearest hundredth.
\newline
Answer:
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Carter measures a line to be
8.75
c
m
8.75 \mathrm{~cm}
8.75
cm
long. If the actual measurement is
9
c
m
9 \mathrm{~cm}
9
cm
, find Carter's relative error to the nearest hundredth.
\newline
Answer:
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294
294
294
.
6
6
6
is what percent of
256
256
256
? Round to the nearest hundredth.
\newline
Answer:
□
\square
□
%
\%
%
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49
49
49
.
8
8
8
is what percent of
128
128
128
? Round to the nearest thousandth.
\newline
Answer:
□
\square
□
%
\%
%
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102
102
102
.
7
7
7
is what percent of
64
64
64
? Round to the nearest hundredth.
\newline
Answer:
□
\square
□
%
\%
%
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Which of the following is a natural number?
\newline
Choices:
\newline
(A)
7
7
7
\newline
(B)
3
7
\frac{3}{7}
7
3
\newline
(C)
7.555
…
7.555\ldots
7.555
…
\newline
(D)
π
\pi
π
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Which of the following is an integer?
\newline
Choices:
\newline
(A)
−
6
-6
−
6
\newline
(B)
10
\sqrt{10}
10
\newline
(C)
8.666
…
8.666\ldots
8.666
…
\newline
(D)
π
\pi
π
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Which decimal is equivalent to
25
6
\frac{25}{6}
6
25
?
\newline
Choose
1
1
1
answer:
\newline
(A)
4.
1
‾
4.\overline{1}
4.
1
\newline
(B)
4.
16
‾
4.\overline{16}
4.
16
\newline
(C)
4.1
6
‾
4.1\overline{6}
4.1
6
\newline
(D)
4.
667
‾
4.\overline{667}
4.
667
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Mia paints interior walls at a rate of
12
m
2
h
12 \frac{\mathrm{m}^{2}}{\mathrm{~h}}
12
h
m
2
.
\newline
At what rate does Mia paint in
c
m
2
min
\frac{\mathrm{cm}^{2}}{\min }
m
i
n
cm
2
?
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Find
b
b
b
.
3
2
+
b
=
7
4
\dfrac{3}{2} + b = \dfrac{7}{4}
2
3
+
b
=
4
7
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Solve the right triangle shown in the figure.
\newline
A
=
55.
8
∘
A=55.8^\circ
A
=
55.
8
∘
,
c
=
51
c=51
c
=
51
\newline
a
≈
a\approx
a
≈
◻ (Round to the nearest hundredth as needed.)
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
23
⋅
2
x
=
16
23 \cdot 2^{x}=16
23
⋅
2
x
=
16
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
48
⋅
3
4
x
=
8
48 \cdot 3^{4 x}=8
48
⋅
3
4
x
=
8
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
2
x
5
=
12
2^{\frac{x}{5}}=12
2
5
x
=
12
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
88
e
x
=
48
88 e^{x}=48
88
e
x
=
48
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
3
x
4
=
35
3^{\frac{x}{4}}=35
3
4
x
=
35
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
7
⋅
3
x
4
=
1
7 \cdot 3^{\frac{x}{4}}=1
7
⋅
3
4
x
=
1
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
1
0
2
x
=
10
10^{2 x}=10
1
0
2
x
=
10
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
4
⋅
2
x
5
=
1
4 \cdot 2^{\frac{x}{5}}=1
4
⋅
2
5
x
=
1
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
2
⋅
3
2
x
=
1
2 \cdot 3^{2 x}=1
2
⋅
3
2
x
=
1
\newline
Answer:
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Solve for
x
x
x
, rounding to the nearest hundredth.
\newline
29
⋅
1
0
x
5
=
203
29 \cdot 10^{\frac{x}{5}}=203
29
⋅
1
0
5
x
=
203
\newline
Answer:
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2
3
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