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Let’s check out your problem:
Simplify to create an equivalent expression.
\newline
−
3
z
−
(
−
z
−
2
)
-3z-(-z-2)
−
3
z
−
(
−
z
−
2
)
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
−
4
-4
−
4
z+
2
2
2
\newline
(B)
\newline
−
2
-2
−
2
z
−
2
-2
−
2
\newline
(C)
\newline
−
2
-2
−
2
z+
2
2
2
\newline
(D)
\newline
4
4
4
z+
2
2
2
View step-by-step help
Home
Math Problems
Precalculus
Average rate of change II
Full solution
Q.
Simplify to create an equivalent expression.
\newline
−
3
z
−
(
−
z
−
2
)
-3z-(-z-2)
−
3
z
−
(
−
z
−
2
)
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
−
4
-4
−
4
z+
2
2
2
\newline
(B)
\newline
−
2
-2
−
2
z
−
2
-2
−
2
\newline
(C)
\newline
−
2
-2
−
2
z+
2
2
2
\newline
(D)
\newline
4
4
4
z+
2
2
2
Combine like terms:
Combine like terms inside the parentheses:
−
(
−
z
−
2
)
=
z
+
2
-(-z - 2) = z + 2
−
(
−
z
−
2
)
=
z
+
2
Rewrite expression:
Rewrite the expression:
−
3
z
+
z
+
2
-3z + z + 2
−
3
z
+
z
+
2
Combine like terms:
Combine like terms:
−
3
z
+
z
=
−
2
z
-3z + z = -2z
−
3
z
+
z
=
−
2
z
Final expression:
Final expression:
−
2
z
+
2
-2z + 2
−
2
z
+
2
More problems from Average rate of change II
Question
The graphs of the functions
f
(
x
)
=
sin
(
x
)
f(x)=\sin (x)
f
(
x
)
=
sin
(
x
)
and
g
(
x
)
=
1
2
g(x)=\frac{1}{2}
g
(
x
)
=
2
1
intersect at
2
2
2
points on the interval
0
<
x
<
π
0<x<\pi
0
<
x
<
π
.
\newline
What is the area of the region bound by the graphs of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
between those points of intersection ?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
3
\frac{\pi}{3}
3
π
\newline
(B)
π
2
\frac{\pi}{2}
2
π
\newline
(C)
2
−
π
2
2-\frac{\pi}{2}
2
−
2
π
\newline
(D)
3
−
π
3
\sqrt{3}-\frac{\pi}{3}
3
−
3
π
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Posted 7 months ago
Question
What is the area of the region between the graphs of
f
(
x
)
=
x
2
+
12
x
f(x)=x^{2}+12 x
f
(
x
)
=
x
2
+
12
x
and
g
(
x
)
=
3
x
2
+
10
g(x)=3 x^{2}+10
g
(
x
)
=
3
x
2
+
10
from
x
=
1
x=1
x
=
1
to
x
=
4
x=4
x
=
4
?
\newline
Choose
1
1
1
answer:
\newline
(A)
77
77
77
\newline
(B)
64
3
\frac{64}{3}
3
64
\newline
(C)
18
18
18
\newline
(D)
45
45
45
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Posted 7 months ago
Question
What is the area of the region between the graphs of
f
(
x
)
=
x
+
1
f(x)=\sqrt{x+1}
f
(
x
)
=
x
+
1
and
g
(
x
)
=
2
x
−
4
g(x)=2 x-4
g
(
x
)
=
2
x
−
4
from
x
=
0
x=0
x
=
0
to
x
=
3
x=3
x
=
3
?
\newline
Choose
1
1
1
answer:
\newline
(A)
23
3
\frac{23}{3}
3
23
\newline
(B)
5
3
\frac{5}{3}
3
5
\newline
(C)
14
3
\frac{14}{3}
3
14
\newline
(D)
−
3
-3
−
3
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Posted 7 months ago
Question
Consider the curve given by the equation
3
x
2
+
y
4
+
6
x
=
253
3 x^{2}+y^{4}+6 x=253
3
x
2
+
y
4
+
6
x
=
253
. It can be shown that
d
y
d
x
=
−
6
(
x
+
1
)
4
y
3
.
\frac{d y}{d x}=\frac{-6(x+1)}{4 y^{3}}.
d
x
d
y
=
4
y
3
−
6
(
x
+
1
)
.
\newline
Write the equation of the horizontal line that is tangent to the curve and is above the
x
x
x
-axis.
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Posted 7 months ago
Question
The learning rate for new skills is proportional to the difference between the maximum potential for learning that skill,
M
M
M
, and the amount of the skill already learned,
L
L
L
.
\newline
Which equation describes this relationship?
\newline
Choose
1
1
1
answer:
\newline
(A)
L
(
t
)
=
k
(
M
−
L
)
L(t)=\frac{k}{(M-L)}
L
(
t
)
=
(
M
−
L
)
k
\newline
(B)
L
(
t
)
=
k
(
M
−
L
)
L(t)=k(M-L)
L
(
t
)
=
k
(
M
−
L
)
\newline
(C)
d
L
d
t
=
k
(
M
−
L
)
\frac{d L}{d t}=k(M-L)
d
t
d
L
=
k
(
M
−
L
)
\newline
(D)
d
L
d
t
=
k
(
M
−
L
)
\frac{d L}{d t}=\frac{k}{(M-L)}
d
t
d
L
=
(
M
−
L
)
k
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Posted 7 months ago
Question
What is the value of
d
d
x
(
1
x
)
\frac{d}{d x}\left(\frac{1}{x}\right)
d
x
d
(
x
1
)
at
x
=
6
x=6
x
=
6
?
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Question
What is the value of
d
d
x
(
x
)
\frac{d}{d x}(\sqrt{x})
d
x
d
(
x
)
at
x
=
9
x=9
x
=
9
?
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Posted 7 months ago
Question
What are the critical points for the plane curve defined by the equations
\newline
x
(
t
)
=
cot
t
x(t)=\cot t
x
(
t
)
=
cot
t
,
y
(
t
)
=
sin
t
y(t)=\sin t
y
(
t
)
=
sin
t
, and
\newline
0
<
t
<
π
0 < t < \pi
0
<
t
<
π
? Write your answer as a list of values of
\newline
t
t
t
, separated by commas. For example, if you found
\newline
t
=
1
t=1
t
=
1
or
\newline
t
=
2
t=2
t
=
2
, you would enter
1
,
2
1,2
1
,
2
.
\newline
Provide your answer below:
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Question
UTA WORKS
\newline
State if the pair of triangles are similar. If so, state how you know they are similar and complete the similarity statement.
\newline
Δ
U
V
W
∼
\Delta UVW \sim
Δ
U
VW
∼
\newline
- similar, SAS similarity;
\newline
-
∠
U
≅
∠
L
∠
K
\angle U\cong\angle L\angle K
∠
U
≅
∠
L
∠
K
\newline
- similar, SSS similarity;
\newline
-
∠
U
≅
∠
L
∠
K
\angle U\cong\angle L\angle K
∠
U
≅
∠
L
∠
K
\newline
- not similar
\newline
- similar, SAS similarity;
\newline
-
∠
U
≅
∠
K
∠
L
\angle U\cong\angle K\angle L
∠
U
≅
∠
K
∠
L
\newline
- similar, SSS similarity;
\newline
-
∠
U
≅
∠
K
∠
L
\angle U\cong\angle K\angle L
∠
U
≅
∠
K
∠
L
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Posted 6 months ago
Question
Geometry
\newline
> E.
5
5
5
Equations of parallel and perpendicular lines VEB
\newline
Video (D)
\newline
Questions
\newline
answered
\newline
The equation for line
\newline
v can be written as
\newline
y
=
−
9
7
x
−
5
y=-\frac{9}{7}x-5
y
=
−
7
9
x
−
5
. Line
\newline
w, which is perpendicular to line
\newline
v, includes the point
\newline
(
9
,
6
)
(9,6)
(
9
,
6
)
. What is the equation of line
\newline
w ?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
\newline
Submit
\newline
501
501
501
\newline
Time
\newline
elapsed
\newline
\newline
06
06
06
\newline
00
00
00
\newline
22
22
22
\newline
\newline
HR
\newline
MIN
\newline
SEC
\newline
\newline
Smartscore
\newline
out of
100
100
100
?
\newline
22
22
22
\newline
i
1
1
1
.
\newline
Work it out
\newline
Not feeling ready yet? These can help:
\newline
Slopes of parallel and perpendicular lines (
83
83
83
)
\newline
N
\newline
Equations of lines (
26
26
26
)
\newline
Lesson: Equations of parallel and perpendicular lines
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Posted 6 months ago
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