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Math
Math Statement
Problem 14801
Solve the equation:
3
(
−
4
x
−
3
)
+
5
x
−
5
=
0
3(-4x - 3) + 5x - 5 = 0
3
(
−
4
x
−
3
)
+
5
x
−
5
=
0
.
See Solution
Problem 14802
Calculate the product:
5
7
⋅
14
15
⋅
30
20
\frac{5}{7} \cdot \frac{14}{15} \cdot \frac{30}{20}
7
5
⋅
15
14
⋅
20
30
.
See Solution
Problem 14803
Calculate the product of
s
(
x
)
=
x
−
3
x
2
−
36
s(x)=\frac{x-3}{x^{2}-36}
s
(
x
)
=
x
2
−
36
x
−
3
and
t
(
x
)
=
x
−
6
3
−
x
t(x)=\frac{x-6}{3-x}
t
(
x
)
=
3
−
x
x
−
6
, and state its domain in interval notation.
See Solution
Problem 14804
Solve the equation:
3
(
2
x
+
2
)
+
x
+
5
=
−
10
3(2x + 2) + x + 5 = -10
3
(
2
x
+
2
)
+
x
+
5
=
−
10
.
See Solution
Problem 14805
Calculate:
1
2
×
9
=
\frac{1}{2} \times 9=
2
1
×
9
=
See Solution
Problem 14806
Solve the equation:
5
4
x
+
5
(
−
x
+
1
)
−
7
=
−
(
5
2
x
−
5
2
)
\frac{5}{4} x + 5(-x + 1) - 7 = -\left(\frac{5}{2} x - \frac{5}{2}\right)
4
5
x
+
5
(
−
x
+
1
)
−
7
=
−
(
2
5
x
−
2
5
)
See Solution
Problem 14807
Find
(
f
∘
g
)
(
x
)
(f \circ g)(x)
(
f
∘
g
)
(
x
)
and its domain. Given
f
(
x
)
=
x
x
−
1
f(x)=\frac{x}{x-1}
f
(
x
)
=
x
−
1
x
and
g
(
x
)
=
13
x
2
−
36
g(x)=\frac{13}{x^{2}-36}
g
(
x
)
=
x
2
−
36
13
.
See Solution
Problem 14808
Calculate
11
×
1
12
11 \times \frac{1}{12}
11
×
12
1
.
See Solution
Problem 14809
Solve these two problems: 1.
9.002
−
3
=
?
9.002 - 3 = ?
9.002
−
3
=
?
2.
400.06
−
0.03
=
?
400.06 - 0.03 = ?
400.06
−
0.03
=
?
See Solution
Problem 14810
9.002 - 3 = 1.001
See Solution
Problem 14811
Calculate:
1
5
×
5
=
\frac{1}{5} \times 5=
5
1
×
5
=
See Solution
Problem 14812
Calculate
10
×
2
3
10 \times \frac{2}{3}
10
×
3
2
.
See Solution
Problem 14813
Find
(
f
∘
g
)
(
x
)
(f \circ g)(x)
(
f
∘
g
)
(
x
)
and its domain in interval notation, where
f
(
x
)
=
x
x
−
1
f(x)=\frac{x}{x-1}
f
(
x
)
=
x
−
1
x
and
g
(
x
)
=
13
x
2
−
36
g(x)=\frac{13}{x^{2}-36}
g
(
x
)
=
x
2
−
36
13
.
See Solution
Problem 14814
Calculate:
5
×
5
6
=
5 \times \frac{5}{6}=
5
×
6
5
=
See Solution
Problem 14815
Calculate
(
13.2
+
0.9
)
÷
0.6
(13.2 + 0.9) \div 0.6
(
13.2
+
0.9
)
÷
0.6
.
See Solution
Problem 14816
Calculate
41.84
−
0.9
41.84 - 0.9
41.84
−
0.9
.
See Solution
Problem 14817
Solve using the standard algorithm:
1.8
−
0.9
=
1.8 - 0.9 =
1.8
−
0.9
=
See Solution
Problem 14818
Calculate
5.182
−
0.09
5.182 - 0.09
5.182
−
0.09
.
See Solution
Problem 14819
Calculate
341.84
−
21.92
341.84 - 21.92
341.84
−
21.92
.
See Solution
Problem 14820
Solve the system:
2
x
+
3
y
=
1240
2x + 3y = 1240
2
x
+
3
y
=
1240
and
x
=
2
y
−
10
x = 2y - 10
x
=
2
y
−
10
. Find food and ride tickets sold.
See Solution
Problem 14821
Find the equation of the line that passes through the point
(
0
,
5
)
(0,5)
(
0
,
5
)
with a slope of
m
=
−
3
m=-3
m
=
−
3
.
See Solution
Problem 14822
Divide 239 by 119 and find the approximate result.
See Solution
Problem 14823
Find the complex zeros of
f
(
x
)
=
x
2
−
10
x
+
29
f(x)=x^{2}-10x+29
f
(
x
)
=
x
2
−
10
x
+
29
and graph the function.
See Solution
Problem 14824
Find the complex zeros of
f
(
x
)
=
5
x
2
+
2
x
+
1
f(x)=5x^{2}+2x+1
f
(
x
)
=
5
x
2
+
2
x
+
1
and graph the function.
x
=
\mathrm{x}=
x
=
(simplify to a
+
b
+b
+
b
form).
See Solution
Problem 14825
Solve the equation:
6
=
1
−
2
x
+
5
6=1-2 x+5
6
=
1
−
2
x
+
5
.
See Solution
Problem 14826
Solve the equation:
1.5
x
−
1.2
−
x
=
0.5
1.5x - 1.2 - x = 0.5
1.5
x
−
1.2
−
x
=
0.5
.
See Solution
Problem 14827
Solve the inequality:
x
+
11
−
2
<
−
2
\frac{x+11}{-2} < -2
−
2
x
+
11
<
−
2
See Solution
Problem 14828
Find the value of the function
f
(
x
)
=
−
3
x
2
+
10
x
+
2
f(x)=-3 x^{2}+10 x+2
f
(
x
)
=
−
3
x
2
+
10
x
+
2
at
x
=
−
6
x=-6
x
=
−
6
. What is
f
(
−
6
)
f(-6)
f
(
−
6
)
?
See Solution
Problem 14829
Solve the inequality:
2
(
x
−
1
)
+
3
>
9
2(x-1)+3>9
2
(
x
−
1
)
+
3
>
9
See Solution
Problem 14830
Solve the equation
x
2
−
4
x
+
13
=
0
x^{2}-4 x+13=0
x
2
−
4
x
+
13
=
0
using the quadratic formula. Provide the exact solution with radicals and
i
i
i
.
See Solution
Problem 14831
Solve the equation
x
2
−
8
x
+
32
=
0
x^{2}-8x+32=0
x
2
−
8
x
+
32
=
0
using the quadratic formula. Provide exact answers with radicals and
i
i
i
if needed.
See Solution
Problem 14832
Find the absolute values:
∣
−
9
∣
|-9|
∣
−
9∣
and
∣
6
∣
|6|
∣6∣
.
See Solution
Problem 14833
Determine the marginal cost from the cost function
C
(
x
,
y
)
=
240
,
000
+
6
,
000
x
+
4
,
000
y
C(x, y) = 240,000 + 6,000x + 4,000y
C
(
x
,
y
)
=
240
,
000
+
6
,
000
x
+
4
,
000
y
.
See Solution
Problem 14834
Find the real zeros and
x
x
x
-intercepts of the function
f
(
x
)
=
x
4
−
41
x
2
+
400
f(x)=x^{4}-41 x^{2}+400
f
(
x
)
=
x
4
−
41
x
2
+
400
.
See Solution
Problem 14835
Solve for
q
q
q
in the equation
12
q
u
=
4
12 q u=4
12
q
u
=
4
.
See Solution
Problem 14836
Solve for
a
a
a
in the equation
2
a
b
=
8
c
2 a b = 8 c
2
ab
=
8
c
.
See Solution
Problem 14837
Find the absolute value of -11. What is
∣
−
11
∣
|-11|
∣
−
11∣
?
See Solution
Problem 14838
Simplify
x
4
⋅
x
3
x^{4} \cdot x^{3}
x
4
⋅
x
3
.
See Solution
Problem 14839
Divide 545 by 5.
See Solution
Problem 14840
Find the zeros of the function
f
(
x
)
=
4
x
2
+
2
x
−
1
f(x)=4x^{2}+2x-1
f
(
x
)
=
4
x
2
+
2
x
−
1
using the quadratic formula. Are they the same as the
x
x
x
-intercepts?
See Solution
Problem 14841
Find the zeros of
f
(
x
)
=
2
x
2
+
10
x
+
9
f(x)=2x^2+10x+9
f
(
x
)
=
2
x
2
+
10
x
+
9
and determine their relationship to the
x
x
x
-intercepts.
See Solution
Problem 14842
Graph
f
(
x
)
=
x
2
−
4
x
f(x) = x^2 - 4x
f
(
x
)
=
x
2
−
4
x
. Determine if it opens up or down, and find the vertex, axis of symmetry,
y
y
y
-intercept, and
x
x
x
-intercepts.
See Solution
Problem 14843
Calculate the product of 921 and 33.
See Solution
Problem 14844
Identify the logic law shown: If
x
>
12
x>12
x
>
12
, then
x
+
9
>
20
x+9>20
x
+
9
>
20
. Given
x
=
14
x=14
x
=
14
, confirm
x
+
9
>
20
x+9>20
x
+
9
>
20
.
See Solution
Problem 14845
Identify the line of fit among
y
=
1.6
x
+
1.75
y=1.6 x+1.75
y
=
1.6
x
+
1.75
,
y
=
4.25
x
+
1.75
y=4.25 x+1.75
y
=
4.25
x
+
1.75
,
y
=
4.4
x
+
1.75
y=4.4 x+1.75
y
=
4.4
x
+
1.75
,
y
=
3.3
x
+
1.75
y=3.3 x+1.75
y
=
3.3
x
+
1.75
. Estimate
y
y
y
for
x
=
15
x=15
x
=
15
.
See Solution
Problem 14846
Find the function
g
(
x
)
g(x)
g
(
x
)
that results from a vertical shrink of
f
(
x
)
=
2
x
+
6
f(x)=2x+6
f
(
x
)
=
2
x
+
6
by a factor of
1
2
\frac{1}{2}
2
1
.
See Solution
Problem 14847
Find the function
g
(
x
)
g(x)
g
(
x
)
that represents a horizontal shrink of
f
(
x
)
=
∣
2
x
∣
+
4
f(x)=|2x|+4
f
(
x
)
=
∣2
x
∣
+
4
by a factor of
1
2
\frac{1}{2}
2
1
.
See Solution
Problem 14848
Find the function
g
(
x
)
g(x)
g
(
x
)
that represents a horizontal stretch of
f
(
x
)
=
∣
x
+
3
∣
f(x)=|x+3|
f
(
x
)
=
∣
x
+
3∣
by a factor of 4.
See Solution
Problem 14849
Simplify the expression:
−
3
(
1
−
3
x
)
+
2
x
-3(1-3 x)+2 x
−
3
(
1
−
3
x
)
+
2
x
.
See Solution
Problem 14850
Simplify the expression:
4
x
+
4
−
1
+
3
x
4x + 4 - 1 + 3x
4
x
+
4
−
1
+
3
x
.
See Solution
Problem 14851
Simplify the expression:
−
2
(
7
−
2
x
)
-2(7-2x)
−
2
(
7
−
2
x
)
.
See Solution
Problem 14852
Calculate
−
111
(
9
)
−
11
-111(9)-11
−
111
(
9
)
−
11
.
See Solution
Problem 14853
1. What is
6
×
7
6 \times 7
6
×
7
?
2. Round 87 to the nearest ten.
See Solution
Problem 14854
What is
365
+
249
365 + 249
365
+
249
?
See Solution
Problem 14855
What is
6
×
7
6 \times 7
6
×
7
?
See Solution
Problem 14856
Divide 9.13 by 0.58 and round the answer to the nearest hundredth.
See Solution
Problem 14857
Find the value of the box in the equation
19
+
□
=
41
19+\square=41
19
+
□
=
41
.
See Solution
Problem 14858
Find the value of
x
x
x
in the equation
5
×
x
=
35
5 \times x = 35
5
×
x
=
35
.
See Solution
Problem 14859
What is
30
÷
5
30 \div 5
30
÷
5
?
See Solution
Problem 14860
Simplify the expression:
x
−
5
x
2
−
6
x
+
5
\frac{x-5}{x^{2}-6 x+5}
x
2
−
6
x
+
5
x
−
5
.
See Solution
Problem 14861
Find
sec
(
6
0
∘
)
\sec(60^{\circ})
sec
(
6
0
∘
)
and
csc
(
6
0
∘
)
\csc(60^{\circ})
csc
(
6
0
∘
)
using their definitions as reciprocals of cosine and sine.
See Solution
Problem 14862
Solve for
b
2
b_{2}
b
2
in the equation
A
=
1
2
h
(
b
1
+
b
2
)
A=\frac{1}{2} h(b_{1}+b_{2})
A
=
2
1
h
(
b
1
+
b
2
)
.
See Solution
Problem 14863
Identify the missing particle in the nuclear equation:
10
43
K
→
20
43
C
a
+
?
_{10}^{43} \mathrm{~K} \rightarrow{ }_{20}^{43} \mathrm{Ca}+?
10
43
K
→
20
43
Ca
+
?
See Solution
Problem 14864
Calculate the expression:
2
5
(
5
−
6
)
+
9
÷
3
2^{5}(5-6)+9 \div 3
2
5
(
5
−
6
)
+
9
÷
3
.
See Solution
Problem 14865
Calculate
915
−
547
915 - 547
915
−
547
.
See Solution
Problem 14866
Find
x
x
x
from
C
=
85
x
+
60
C=85x+60
C
=
85
x
+
60
. How many trips if
C
=
$
315
C=\$ 315
C
=
$315
and
C
=
$
485
C=\$ 485
C
=
$485
?
See Solution
Problem 14867
Calculate the y-values for the equation
y
2
=
x
y^{2}=x
y
2
=
x
using x-values 3 and 7.
See Solution
Problem 14868
Solve for
x
x
x
in the equation
x
−
9
18
=
x
+
45
45
\frac{x-9}{18}=\frac{x+45}{45}
18
x
−
9
=
45
x
+
45
.
See Solution
Problem 14869
Calculate the sum:
(
155
−
151.49
)
2
151.49
+
(
131
−
134.51
)
2
134.51
+
(
179
−
161.03
)
2
161.03
+
(
125
−
142.97
)
2
142.97
+
(
103
−
124.48
)
2
124.48
+
(
132
−
110.52
)
2
110.52
\frac{(155-151.49)^{2}}{151.49} + \frac{(131-134.51)^{2}}{134.51} + \frac{(179-161.03)^{2}}{161.03} + \frac{(125-142.97)^{2}}{142.97} + \frac{(103-124.48)^{2}}{124.48} + \frac{(132-110.52)^{2}}{110.52}
151.49
(
155
−
151.49
)
2
+
134.51
(
131
−
134.51
)
2
+
161.03
(
179
−
161.03
)
2
+
142.97
(
125
−
142.97
)
2
+
124.48
(
103
−
124.48
)
2
+
110.52
(
132
−
110.52
)
2
.
See Solution
Problem 14870
Find the missing particle in the decay:
84
218
P
o
→
2
4
H
e
+
?
{ }_{84}^{218} \mathrm{Po} \rightarrow{ }_{2}^{4} \mathrm{He}+?
84
218
Po
→
2
4
He
+
?
See Solution
Problem 14871
Solve for
a
a
a
in the equation
−
5
=
a
18
-5=\frac{a}{18}
−
5
=
18
a
.
See Solution
Problem 14872
Solve the system of equations: 2y - 3z = 0, x + 3y = -4, 3x + 4y = 3.
See Solution
Problem 14873
Calculate the length of the interval
[
−
6
,
8
]
[-6, 8]
[
−
6
,
8
]
.
See Solution
Problem 14874
Solve for
m
m
m
in the equation
m
4
=
−
13
\frac{m}{4}=-13
4
m
=
−
13
.
See Solution
Problem 14875
Solve for
v
v
v
in the equation
v
7
=
8
\frac{v}{7}=8
7
v
=
8
.
See Solution
Problem 14876
Solve for
x
x
x
in the equation:
−
17
=
x
−
15
-17 = x - 15
−
17
=
x
−
15
.
See Solution
Problem 14877
Given the function
f
(
x
)
=
{
2
x
+
18
if
x
<
−
6
x
+
42
if
x
>
−
6
2
if
x
=
−
6
f(x)=\left\{\begin{array}{lll}2 x+18 & \text { if } & x<-6 \\ \sqrt{x+42} & \text { if } & x>-6 \\ 2 & \text { if } & x=-6\end{array}\right.
f
(
x
)
=
⎩
⎨
⎧
2
x
+
18
x
+
42
2
if
if
if
x
<
−
6
x
>
−
6
x
=
−
6
, determine the truth of the following statements about
f
(
−
6
)
f(-6)
f
(
−
6
)
and its limits.
See Solution
Problem 14878
Find the co-vertices of the ellipse given by
(
y
−
4
)
2
64
+
(
x
−
2
)
2
4
=
1
\frac{(y-4)^{2}}{64}+\frac{(x-2)^{2}}{4}=1
64
(
y
−
4
)
2
+
4
(
x
−
2
)
2
=
1
.
See Solution
Problem 14879
Find the value of
m
m
m
for the continuous piecewise function
f
(
x
)
=
{
m
x
−
7
if
x
<
−
4
x
2
+
5
x
−
3
if
x
≥
−
4
f(x)=\left\{\begin{array}{ll}m x-7 & \text { if } \quad x<-4 \\ x^{2}+5 x-3 & \text { if } \quad x \geq-4\end{array}\right.
f
(
x
)
=
{
m
x
−
7
x
2
+
5
x
−
3
if
x
<
−
4
if
x
≥
−
4
See Solution
Problem 14880
Find the ordered pair that satisfies the inequalities:
3
x
−
5
y
≤
15
3x - 5y \leq 15
3
x
−
5
y
≤
15
and
8
x
+
5
y
>
24
8x + 5y > 24
8
x
+
5
y
>
24
. A)
(
0
,
3
)
(0,3)
(
0
,
3
)
B)
(
3
,
−
3
)
(3,-3)
(
3
,
−
3
)
C)
(
3
,
0
)
(3,0)
(
3
,
0
)
D)
(
3
,
3
)
(3,3)
(
3
,
3
)
See Solution
Problem 14881
A mechanic earns \
14
/
h
o
u
r
,
$
21
f
o
r
o
v
e
r
t
i
m
e
.
F
i
n
d
14/hour, \$21 for overtime. Find
14/
h
o
u
r
,
$21
f
oro
v
er
t
im
e
.
F
in
d
W(30)
,
,
,
W(40)
,
,
,
W(45)
,
a
n
d
, and
,
an
d
W(50)$.
See Solution
Problem 14882
A mechanic earns \$14/hr, with overtime at time-and-a-half. Find wages for 30, 40, 45, and 50 hours. New functions for 36 hrs and \$16/hr?
See Solution
Problem 14883
A mechanic earns \
14
/
h
o
u
r
r
e
g
u
l
a
r
a
n
d
$
21
/
h
o
u
r
o
v
e
r
t
i
m
e
.
F
i
n
d
14/hour regular and \$21/hour overtime. Find
14/
h
o
u
rre
gu
l
a
r
an
d
$21/
h
o
u
ro
v
er
t
im
e
.
F
in
d
W(30), W(40), W(45), W(50)$.
See Solution
Problem 14884
Find
x
x
x
if
f
(
x
)
=
x
2
−
1
f(x) = x^{2} - 1
f
(
x
)
=
x
2
−
1
and
f
(
x
)
=
99
f(x) = 99
f
(
x
)
=
99
.
See Solution
Problem 14885
A mechanic earns \
14
/
h
o
u
r
r
e
g
u
l
a
r
a
n
d
$
21
/
h
o
u
r
o
v
e
r
t
i
m
e
.
F
i
n
d
14/hour regular and \$21/hour overtime. Find
14/
h
o
u
rre
gu
l
a
r
an
d
$21/
h
o
u
ro
v
er
t
im
e
.
F
in
d
W(30)
,
,
,
W(40)
,
,
,
W(45)
,
a
n
d
, and
,
an
d
W(50)$.
(b) What is the new wage function if the work week is 36 hours?
(c) If pay is \$16/hour for 40 hours, what is the new wage function?
See Solution
Problem 14886
A mechanic earns \
14
/
h
o
u
r
r
e
g
u
l
a
r
a
n
d
$
21
/
h
o
u
r
o
v
e
r
t
i
m
e
.
F
i
n
d
14/hour regular and \$21/hour overtime. Find
14/
h
o
u
rre
gu
l
a
r
an
d
$21/
h
o
u
ro
v
er
t
im
e
.
F
in
d
W(30)
,
,
,
W(40)
,
,
,
W(45)
,
,
,
W(50)$ and new function for 36 hours.
See Solution
Problem 14887
Find the value of the function
f
(
x
)
=
x
3
f(x) = x^{3}
f
(
x
)
=
x
3
at
x
=
5
x = 5
x
=
5
.
See Solution
Problem 14888
Find
x
x
x
where
f
(
x
)
=
3
f(x) = 3
f
(
x
)
=
3
.
See Solution
Problem 14889
Find
x
x
x
such that
f
(
x
)
=
−
3
f(x) = -3
f
(
x
)
=
−
3
for the function
f
(
x
)
=
∣
x
∣
f(x) = |x|
f
(
x
)
=
∣
x
∣
.
See Solution
Problem 14890
Find
f
(
2
)
f(2)
f
(
2
)
and
f
(
5
)
f(5)
f
(
5
)
for the function defined as
f
(
x
)
=
2
x
f(x)=2^{x}
f
(
x
)
=
2
x
.
See Solution
Problem 14891
Find
f
(
−
4
)
f(-4)
f
(
−
4
)
using the function
f
(
x
)
=
x
2
−
1
f(x)=x^{2}-1
f
(
x
)
=
x
2
−
1
given that
f
(
−
2
)
=
f
(
0
)
=
f
(
1
)
=
f(-2)=f(0)=f(1)=\;
f
(
−
2
)
=
f
(
0
)
=
f
(
1
)
=
.
See Solution
Problem 14892
Solve for
x
x
x
given that angle 4 is
4
x
−
6
4x - 6
4
x
−
6
and angle 6 is
2
x
−
12
2x - 12
2
x
−
12
.
See Solution
Problem 14893
Solve the equation
2
(
x
+
3
)
+
3
x
=
16
2(x+3) + 3x = 16
2
(
x
+
3
)
+
3
x
=
16
.
See Solution
Problem 14894
Solve the equation
3
(
x
−
4
)
+
15
=
2
(
x
+
5
)
3(x-4)+15=2(x+5)
3
(
x
−
4
)
+
15
=
2
(
x
+
5
)
. What is the solution? A. Solution set is B.
{
x
∣
x
\{x \mid x
{
x
∣
x
is a real number
}
\}
}
C.
∅
\varnothing
∅
.
See Solution
Problem 14895
Rationalize the denominator: (a)
24
3
\frac{24}{\sqrt{3}}
3
24
See Solution
Problem 14896
Solve the equation
2
x
x
+
4
−
8
x
−
4
=
2
x
2
+
32
x
2
−
16
\frac{2 x}{x+4}-\frac{8}{x-4}=\frac{2 x^{2}+32}{x^{2}-16}
x
+
4
2
x
−
x
−
4
8
=
x
2
−
16
2
x
2
+
32
. Is it an identity, conditional, or inconsistent?
See Solution
Problem 14897
Calculate
f
(
2
)
f(2)
f
(
2
)
for the function
f
(
x
)
=
x
2
+
3
x
−
7
f(x)=x^{2}+3x-7
f
(
x
)
=
x
2
+
3
x
−
7
.
See Solution
Problem 14898
Simplify the expression
4
6
\frac{4}{\sqrt{6}}
6
4
.
See Solution
Problem 14899
Calculate
f
(
−
1
)
f(-1)
f
(
−
1
)
for the function
f
(
x
)
=
x
2
−
5
x
+
3
f(x)=\frac{x^{2}-5}{x+3}
f
(
x
)
=
x
+
3
x
2
−
5
.
See Solution
Problem 14900
Calculate
f
(
2
)
f(2)
f
(
2
)
for the function
f
(
x
)
=
x
2
+
3
x
f(x)=\sqrt{x^{2}+3x}
f
(
x
)
=
x
2
+
3
x
.
See Solution
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