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Precalculus
Solve exponential equations by rewriting the base
Given equation:
5
45
=
t
\frac{5}{45} = t
45
5
=
t
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Find the value of each variable.
\newline
127
+
z
=
300
127+z=300
127
+
z
=
300
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Suppose that you are headed toward a plateau
21
21
21
meters high. If the angle of elevation to the top of the plateau is
2
5
∘
25^{\circ}
2
5
∘
, how far are you from the base of the plateau?
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0.25
=
0.9
5
x
0.25=0.95^x
0.25
=
0.9
5
x
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2
=
1.0
8
n
2 = 1.08^n
2
=
1.0
8
n
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In
△
D
E
F
,
f
=
83
c
m
,
e
=
60
c
m
\triangle \mathrm{DEF}, f=83 \mathrm{~cm}, e=60 \mathrm{~cm}
△
DEF
,
f
=
83
cm
,
e
=
60
cm
and
∠
E
=
2
9
∘
\angle \mathrm{E}=29^{\circ}
∠
E
=
2
9
∘
. Find all possible values of
∠
F
\angle \mathrm{F}
∠
F
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
△
K
L
M
,
k
=
550
c
m
,
m
=
540
c
m
\triangle \mathrm{KLM}, k=550 \mathrm{~cm}, m=540 \mathrm{~cm}
△
KLM
,
k
=
550
cm
,
m
=
540
cm
and
∠
M
=
7
4
∘
\angle \mathrm{M}=74^{\circ}
∠
M
=
7
4
∘
. Find all possible values of
∠
K
\angle \mathrm{K}
∠
K
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
x
2
−
16
x
+
51
=
4
x
−
2
x^{2}-16 x+51=4 x-2
x
2
−
16
x
+
51
=
4
x
−
2
\newline
Answer:
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What is the discriminant of the quadratic equation
4
x
2
−
7
x
+
1
=
0
4 x^{2}-7 x+1=0
4
x
2
−
7
x
+
1
=
0
?
\newline
33
33
33
\newline
−
65
-65
−
65
\newline
−
33
-33
−
33
\newline
65
65
65
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For the following quadratic equation, find the discriminant.
\newline
−
4
x
2
+
18
x
+
112
=
2
x
-4 x^{2}+18 x+112=2 x
−
4
x
2
+
18
x
+
112
=
2
x
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
3
x
2
+
18
x
−
81
=
4
x
2
3 x^{2}+18 x-81=4 x^{2}
3
x
2
+
18
x
−
81
=
4
x
2
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
3
x
2
−
18
x
−
72
=
−
2
x
2
-3 x^{2}-18 x-72=-2 x^{2}
−
3
x
2
−
18
x
−
72
=
−
2
x
2
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
6
6
6
.
\newline
y
=
x
2
+
12
y=x^{2}+12
y
=
x
2
+
12
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
9
9
9
.
\newline
y
=
x
2
+
12
y=x^{2}+12
y
=
x
2
+
12
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
3
3
3
.
\newline
y
=
x
2
+
12
y=x^{2}+12
y
=
x
2
+
12
\newline
Answer:
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Factor.
\newline
x
2
−
11
x
+
28
x^{2}-11 x+28
x
2
−
11
x
+
28
\newline
Answer:
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Factor the expression completely.
\newline
6
x
−
9
6 x-9
6
x
−
9
\newline
Answer:
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Factor the expression completely.
\newline
−
16
x
4
+
40
-16 x^{4}+40
−
16
x
4
+
40
\newline
Answer:
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Factor the expression completely.
\newline
28
x
3
+
49
x
28 x^{3}+49 x
28
x
3
+
49
x
\newline
Answer:
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