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Math
Algebra
Problem 31101
Simplify the expression by combining like terms:
−
2
x
−
2
y
2
−
3
−
4
y
2
−
5
x
+
1
-2 x - 2 y^{2} - 3 - 4 y^{2} - 5 x + 1
−
2
x
−
2
y
2
−
3
−
4
y
2
−
5
x
+
1
See Solution
Problem 31102
Simplify the expression:
(
4
x
2
+
7
x
−
4
x
4
)
−
(
6
x
4
−
5
x
+
1
)
(4 x^{2}+7 x-4 x^{4})-(6 x^{4}-5 x+1)
(
4
x
2
+
7
x
−
4
x
4
)
−
(
6
x
4
−
5
x
+
1
)
.
See Solution
Problem 31103
A ball is thrown down at
50
f
t
/
s
50 \mathrm{ft/s}
50
ft/s
from a 56 ft building. Find the time it stays in the air using
s
(
t
)
=
−
16
t
2
−
50
t
+
56
s(t)=-16 t^{2}-50 t+56
s
(
t
)
=
−
16
t
2
−
50
t
+
56
.
See Solution
Problem 31104
Simplify the expression:
3
(
x
2
+
2
x
+
5
)
+
2
(
x
2
+
3
x
+
2
)
3(x^{2}+2x+5)+2(x^{2}+3x+2)
3
(
x
2
+
2
x
+
5
)
+
2
(
x
2
+
3
x
+
2
)
.
See Solution
Problem 31105
Graph the function
f
(
x
)
=
1
9
x
2
f(x)=\frac{1}{9} x^{2}
f
(
x
)
=
9
1
x
2
and find its domain and range.
See Solution
Problem 31106
Combine the polynomials:
(
4
v
4
+
v
+
4
v
3
)
+
(
8
v
4
+
7
v
+
3
v
3
)
(4v^4 + v + 4v^3) + (8v^4 + 7v + 3v^3)
(
4
v
4
+
v
+
4
v
3
)
+
(
8
v
4
+
7
v
+
3
v
3
)
.
See Solution
Problem 31107
Find the equation of the line that goes through the point
(
10
,
3
)
(10,3)
(
10
,
3
)
with a slope of
−
3
2
-\frac{3}{2}
−
2
3
.
See Solution
Problem 31108
Simplify the expression:
(
3
b
4
+
2
b
3
+
6
b
)
+
(
8
b
2
−
7
b
4
−
3
b
)
(3 b^{4}+2 b^{3}+6 b)+(8 b^{2}-7 b^{4}-3 b)
(
3
b
4
+
2
b
3
+
6
b
)
+
(
8
b
2
−
7
b
4
−
3
b
)
.
See Solution
Problem 31109
Graph the function
f
(
x
)
=
1
9
x
2
f(x)=\frac{1}{9} x^{2}
f
(
x
)
=
9
1
x
2
and find its domain and range. Choose from A, B, C, or D.
See Solution
Problem 31110
16
x
4
−
25
x
=
021
−
18011
16 x^{4}-25 x=021-18011
16
x
4
−
25
x
=
021
−
18011
See Solution
Problem 31111
ب) جد المعادلة الديكارتبة للمعادللتين البار امتريتين :
0
≤
t
≤
2
،
x
=
4
−
t
2
0 \leq t \leq 2 ، x=\sqrt{4-t^{2}}
0
≤
t
≤
2،
x
=
4
−
t
2
،
See Solution
Problem 31112
9. Find the equation of a line perpendicular to the line
x
−
2
y
−
3
=
0
x-2 y-3=0
x
−
2
y
−
3
=
0
and passing through the point
(
1
,
−
2
)
(1,-2)
(
1
,
−
2
)
See Solution
Problem 31113
Simplify.
x
2
x
7
\frac{x^{2}}{x^{7}}
x
7
x
2
See Solution
Problem 31114
Simplify.
5
b
c
35
c
d
\begin{array}{l} 5 b c \\ 35 c d \end{array}
5
b
c
35
c
d
See Solution
Problem 31115
Simplify.
8
u
2
48
u
5
\frac{8 u^{2}}{48 u^{5}}
48
u
5
8
u
2
See Solution
Problem 31116
Rewrite without parentheses and simplify.
(
x
−
4
)
2
(x-4)^{2}
(
x
−
4
)
2
See Solution
Problem 31117
\begin{align*} f(-6) &= 1, \\ f(-5) &= 3, \\ f(-2) &= 0, \\ f(-1) &= -1, \\ f(0) &= 0, \\ f(4) &= 4, \\ f(6) &= 2, \\ f(8) &= 2. \end{align*} Determine if the function
f
(
x
)
f(x)
f
(
x
)
is even, odd, or neither based on the given values.
See Solution
Problem 31118
Find the slope-intercept form of a line that passes through
(
5
,
−
3
)
(5,-3)
(
5
,
−
3
)
with a slope of -4.
See Solution
Problem 31119
Simplify the expression:
(
2
v
4
+
3
v
−
3
v
2
)
+
(
v
4
−
5
v
2
+
5
v
)
(2 v^{4}+3 v-3 v^{2})+(v^{4}-5 v^{2}+5 v)
(
2
v
4
+
3
v
−
3
v
2
)
+
(
v
4
−
5
v
2
+
5
v
)
.
See Solution
Problem 31120
Simplify the expression:
1
0
+
14
+
14
\frac{1}{\sqrt{0+14}+\sqrt{14}}
0
+
14
+
14
1
See Solution
Problem 31121
Solve the inequality
x
+
5
≤
3
x + 5 \leq 3
x
+
5
≤
3
and express the solution in interval notation.
See Solution
Problem 31122
Find the slope-intercept form of the line through
(
−
1
,
2
)
(-1,2)
(
−
1
,
2
)
with slope 5.
See Solution
Problem 31123
Solve the inequality
−
2
x
≤
12
-2 x \leq 12
−
2
x
≤
12
and express the solution in interval notation.
See Solution
Problem 31124
Simplify the expression:
(
x
3
−
4
x
2
−
5
x
)
−
(
2
x
3
+
7
x
2
+
2
x
)
(x^{3}-4 x^{2}-5 x)-(2 x^{3}+7 x^{2}+2 x)
(
x
3
−
4
x
2
−
5
x
)
−
(
2
x
3
+
7
x
2
+
2
x
)
.
See Solution
Problem 31125
Find the equation in point-slope form for a line through
(
−
3
,
−
2
)
(-3,-2)
(
−
3
,
−
2
)
with a slope of 5.
See Solution
Problem 31126
Find the equation in point-slope form for the line through
(
−
10
,
4
)
(-10,4)
(
−
10
,
4
)
with a slope of
1
2
\frac{1}{2}
2
1
.
See Solution
Problem 31127
Find the equation in point-slope form for a line through
(
4
,
4
)
(4,4)
(
4
,
4
)
with slope
−
5
2
-\frac{5}{2}
−
2
5
.
See Solution
Problem 31128
Graph the function
f
(
x
)
=
∣
x
+
4
∣
−
4
f(x)=|x+4|-4
f
(
x
)
=
∣
x
+
4∣
−
4
and identify its domain and range.
See Solution
Problem 31129
Simplify the expression
a
57
b
34
⋅
a
b
33
⋅
a
33
⋅
a
27
b
24
\frac{a^{57}}{b^{34}} \cdot a b^{33} \cdot a^{33} \cdot \frac{a^{27}}{b^{24}}
b
34
a
57
⋅
a
b
33
⋅
a
33
⋅
b
24
a
27
.
See Solution
Problem 31130
Simplify
t
400
t
100
\frac{t^{400}}{t^{100}}
t
100
t
400
. What is the result? Options:
t
500
t^{500}
t
500
,
300
300
300
,
t
300
t^{300}
t
300
,
t
4
t^{4}
t
4
.
See Solution
Problem 31131
Simplify the expression:
(
3
x
2
−
7
−
x
3
)
−
(
5
−
8
x
3
+
3
x
2
)
(3 x^{2}-7-x^{3})-(5-8 x^{3}+3 x^{2})
(
3
x
2
−
7
−
x
3
)
−
(
5
−
8
x
3
+
3
x
2
)
.
See Solution
Problem 31132
A potato is shot up with a speed of
34
f
t
/
s
34 \mathrm{ft/s}
34
ft/s
from a 15 ft tall building. Find how long it's in the air using
s
(
t
)
=
−
16
t
2
+
34
t
+
15
s(t)=-16 t^{2}+34 t+15
s
(
t
)
=
−
16
t
2
+
34
t
+
15
.
See Solution
Problem 31133
A ball is thrown down at
38
f
t
/
s
38 \mathrm{ft/s}
38
ft/s
from a 63 ft building. Find the time it is in the air using
s
(
t
)
=
−
16
t
2
−
38
t
+
63
s(t)=-16 t^{2}-38 t+63
s
(
t
)
=
−
16
t
2
−
38
t
+
63
.
See Solution
Problem 31134
Determine the slope and
y
y
y
-intercept of the line given by the equation
6
x
−
2
y
=
3
6x - 2y = 3
6
x
−
2
y
=
3
.
See Solution
Problem 31135
Simplify the expression:
(
5
p
+
p
3
+
3
p
4
)
+
(
3
p
4
−
2
p
2
+
4
p
)
(5p + p^3 + 3p^4) + (3p^4 - 2p^2 + 4p)
(
5
p
+
p
3
+
3
p
4
)
+
(
3
p
4
−
2
p
2
+
4
p
)
.
See Solution
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