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Math
Math Statement
Problem 14201
Simplify the expression:
5
112
x
3
−
3
x
63
x
5 \sqrt{112 x^{3}} - 3 x \sqrt{63 x}
5
112
x
3
−
3
x
63
x
.
See Solution
Problem 14202
Simplify the expression:
−
5
x
2
−
4
x
5
-\sqrt{5 x^{2}}-4 x \sqrt{5}
−
5
x
2
−
4
x
5
.
See Solution
Problem 14203
Evaluate
∣
−
6
∣
+
3
∣
4
∣
+
∣
−
5
∣
−
0
⋅
6
|-6| + 3|4| + |-5| - 0 \cdot 6
∣
−
6∣
+
3∣4∣
+
∣
−
5∣
−
0
⋅
6
. What is the result?
See Solution
Problem 14204
Simplify
−
x
2
20
−
x
80
x
2
-x^{2} \sqrt{20}-x \sqrt{80 x^{2}}
−
x
2
20
−
x
80
x
2
to its simplest radical form.
See Solution
Problem 14205
Evaluate
∣
c
2
+
b
2
∣
\left|c^{2}+b^{2}\right|
∣
∣
c
2
+
b
2
∣
∣
for
a
=
5
a=5
a
=
5
,
b
=
−
3
b=-3
b
=
−
3
, and
c
=
−
2
c=-2
c
=
−
2
.
See Solution
Problem 14206
Calculate
∣
5
∣
−
∣
−
3
∣
|5| - |-3|
∣5∣
−
∣
−
3∣
.
See Solution
Problem 14207
Simplify the expression
−
4
x
2
3
x
3
+
7
x
3
12
x
-4x^2\sqrt{3x^3} + 7x^3\sqrt{12x}
−
4
x
2
3
x
3
+
7
x
3
12
x
into simplest radical form.
See Solution
Problem 14208
Evaluate
13
−
5
+
7
13 - 5 + 7
13
−
5
+
7
and determine which of the following is correct: 15, 5, -15, -5.
See Solution
Problem 14209
Simplify:
3
0
3^{0}
3
0
. What is the result?
See Solution
Problem 14210
Evaluate
∣
5
∣
−
∣
−
5
∣
|5| - |-5|
∣5∣
−
∣
−
5∣
. Options: -25, 10, 25, 0.
See Solution
Problem 14211
Calculate the value of the expression
(
6
2
)
4
\left(6^{2}\right)^{4}
(
6
2
)
4
.
See Solution
Problem 14212
Simplify
−
4
x
2
3
x
3
+
7
x
3
12
x
-4 x^{2} \sqrt{3 x^{3}}+7 x^{3} \sqrt{12 x}
−
4
x
2
3
x
3
+
7
x
3
12
x
to its simplest radical form.
See Solution
Problem 14213
Simplify
9
175
x
2
−
3
x
7
9 \sqrt{175 x^{2}} - 3 x \sqrt{7}
9
175
x
2
−
3
x
7
to its simplest radical form.
See Solution
Problem 14214
Simplify
−
4
x
2
3
x
3
+
7
x
3
12
x
-4 x^{2} \sqrt{3 x^{3}} + 7 x^{3} \sqrt{12 x}
−
4
x
2
3
x
3
+
7
x
3
12
x
to its simplest radical form.
See Solution
Problem 14215
Solve the inequality
−
3
∣
x
+
2
∣
<
−
9
-3|x+2|<-9
−
3∣
x
+
2∣
<
−
9
.
See Solution
Problem 14216
Use the Distributive Property to solve the equation
4
(
x
+
2
)
=
16
4(x+2)=16
4
(
x
+
2
)
=
16
.
See Solution
Problem 14217
Solve the equation:
∣
0.04
x
−
1
∣
=
6.04
|0.04 x-1|=6.04
∣0.04
x
−
1∣
=
6.04
See Solution
Problem 14218
Solve for n:
−
2
n
−
4
=
32
-2n - 4 = 32
−
2
n
−
4
=
32
See Solution
Problem 14219
Simplify the expression:
1
1
6
1
1
4
\frac{11^{6}}{11^{4}}
1
1
4
1
1
6
. What is the result?
See Solution
Problem 14220
Solve the equation
2
k
−
6
+
3
k
=
14
2k - 6 + 3k = 14
2
k
−
6
+
3
k
=
14
for
k
k
k
.
See Solution
Problem 14221
Simplify the expression:
(
3
x
2
y
3
x
3
)
3
\left(\frac{3 x^{2} y^{3}}{x^{3}}\right)^{3}
(
x
3
3
x
2
y
3
)
3
.
See Solution
Problem 14222
Simplify
−
x
3
x
5
−
3
x
2
3
x
3
-x \sqrt{3 x^{5}}-3 x^{2} \sqrt{3 x^{3}}
−
x
3
x
5
−
3
x
2
3
x
3
to its simplest radical form.
See Solution
Problem 14223
Solve for
k
k
k
in the equation:
2
k
−
6
+
3
k
=
14
2 k - 6 + 3 k = 14
2
k
−
6
+
3
k
=
14
.
See Solution
Problem 14224
Simplify
4
x
192
−
3
x
2
4 x \sqrt{192}-\sqrt{3 x^{2}}
4
x
192
−
3
x
2
to its simplest radical form.
See Solution
Problem 14225
Simplify the expression:
12
a
3
b
6
c
5
3
a
2
b
4
c
5
\frac{12 a^{3} b^{6} c^{5}}{3 a^{2} b^{4} c^{5}}
3
a
2
b
4
c
5
12
a
3
b
6
c
5
See Solution
Problem 14226
Simplify:
(
3
x
2
y
3
z
3
)
3
\left(\frac{3 x^{2} y^{3}}{z^{3}}\right)^{3}
(
z
3
3
x
2
y
3
)
3
See Solution
Problem 14227
Find the slope and
y
y
y
-intercept of the line given by the equation
y
=
2
x
+
1
y=2x+1
y
=
2
x
+
1
.
See Solution
Problem 14228
Find the equivalent expression for
(
2
w
−
2
)
3
(
8
w
6
)
\left(2 w^{-2}\right)^{3}\left(8 w^{6}\right)
(
2
w
−
2
)
3
(
8
w
6
)
.
See Solution
Problem 14229
Find the equivalent expression for
c
d
4
c
2
d
8
\frac{c d^{4}}{c^{2} d^{8}}
c
2
d
8
c
d
4
.
See Solution
Problem 14230
Find the
y
y
y
-intercept of the line given by the equation
y
=
−
2
x
+
1
y=-2x+1
y
=
−
2
x
+
1
.
See Solution
Problem 14231
Convert 6873 x 10^6 into scientific notation: [?] x 10^[?].
See Solution
Problem 14232
Calculate
0.0003
162
\frac{0.0003}{162}
162
0.0003
and express the answer in scientific notation with the correct significant figures.
See Solution
Problem 14233
Encuentra el valor mínimo de
x
x
x
en la inecuación:
(
x
−
1
)
2
+
(
x
−
2
)
2
≤
x
2
+
x
−
1
(x-1)^{2}+(x-2)^{2} \leq x^{2}+x-1
(
x
−
1
)
2
+
(
x
−
2
)
2
≤
x
2
+
x
−
1
. Opciones: a. -1, b. 0, c. 1, d. 2.
See Solution
Problem 14234
Find the value of ? in
c
b
?
=
a
0
b
−
2
c
\frac{c}{b^{?}} = a^{0} b^{-2} c
b
?
c
=
a
0
b
−
2
c
.
See Solution
Problem 14235
Graph the line given by the equation
y
=
−
2
y=-2
y
=
−
2
on a coordinate plane.
See Solution
Problem 14236
Determine the range of the function
y
=
−
4
x
+
3
y=-4x+3
y
=
−
4
x
+
3
.
See Solution
Problem 14237
Find the number of significant figures in 0.0080.
See Solution
Problem 14238
How many significant figures are in the number 45000?
See Solution
Problem 14239
Calculate
1
0
4
×
1
0
7
10^{4} \times 10^{7}
1
0
4
×
1
0
7
.
See Solution
Problem 14240
Calculate the sum of 3.42, 4, 5.2, and 12, and report your answer with the correct significant figures.
See Solution
Problem 14241
Calculate
1
0
6
1
0
2
\frac{10^{6}}{10^{2}}
1
0
2
1
0
6
.
See Solution
Problem 14242
Calculate and report the answer with significant figures:
12306
×
2451
12306 \times 2451
12306
×
2451
See Solution
Problem 14243
Multiply the numerator and denominator of
x
x
−
2
−
1
x
+
1
2
x
x
−
2
\frac{\frac{x}{x-2}-\frac{1}{x+1}}{\frac{2 x}{x-2}}
x
−
2
2
x
x
−
2
x
−
x
+
1
1
by which expression to simplify?
See Solution
Problem 14244
Find the minimum value of the function
f
(
x
)
=
x
2
−
6
x
+
14
f(x) = x^{2} - 6x + 14
f
(
x
)
=
x
2
−
6
x
+
14
. Options: A) -3, B) 3, C) 5, D) 14.
See Solution
Problem 14245
Solve the equation
x
2
−
9
x
−
9
=
x
+
9
\frac{x^{2}-9}{x-9}=x+9
x
−
9
x
2
−
9
=
x
+
9
for all values of
x
x
x
.
See Solution
Problem 14246
Analiza la inecuación:
(
x
+
2
)
2
+
(
x
+
3
)
2
⩾
2
x
2
+
63
(x+2)^{2}+(x+3)^{2} \geqslant 2 x^{2}+63
(
x
+
2
)
2
+
(
x
+
3
)
2
⩾
2
x
2
+
63
. ¿Cuál es su conjunto solución?
See Solution
Problem 14247
Calculate
3.0
×
5
3.0 \times 5
3.0
×
5
and report the answer using significant figures.
See Solution
Problem 14248
Graph the inequalities
y
≥
−
1
5
x
+
5
y \geq -\frac{1}{5} x + 5
y
≥
−
5
1
x
+
5
and
y
>
2
x
−
6
y > 2x - 6
y
>
2
x
−
6
. Find a point in the solution set.
See Solution
Problem 14249
Find the missing element X in the nuclear equation:
6
11
C
→
X
+
1
0
e
{ }_{6}^{11} \mathrm{C} \rightarrow \mathrm{X}+{ }_{1}^{0} \mathrm{e}
6
11
C
→
X
+
1
0
e
.
See Solution
Problem 14250
Solve the equation:
2
−
4
x
−
14
=
9
2 - 4x - 14 = 9
2
−
4
x
−
14
=
9
.
See Solution
Problem 14251
Calculate
(
3
×
1
0
5
)
×
(
2
×
1
0
2
)
(3 \times 10^{5}) \times (2 \times 10^{2})
(
3
×
1
0
5
)
×
(
2
×
1
0
2
)
and express the answer in the form
V
×
1
0
n
V \times 10^{n}
V
×
1
0
n
.
See Solution
Problem 14252
Find the missing component in the equation:
6
11
C
→
X
+
1
0
e
{ }_{6}^{11} \mathrm{C} \rightarrow \mathrm{X}+{ }_{1}^{0} \mathrm{e}
6
11
C
→
X
+
1
0
e
See Solution
Problem 14253
Solve for
x
x
x
in the equation:
−
3
x
=
1
3
-3 x=\frac{1}{3}
−
3
x
=
3
1
.
See Solution
Problem 14254
Find the absolute value of 18:
∣
18
∣
|18|
∣18∣
.
See Solution
Problem 14255
Identify expressions that can be factored as
(
a
x
+
b
)
(
a
x
−
b
)
(a x+b)(a x-b)
(
a
x
+
b
)
(
a
x
−
b
)
with integers
a
a
a
and
b
b
b
. Options: A
x
2
−
9
x^{2}-9
x
2
−
9
, B
x
2
−
11
x^{2}-11
x
2
−
11
, C
4
x
2
−
1
4 x^{2}-1
4
x
2
−
1
, D
4
x
2
−
2
4 x^{2}-2
4
x
2
−
2
, E
9
x
2
−
4
9 x^{2}-4
9
x
2
−
4
.
See Solution
Problem 14256
Resuelve la inecuación:
(
x
+
2
)
2
+
(
x
+
3
)
2
⩾
2
x
2
+
63
(x+2)^{2}+(x+3)^{2} \geqslant 2 x^{2}+63
(
x
+
2
)
2
+
(
x
+
3
)
2
⩾
2
x
2
+
63
. ¿Cuál es el conjunto solución?
See Solution
Problem 14257
Is
10
\sqrt{10}
10
a rational number? Choose true or false with reasons: A. True, it's an integer. B. False, it doesn't end/repeat. C. True, it has repeating digits. D. True, it's a terminating decimal.
See Solution
Problem 14258
Encuentra el menor valor de
x
x
x
en la inecuación:
(
x
−
1
)
2
+
(
x
−
2
)
2
⩽
x
2
+
x
−
1
(x-1)^{2}+(x-2)^{2} \leqslant x^{2}+x-1
(
x
−
1
)
2
+
(
x
−
2
)
2
⩽
x
2
+
x
−
1
. Opciones: a. -2 b. -1 c. 0 d. 1 e. 2
See Solution
Problem 14259
Is the statement true or false? -8 is a rational number. Choose: True or False.
See Solution
Problem 14260
Is the statement true or false?
2
2
6
2 \frac{2}{6}
2
6
2
is an irrational number. Choose: True or False.
See Solution
Problem 14261
Solve for
a
a
a
in the equation:
3
(
2
a
−
6
)
=
36
3(2 a-6)=36
3
(
2
a
−
6
)
=
36
.
See Solution
Problem 14262
Solve the equation:
3
x
+
4
x
−
9
=
12
3x + 4x - 9 = 12
3
x
+
4
x
−
9
=
12
.
See Solution
Problem 14263
Resuelve la inecuación:
(
x
+
2
)
2
+
(
x
+
3
)
2
⩾
2
x
2
+
63
(x+2)^{2}+(x+3)^{2} \geqslant 2 x^{2}+63
(
x
+
2
)
2
+
(
x
+
3
)
2
⩾
2
x
2
+
63
. ¿Cuál es el conjunto solución?
See Solution
Problem 14264
In a G.P., if the
p
th
p^{\text{th}}
p
th
,
q
th
q^{\text{th}}
q
th
, and
r
th
r^{\text{th}}
r
th
terms are
a
,
b
,
c
a, b, c
a
,
b
,
c
, prove that:
a
q
−
r
⋅
b
r
−
p
⋅
c
p
−
q
=
1
a^{q-r} \cdot b^{r-p} \cdot c^{p-q}=1
a
q
−
r
⋅
b
r
−
p
⋅
c
p
−
q
=
1
.
See Solution
Problem 14265
Is every negative number a negative integer? Choose true or false: A. True, B. False (-2), C. False (
−
1
2
-\frac{1}{2}
−
2
1
), D. True.
See Solution
Problem 14266
Solve the equation:
2
g
−
2
(
5
g
+
12
)
=
8
2g - 2(5g + 12) = 8
2
g
−
2
(
5
g
+
12
)
=
8
See Solution
Problem 14267
Resuelve la inecuación
1
x
−
1
x
−
1
<
0
\frac{1}{x}-\frac{1}{x-1}<0
x
1
−
x
−
1
1
<
0
y encuentra el intervalo solución.
See Solution
Problem 14268
Use the distributive property to simplify:
4
(
6
+
7
)
=
4(6+7)=
4
(
6
+
7
)
=
See Solution
Problem 14269
Solve the equation
−
8
x
=
−
6
x
+
10
-8 x=-6 x+10
−
8
x
=
−
6
x
+
10
and verify your solution.
See Solution
Problem 14270
Prove that if
a
,
b
,
c
a, b, c
a
,
b
,
c
are in A.P. and
x
,
y
,
z
x, y, z
x
,
y
,
z
are in G.P., then
x
b
−
c
⋅
y
c
−
a
⋅
z
a
−
b
=
1
x^{b-c} \cdot y^{c-a} \cdot z^{a-b}=1
x
b
−
c
⋅
y
c
−
a
⋅
z
a
−
b
=
1
.
See Solution
Problem 14271
Determine the property illustrated by the equation
4
(
0.25
)
=
1
4(0.25)=1
4
(
0.25
)
=
1
.
See Solution
Problem 14272
Determine the x-intercepts and y-intercepts of the equation
y
=
x
2
−
64
y=x^{2}-64
y
=
x
2
−
64
.
See Solution
Problem 14273
Solve for
q
q
q
in the equation:
19
−
4
q
=
q
−
11
19 - 4q = q - 11
19
−
4
q
=
q
−
11
.
See Solution
Problem 14274
Identify the property of the equation:
(
8
+
2
)
+
3
=
8
+
(
2
+
3
)
(8+2)+3=8+(2+3)
(
8
+
2
)
+
3
=
8
+
(
2
+
3
)
.
See Solution
Problem 14275
Use a graphing tool to find the roots of the equation
x
3
−
5
x
2
+
4
x
=
0
x^{3}-5 x^{2}+4 x=0
x
3
−
5
x
2
+
4
x
=
0
.
See Solution
Problem 14276
Find the value of
a
10
a_{10}
a
10
in the sequence defined by
a
n
=
−
5
+
(
n
−
1
)
14
a_{n}=-5+(n-1) 14
a
n
=
−
5
+
(
n
−
1
)
14
.
See Solution
Problem 14277
Find the meaning of
f
(
1400
)
=
60
f(1400)=60
f
(
1400
)
=
60
.
See Solution
Problem 14278
Identify the property demonstrated by
12
+
3
+
4
=
4
+
3
+
12
12 + 3 + 4 = 4 + 3 + 12
12
+
3
+
4
=
4
+
3
+
12
.
See Solution
Problem 14279
Calcular el área total usando la fórmula:
=
(
4
∗
(
5
∗
5
/
2
)
)
+
(
4
∗
25
)
+
(
4
∗
18
)
=(4 *(5 * 5 / 2))+(4 * 25)+(4 * 18)
=
(
4
∗
(
5
∗
5/2
))
+
(
4
∗
25
)
+
(
4
∗
18
)
y encuentra el resultado.
See Solution
Problem 14280
Determine the slope
m
m
m
and
y
y
y
-intercept
b
b
b
from the equation of the line:
5
x
−
y
=
2
5 x - y = 2
5
x
−
y
=
2
.
See Solution
Problem 14281
Identify the property: "The product of numbers remains the same regardless of the order of the factors."
See Solution
Problem 14282
Identify the property: "For any numbers
a
a
a
and
b
b
b
,
a
×
b
=
b
×
a
a \times b = b \times a
a
×
b
=
b
×
a
."
See Solution
Problem 14283
Find the percent change in beer shipments from 2007 to 2010 using the equation
y
=
−
4.3
x
+
30.1
y=-4.3 x+30.1
y
=
−
4.3
x
+
30.1
with
x
=
10
x=10
x
=
10
.
See Solution
Problem 14284
Find the first full year when the percent change in beer shipments reaches
−
33
%
-33\%
−
33%
using the model
y
=
−
3.5
x
+
24.5
y=-3.5x+24.5
y
=
−
3.5
x
+
24.5
.
See Solution
Problem 14285
What is the mole ratio of water to carbon dioxide in the reaction:
C
2
H
5
O
H
+
2
O
2
→
2
C
O
2
+
3
H
2
O
+
1367
k
J
C_{2}H_{5}OH + 2 O_{2} \rightarrow 2 CO_{2} + 3 H_{2}O + 1367 kJ
C
2
H
5
O
H
+
2
O
2
→
2
C
O
2
+
3
H
2
O
+
1367
k
J
?
See Solution
Problem 14286
How many moles of
C
6
H
12
O
6
\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}
C
6
H
12
O
6
are needed for 6.0 moles of
O
2
\mathrm{O}_{2}
O
2
?
See Solution
Problem 14287
Calculate
9.725
×
1
0
3
+
3.58
×
1
0
2
+
6.1
9.725 \times 10^{3}+3.58 \times 10^{2}+6.1
9.725
×
1
0
3
+
3.58
×
1
0
2
+
6.1
and round to the correct significant figures.
See Solution
Problem 14288
Find the answer to
6.525
−
0.55
−
1.87
6.525 - 0.55 - 1.87
6.525
−
0.55
−
1.87
with the correct significant figures.
See Solution
Problem 14289
Calculate the sum:
3.25
×
1
0
−
2
+
3.572
×
1
0
−
3
+
6.125
×
1
0
−
1
3.25 \times 10^{-2} + 3.572 \times 10^{-3} + 6.125 \times 10^{-1}
3.25
×
1
0
−
2
+
3.572
×
1
0
−
3
+
6.125
×
1
0
−
1
and round to correct significant figures.
See Solution
Problem 14290
Calculate the sum:
0.5
+
3.25
+
2.8
0.5 + 3.25 + 2.8
0.5
+
3.25
+
2.8
and report it with the correct significant figures.
See Solution
Problem 14291
Calculate
95.325
−
43.35
−
16.12
95.325 - 43.35 - 16.12
95.325
−
43.35
−
16.12
and round to the correct significant figures.
See Solution
Problem 14292
Find the sum of
19.25
19.25
19.25
,
31.535
31.535
31.535
, and
16.7125
16.7125
16.7125
with the correct significant figures.
See Solution
Problem 14293
Write the repeating decimal
3.0
1
‾
3.0 \overline{1}
3.0
1
as a mixed number.
See Solution
Problem 14294
Calculate
275.75
−
113.5
+
36.125
275.75 - 113.5 + 36.125
275.75
−
113.5
+
36.125
and round to the correct significant figures based on the + or - rule.
See Solution
Problem 14295
Calculate
9.2875
+
23.65
−
14.357
9.2875 + 23.65 - 14.357
9.2875
+
23.65
−
14.357
and round to the correct significant figures based on addition and subtraction rules.
See Solution
Problem 14296
Calculate the sum:
39.25
+
13.5
+
66.125
−
0.3
39.25 + 13.5 + 66.125 - 0.3
39.25
+
13.5
+
66.125
−
0.3
and round to the correct significant figures.
See Solution
Problem 14297
Solve for
x
x
x
in the equation:
1
4
x
−
5
=
3
8
x
\frac{1}{4} x - 5 = \frac{3}{8} x
4
1
x
−
5
=
8
3
x
.
See Solution
Problem 14298
Solve for
x
x
x
in the equation:
x
+
4
4
+
x
+
1
3
=
5
\frac{x+4}{4}+\frac{x+1}{3}=5
4
x
+
4
+
3
x
+
1
=
5
.
See Solution
Problem 14299
Calculate the expression:
3
16
−
4
36
3 \sqrt{16}-4 \sqrt{36}
3
16
−
4
36
.
See Solution
Problem 14300
Solve the equation
8
3
x
−
4
=
3
x
+
4
\frac{8}{3 x-4}=\frac{3}{x+4}
3
x
−
4
8
=
x
+
4
3
.
See Solution
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