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Math
Algebra
Problem 101
Solve for
f
f
f
in the equation
5
f
=
125
5^{f} = 125
5
f
=
125
.
See Solution
Problem 102
Find the value of
g
(
x
)
=
2
x
−
5
g(x)=2x-5
g
(
x
)
=
2
x
−
5
evaluated at
x
=
−
2.4
x=-2.4
x
=
−
2.4
.
See Solution
Problem 103
Find the number that, when multiplied by 3, equals 18.
See Solution
Problem 104
Solve the linear rational equation
8
x
+
7
16
x
+
30
=
0
\frac{8 x+7}{16 x+30}=0
16
x
+
30
8
x
+
7
=
0
for the value of
x
x
x
.
See Solution
Problem 105
Find the value of
H
(
−
1
)
−
4
H(-1)-4
H
(
−
1
)
−
4
given that
H
(
x
)
=
8
x
+
4
H(x)=8x+4
H
(
x
)
=
8
x
+
4
.
See Solution
Problem 106
Solve for
b
b
b
in the equation
b
−
6
−
7
=
−
10
\frac{b-6}{-7}=-10
−
7
b
−
6
=
−
10
.
See Solution
Problem 107
Find all real values of
x
x
x
such that
x
≤
22
11
x \leq \frac{22}{11}
x
≤
11
22
.
See Solution
Problem 108
Solve the linear-quadratic system algebraically:
y
=
2
x
2
+
13
x
y=2x^2+13x
y
=
2
x
2
+
13
x
and
y
+
6
x
=
−
9
y+6x=-9
y
+
6
x
=
−
9
. Express the solution in fraction form.
See Solution
Problem 109
Solve the equation
1
6
3
x
−
2
=
3
2
x
+
4
16^{3x-2} = 32^{x+4}
1
6
3
x
−
2
=
3
2
x
+
4
for the value of
x
x
x
.
See Solution
Problem 110
Find the value of
k
k
k
in the equation
60
−
92
45
−
92
=
e
−
k
(
43
)
\frac{60-92}{45-92}=e^{-k(43)}
45
−
92
60
−
92
=
e
−
k
(
43
)
.
See Solution
Problem 111
Solve the absolute value equation
2
∣
4
x
+
5
∣
=
0
2|4x+5| = 0
2∣4
x
+
5∣
=
0
and choose the correct solution.
See Solution
Problem 112
Solve the linear equation
6
a
−
11
=
13
6a - 11 = 13
6
a
−
11
=
13
for the variable
a
a
a
.
See Solution
Problem 113
Solve the system of linear equations
2
x
+
4
y
=
26
2x + 4y = 26
2
x
+
4
y
=
26
and
3
x
+
3
y
=
6
3x + 3y = 6
3
x
+
3
y
=
6
using elimination.
See Solution
Problem 114
Select the correct equation for
b
=
10
b=10
b
=
10
. A.
2
(
10
+
4
)
=
16
2(10+4)=16
2
(
10
+
4
)
=
16
B.
2
(
10
+
2
)
=
40
2(10+2)=40
2
(
10
+
2
)
=
40
C.
3
(
10
−
2
)
=
24
3(10-2)=24
3
(
10
−
2
)
=
24
D.
2
(
8
+
10
)
=
42
2(8+10)=42
2
(
8
+
10
)
=
42
E.
3
(
10
−
4
)
=
20
3(10-4)=20
3
(
10
−
4
)
=
20
See Solution
Problem 115
The math club's membership grows by
3
%
3\%
3%
weekly. Find the function
S
(
x
)
S(x)
S
(
x
)
representing the number of members after
x
x
x
weeks, starting with 10 members.
See Solution
Problem 116
Evaluate
1.
4
3
1.4^{3}
1.
4
3
and enter the decimal result.
See Solution
Problem 117
Simplify the expression
e
2
ln
x
−
5
e^{2 \ln x - 5}
e
2
l
n
x
−
5
.
See Solution
Problem 118
Divide
5
90
a
x
3
25
5
a
x
\frac{5 \sqrt{90 a x^{3}}}{25 \sqrt{5 a x}}
25
5
a
x
5
90
a
x
3
to simplify the expression.
See Solution
Problem 119
Solve for
d
d
d
and graph the solution.
d
−
1
>
11
d-1>11
d
−
1
>
11
or
d
−
11
3
<
−
3
\frac{d-11}{3}<-3
3
d
−
11
<
−
3
. Plot the endpoints, change a closed endpoint to open, delete a segment.
See Solution
Problem 120
Solve for
y
y
y
and graph the solution. Solve the system of linear inequalities:
−
13
y
+
6
<
−
15
y
−
6
-13y+6<-15y-6
−
13
y
+
6
<
−
15
y
−
6
or
2
y
+
3
≥
8
−
3
y
2y+3\geq8-3y
2
y
+
3
≥
8
−
3
y
. Plot the endpoints and modify the graph.
See Solution
Problem 121
Find the solutions to the quadratic equation
x
2
+
7
x
+
12
=
0
x^2 + 7x + 12 = 0
x
2
+
7
x
+
12
=
0
.
See Solution
Problem 122
Write the equation
y
=
−
3
x
+
9
y = -3x + 9
y
=
−
3
x
+
9
in function notation as
f
(
x
)
f(x)
f
(
x
)
.
See Solution
Problem 123
Find
f
f
f
when it varies inversely with
g
g
g
and
f
=
22
f=22
f
=
22
when
g
=
3
g=3
g
=
3
.
See Solution
Problem 124
Find the value of the expression
(
7
x
y
)
2
\left(7 x y\right)^{2}
(
7
x
y
)
2
.
See Solution
Problem 125
Solve for
c
c
c
where
c
3
+
5.48
=
7.29
\frac{c}{3} + 5.48 = 7.29
3
c
+
5.48
=
7.29
.
See Solution
Problem 126
Simplify
(
5
×
1
0
8
)
4
\left(5 \times 10^{8}\right)^{4}
(
5
×
1
0
8
)
4
and express the result in scientific notation.
See Solution
Problem 127
Find the value of
x
x
x
if the mean of 4, 8, and
x
x
x
is 7.
See Solution
Problem 128
Solve for the variable
g
g
g
in the equation
2
g
−
1
=
1
2g - 1 = 1
2
g
−
1
=
1
.
See Solution
Problem 129
Find the number line that shows the solution to the equation
6
x
−
8
=
28
6x - 8 = 28
6
x
−
8
=
28
.
See Solution
Problem 130
Find the range of
p
p
p
for which the simultaneous equations
p
2
x
+
log
2
y
=
2
p 2^{x} + \log_{2} y = 2
p
2
x
+
lo
g
2
y
=
2
and
2
x
+
log
2
y
=
1
2^{x} + \log_{2} y = 1
2
x
+
lo
g
2
y
=
1
have a real solution
(
x
,
y
)
(x, y)
(
x
,
y
)
.
See Solution
Problem 131
Solve for the value of
w
w
w
in the equation
5
(
3
+
2
w
)
=
46
5(3+2w)=46
5
(
3
+
2
w
)
=
46
.
See Solution
Problem 132
Use polynomial division to express the rational function
R
(
x
)
=
3
x
+
5
x
+
2
R(x)=\frac{3x+5}{x+2}
R
(
x
)
=
x
+
2
3
x
+
5
in the form
R
(
x
)
=
±
1
x
−
a
+
b
R(x)=\pm\frac{1}{x-a}+b
R
(
x
)
=
±
x
−
a
1
+
b
. Then sketch the graph of
R
(
x
)
R(x)
R
(
x
)
using transformations of
1
x
\frac{1}{x}
x
1
.
See Solution
Problem 133
Solve for
b
b
b
in the equation
a
=
c
b
K
b
+
c
a=\frac{c b}{K b+c}
a
=
K
b
+
c
c
b
.
See Solution
Problem 134
Solve the linear equation
4
v
−
15
=
9
v
4v - 15 = 9v
4
v
−
15
=
9
v
for the variable
v
v
v
.
See Solution
Problem 135
Find the expression equal to
4
5
×
4
−
7
÷
4
−
2
4^{5} \times 4^{-7} \div 4^{-2}
4
5
×
4
−
7
÷
4
−
2
.
See Solution
Problem 136
k
∈
(
−
∞
,
11
7
)
∪
(
11
7
,
∞
)
k \in \left(-\infty, \frac{11}{7}\right) \cup \left(\frac{11}{7}, \infty\right)
k
∈
(
−
∞
,
7
11
)
∪
(
7
11
,
∞
)
See Solution
Problem 137
Plant B produced
x
x
x
panels, where
x
x
x
is the solution to the equation:
3000
+
0.02
(
3000
)
+
0.03
(
x
)
=
790
3000 + 0.02(3000) + 0.03(x) = 790
3000
+
0.02
(
3000
)
+
0.03
(
x
)
=
790
.
See Solution
Problem 138
Polynomial function
f
(
x
)
=
2
x
3
−
3
x
2
−
23
x
+
12
f(x)=2x^3-3x^2-23x+12
f
(
x
)
=
2
x
3
−
3
x
2
−
23
x
+
12
. Determine properties of
f
(
x
)
x
+
3
\frac{f(x)}{x+3}
x
+
3
f
(
x
)
, such as remainder and factorization of the quotient.
See Solution
Problem 139
Determine if
7
x
−
2
=
7
(
x
−
7
)
7x-2=7(x-7)
7
x
−
2
=
7
(
x
−
7
)
has one, no, or infinitely many solutions. If one, solve for
x
x
x
.
See Solution
Problem 140
Find the value of
v
v
v
that solves the equation
−
6
(
11
+
v
)
=
−
30
-6(11+v)=-30
−
6
(
11
+
v
)
=
−
30
.
See Solution
Problem 141
Determine time to bike 20 laps given trend line equation
y
=
1
2
x
+
1
y=\frac{1}{2} x+1
y
=
2
1
x
+
1
.
See Solution
Problem 142
Solve the linear equation
4
m
+
5
=
35
−
2
m
4m + 5 = 35 - 2m
4
m
+
5
=
35
−
2
m
for the value of
m
m
m
.
See Solution
Problem 143
Solve the quadratic equation
2
(
x
+
3
)
2
−
6
=
12
2(x+3)^{2} - 6 = 12
2
(
x
+
3
)
2
−
6
=
12
for
x
x
x
.
See Solution
Problem 144
Find the equivalent of
14
⋅
8
\sqrt{14} \cdot \sqrt{8}
14
⋅
8
.
See Solution
Problem 145
Solve the proportion
6.77
9
=
4.63
x
\frac{6.77}{9}=\frac{4.63}{x}
9
6.77
=
x
4.63
and round the solution to four significant digits.
See Solution
Problem 146
Solve for
x
x
x
in the equation
2
x
⋅
2
x
−
2
=
2
2^{x} \cdot 2^{x-2} = \sqrt{2}
2
x
⋅
2
x
−
2
=
2
.
See Solution
Problem 147
Find the values of
y
y
y
for the given values of
x
x
x
in the linear equation
y
=
x
+
1
y=x+1
y
=
x
+
1
.
See Solution
Problem 148
Solve the linear inequality
9
y
≤
16
+
7
y
9y \leq 16 + 7y
9
y
≤
16
+
7
y
for the value of
y
y
y
.
See Solution
Problem 149
Subtract the complex numbers
−
5
i
-5i
−
5
i
and
16
i
16i
16
i
.
See Solution
Problem 150
Find the number and type of roots for the quadratic equation
y
=
2
x
2
+
5
x
+
4
y=2x^2+5x+4
y
=
2
x
2
+
5
x
+
4
using the discriminant.
See Solution
Problem 151
Solve for the value of
x
x
x
that satisfies the equation
(
x
+
4
)
2
/
7
=
9
(x+4)^{2/7} = 9
(
x
+
4
)
2/7
=
9
.
See Solution
Problem 152
Find the value of
x
x
x
when
6
−
4
x
=
2
x
+
12
6-4x = 2x+12
6
−
4
x
=
2
x
+
12
. The value of
x
x
x
is
x
=
3
x=3
x
=
3
.
See Solution
Problem 153
Find the solution to the equation
3
(
2
x
+
5
)
=
3
x
+
4
x
3(2x+5)=3x+4x
3
(
2
x
+
5
)
=
3
x
+
4
x
. The possible solutions are
x
=
0
x=0
x
=
0
,
x
=
4
x=4
x
=
4
,
x
=
5
x=5
x
=
5
, or
x
=
15
x=15
x
=
15
.
See Solution
Problem 154
Solve for y in the linear equation
7
x
+
3
y
=
8
7x + 3y = 8
7
x
+
3
y
=
8
.
See Solution
Problem 155
Find the sum of the solutions to the quadratic equation
4
(
x
2
−
5
x
)
=
16
4(x^2 - 5x) = 16
4
(
x
2
−
5
x
)
=
16
.
See Solution
Problem 156
Solve the linear equation
6
x
−
12
=
3
x
6x - 12 = 3x
6
x
−
12
=
3
x
to find the value of
x
x
x
.
See Solution
Problem 157
Evaluate
−
5
x
3
−
x
3
−
x
-5x^3 - x^3 - x
−
5
x
3
−
x
3
−
x
when
x
=
0
x=0
x
=
0
See Solution
Problem 158
Find the value of
y
y
y
when
x
x
x
is 92, given the equation
y
=
x
−
11
y=\sqrt{x-11}
y
=
x
−
11
.
See Solution
Problem 159
Hay
x
x
x
gallinas en la granja. Calcula el número total de patas en la granja, dado que hay 20 conejos más que gallinas.
T
(
x
)
=
6
x
−
80
T(x)=6x-80
T
(
x
)
=
6
x
−
80
See Solution
Problem 160
Rental company charges
$
47
\$ 47
$47
for 3 chairs and 5 tables, and
$
35
\$ 35
$35
for 12 chairs and 2 tables. Find the cost to rent each chair and table.
See Solution
Problem 161
Solve the quadratic equation
3
k
2
+
30
k
=
−
69
3 k^{2} + 30 k = -69
3
k
2
+
30
k
=
−
69
for the value of
k
k
k
.
See Solution
Problem 162
Solve for
x
x
x
where
(
x
+
7
)
5
/
3
=
32
(x+7)^{5/3} = 32
(
x
+
7
)
5/3
=
32
.
See Solution
Problem 163
Expand the expression
(
x
−
8
)
(
x
+
8
)
(x-8)(x+8)
(
x
−
8
)
(
x
+
8
)
to find the product.
See Solution
Problem 164
Solve for
x
x
x
in the equation
x
(
.
0742857
+
x
)
(
.
01857
−
x
)
=
1.23
×
1
0
−
2
\frac{x(.0742857+x)}{(.01857-x)}=1.23 \times 10^{-2}
(
.01857
−
x
)
x
(
.0742857
+
x
)
=
1.23
×
1
0
−
2
.
See Solution
Problem 165
Solve for
y
y
y
in the linear equation
5
x
+
7
y
=
−
11
5x + 7y = -11
5
x
+
7
y
=
−
11
and express
y
y
y
as a function of
x
x
x
.
See Solution
Problem 166
Solve for the variable
w
w
w
in the equation
A
=
z
w
+
x
A=zw+x
A
=
z
w
+
x
.
See Solution
Problem 167
Find the coordinates of point D given that its y-coordinate is the solution to
10
y
+
4
=
34
10y+4=34
10
y
+
4
=
34
and
x
+
y
=
5
x+y=5
x
+
y
=
5
.
See Solution
Problem 168
Solve the inequality
7
∣
w
−
3
∣
+
2
≥
30
7|w-3|+2 \geq 30
7∣
w
−
3∣
+
2
≥
30
and determine if all real numbers are solutions or if there is no solution.
See Solution
Problem 169
Solve for
H
:
64
+
2
H
=
5
H
+
10
\mathrm{H}: 64+2\mathrm{H}=5\mathrm{H}+10
H
:
64
+
2
H
=
5
H
+
10
, enter the value of
H
\mathrm{H}
H
.
See Solution
Problem 170
Dado que
y
y
y
varía inversamente con
x
x
x
, y
y
=
12
y=12
y
=
12
cuando
x
=
12
x=12
x
=
12
, calcule
y
y
y
cuando
x
=
132
x=132
x
=
132
.
See Solution
Problem 171
Convert
6
b
+
(
−
3
b
)
=
41
6b + (-3b) = 41
6
b
+
(
−
3
b
)
=
41
to find
b
b
b
. Solve for
b
=
8
b = 8
b
=
8
.
See Solution
Problem 172
Solve the linear equation
8.4
c
=
6
(
c
+
12
)
8.4c = 6(c + 12)
8.4
c
=
6
(
c
+
12
)
for the unknown variable
c
c
c
.
See Solution
Problem 173
Find the value of
k
(
0
)
k(0)
k
(
0
)
for the function
k
(
x
)
=
∣
x
+
8
∣
k(x) = |x+8|
k
(
x
)
=
∣
x
+
8∣
. Simplify.
See Solution
Problem 174
Solve the absolute value equation
3
∣
x
−
3
∣
=
18
3|x-3|=18
3∣
x
−
3∣
=
18
or indicate if no solution exists.
See Solution
Problem 175
Find the value of
m
m
m
when
m
=
4
(
2
p
2
+
5
p
−
3
)
m=4(2p^2 + 5p - 3)
m
=
4
(
2
p
2
+
5
p
−
3
)
and
p
=
−
2
p=-2
p
=
−
2
.
See Solution
Problem 176
Find the recursive rule for the sequence
4
,
−
12
,
36
,
−
108
,
…
4, -12, 36, -108, \ldots
4
,
−
12
,
36
,
−
108
,
…
.
See Solution
Problem 177
Expand as many logarithms as possible:
log
x
4
y
3
z
2
\log \frac{x^{4} y^{3}}{z^{2}}
lo
g
z
2
x
4
y
3
See Solution
Problem 178
Find the solution set for the equation
x
=
2
x
x=2x
x
=
2
x
with the given domain
x
:
{
0
,
1
,
2
,
3
}
x:\{0,1,2,3\}
x
:
{
0
,
1
,
2
,
3
}
.
See Solution
Problem 179
Solve
3
x
=
12
3x=12
3
x
=
12
. How does the solution relate to
3
x
≥
12
3x \geq 12
3
x
≥
12
? The solution is
□
\square
□
. The solutions of
3
x
≥
12
3x \geq 12
3
x
≥
12
are all values
≥
?
\geq ?
≥
?
.
See Solution
Problem 180
Find the value of
x
x
x
in the equation
1.5
(
x
+
4
)
−
3
=
4.5
(
x
−
2
)
1.5(x+4)-3=4.5(x-2)
1.5
(
x
+
4
)
−
3
=
4.5
(
x
−
2
)
.
See Solution
Problem 181
Find the values of
a
,
b
,
c
a, b, c
a
,
b
,
c
given the rule
a
−
2
b
+
3
c
=
9
a-2b+3c=9
a
−
2
b
+
3
c
=
9
and different variable assignments.
See Solution
Problem 182
Find the slope of the linear equation
y
=
4
x
−
1
5
y=4x-\frac{1}{5}
y
=
4
x
−
5
1
.
See Solution
Problem 183
Which equations have exactly one y-value for any given x-value? Select all that apply: A.
y
=
−
x
y=-x
y
=
−
x
, B.
x
=
4
x=4
x
=
4
, D.
y
=
x
3
y=x^{3}
y
=
x
3
See Solution
Problem 184
Which
25
36
\frac{\sqrt{25}}{\sqrt{36}}
36
25
is equivalent? A.
25
36
\sqrt{\frac{25}{36}}
36
25
B.
25
36
\frac{25}{36}
36
25
C.
25
3
36
3
\frac{\sqrt[3]{25}}{\sqrt[3]{36}}
3
36
3
25
D.
5
6
\frac{\sqrt{5}}{\sqrt{6}}
6
5
See Solution
Problem 185
Find the value of
v
v
v
when
b
=
4
b=4
b
=
4
in the equation
3
v
=
b
+
5
3v=b+5
3
v
=
b
+
5
.
See Solution
Problem 186
Find
A
+
B
A+B
A
+
B
given
A
=
2
x
−
7
x
2
+
3
A=2x-7x^2+3
A
=
2
x
−
7
x
2
+
3
and
B
=
4
x
2
−
12
x
B=4x^2-12x
B
=
4
x
2
−
12
x
. Options:
−
3
x
2
+
10
x
+
3
-3x^2+10x+3
−
3
x
2
+
10
x
+
3
,
−
3
x
2
−
10
x
+
3
-3x^2-10x+3
−
3
x
2
−
10
x
+
3
,
3
x
2
−
10
x
+
3
3x^2-10x+3
3
x
2
−
10
x
+
3
,
6
x
2
−
7
x
−
9
6x^2-7x-9
6
x
2
−
7
x
−
9
.
See Solution
Problem 187
Find the value of
c
c
c
in the parabolic equation
y
=
4
x
2
+
x
+
c
y=4x^2+x+c
y
=
4
x
2
+
x
+
c
given that one
x
x
x
-intercept is -3.
See Solution
Problem 188
Find the value of
−
14
−
8
×
0.5
+
0.75
-14-8 \times 0.5+0.75
−
14
−
8
×
0.5
+
0.75
: is it
−
9.25
-9.25
−
9.25
,
−
10.25
-10.25
−
10.25
, or
−
17.25
-17.25
−
17.25
?
See Solution
Problem 189
Solve for
c
c
c
given the equation
2
3
c
=
d
\frac{2}{3}c=d
3
2
c
=
d
.
See Solution
Problem 190
Find the value of
x
x
x
that makes the statement
x
−
4
2
x
=
1
3
\frac{x-4}{2x} = \frac{1}{3}
2
x
x
−
4
=
3
1
true.
See Solution
Problem 191
Solve the system of linear equations:
−
2
x
+
y
=
−
2
-2x + y = -2
−
2
x
+
y
=
−
2
and
2
x
−
y
+
2
=
0
2x - y + 2 = 0
2
x
−
y
+
2
=
0
.
See Solution
Problem 192
Determine the sign of the product
(
−
86
)
(
25
)
(-86)(25)
(
−
86
)
(
25
)
.
See Solution
Problem 193
Solve the quadratic equation
−
7
−
5
x
2
=
−
102
-7-5x^2 = -102
−
7
−
5
x
2
=
−
102
for the value of
x
x
x
.
See Solution
Problem 194
Find the value of
c
c
c
that satisfies the equation
7
=
c
+
12
3
7 = \frac{c+12}{3}
7
=
3
c
+
12
, which has solutions
c
=
−
9
c = -9
c
=
−
9
and
c
=
9
c = 9
c
=
9
.
See Solution
Problem 195
Solve the linear equation
2
y
+
7
=
14
2y + 7 = 14
2
y
+
7
=
14
for the unknown variable
y
y
y
.
See Solution
Problem 196
Solve the equation
e
x
=
e
8
x
+
14
e^{x}=e^{8 x+14}
e
x
=
e
8
x
+
14
. The solution set is a simplified fraction or integer.
See Solution
Problem 197
Solve the equation
3
2
x
=
1
4
32^{x}=\frac{1}{4}
3
2
x
=
4
1
using the like bases property to find the value of
x
x
x
.
See Solution
Problem 198
What is the value of
b
b
b
in the equation
4
(
b
−
6
)
=
48
4(b-6)=48
4
(
b
−
6
)
=
48
?
See Solution
Problem 199
Find the values of x that satisfy the inequality
4
>
x
+
6
4 > x + 6
4
>
x
+
6
.
See Solution
Problem 200
Solve for the value of
p
p
p
in the equation
3
p
=
5
−
2
p
3p = 5 - 2p
3
p
=
5
−
2
p
.
See Solution
1
2
3
4
5
6
7
8
9
10
11
12
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14
15
16
17
18
19
20
21
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23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
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48
49
50
51
52
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59
60
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