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Math Problems
Grade 8
Write variable expressions for arithmetic sequences
Baind
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Math
1
1
1
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Updated:
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3
/
12
/
24
3/12/24
3/12/24
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7.7
7.7
7.7
Assigned Practice
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Name
\newline
Mattha-Burleigperiod
5
5
5
\newline
Mark the information in the diagram and then complete the flowchart proof.
\newline
1.
1.
1.
\newline
Given:
\newline
A
B
‾
≅
C
B
‾
\overline{AB} \cong \overline{CB}
A
B
≅
CB
and
\newline
D
A
‾
≅
D
C
‾
\overline{DA} \cong \overline{DC}
D
A
≅
D
C
\newline
Prove:
\newline
∠
B
A
D
≅
∠
B
C
D
\angle BAD \cong \angle BCD
∠
B
A
D
≅
∠
BC
D
\newline
List the three congruencies from the given statement or the diagram:
\newline
List Remaining Congruent Parts:
\newline
because...
\newline
Therefore...
\newline
(What you wanted to prove)
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Find the accumulation function
\newline
F
F
F
.
\newline
f
(
x
)
=
∫
−
π
x
(
3
+
sin
t
)
d
t
,
F
(
x
)
=
□
\begin{aligned} f(x) &= \int_{-\pi}^{x} (3 + \sin t) \, dt, \ F(x) &= \square \end{aligned}
f
(
x
)
=
∫
−
π
x
(
3
+
sin
t
)
d
t
,
F
(
x
)
=
□
\newline
(
a
)
(a)
(
a
)
\newline
F
(
−
π
)
=
F(-\pi) =
F
(
−
π
)
=
\newline
(
B
)
(B)
(
B
)
\newline
F
(
0
)
=
F(0) =
F
(
0
)
=
\newline
(
c
)
(c)
(
c
)
\newline
F
(
2
π
)
=
F(2\pi) =
F
(
2
π
)
=
Get tutor help
Solve for
r
r
r
.\begin{align*} \left(\frac{4}{r}\right)&=\left(\frac{5}{7}\right),\ r&= \end{align*}
Get tutor help
Solve for
t
t
t
.
(
7
3
)
=
(
4
t
)
,
t
=
\begin{align*} \left(\frac{7}{3}\right)&=\left(\frac{4}{t}\right), t&= \end{align*}
(
3
7
)
=
(
t
4
)
,
t
=
Get tutor help
Let
y
=
1
−
2
x
3
x
2
y=\frac{1-2 x}{3 x^{2}}
y
=
3
x
2
1
−
2
x
.
\newline
What is the value of
d
y
d
x
\frac{d y}{d x}
d
x
d
y
at
x
=
1
x=1
x
=
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
−
1
3
-\frac{1}{3}
−
3
1
\newline
(C)
1
1
1
\newline
(D)
1
9
\frac{1}{9}
9
1
Get tutor help
- Let
f
f
f
be a function such that
f
(
−
2
)
=
8
f(-2)=8
f
(
−
2
)
=
8
and
f
′
(
−
2
)
=
4
f^{\prime}(-2)=4
f
′
(
−
2
)
=
4
.
\newline
- Let
h
h
h
be the function
h
(
x
)
=
x
3
h(x)=x^{3}
h
(
x
)
=
x
3
.
\newline
Evaluate
d
d
x
[
f
(
x
)
h
(
x
)
]
\frac{d}{d x}\left[\frac{f(x)}{h(x)}\right]
d
x
d
[
h
(
x
)
f
(
x
)
]
at
x
=
−
2
x=-2
x
=
−
2
.
Get tutor help
- Let
g
g
g
be a function such that
g
(
−
1
)
=
5
g(-1)=5
g
(
−
1
)
=
5
and
g
′
(
−
1
)
=
6
g^{\prime}(-1)=6
g
′
(
−
1
)
=
6
.
\newline
- Let
h
h
h
be the function
h
(
x
)
=
2
x
2
h(x)=2 x^{2}
h
(
x
)
=
2
x
2
.
\newline
Evaluate
d
d
x
[
g
(
x
)
h
(
x
)
]
\frac{d}{d x}\left[\frac{g(x)}{h(x)}\right]
d
x
d
[
h
(
x
)
g
(
x
)
]
at
x
=
−
1
x=-1
x
=
−
1
.
Get tutor help
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)
64
3
\frac{64}{3}
3
64
\newline
(B)
77
77
77
\newline
(C)
45
45
45
\newline
(D)
18
18
18
Get tutor help
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)
5
3
\frac{5}{3}
3
5
\newline
(B)
−
3
-3
−
3
\newline
(C)
14
3
\frac{14}{3}
3
14
\newline
(D)
23
3
\frac{23}{3}
3
23
Get tutor help
What is the area of the region between the graphs of
f
(
x
)
=
x
+
10
f(x)=\sqrt{x+10}
f
(
x
)
=
x
+
10
and
g
(
x
)
=
x
−
2
g(x)=x-2
g
(
x
)
=
x
−
2
from
x
=
−
10
x=-10
x
=
−
10
to
x
=
6
x=6
x
=
6
?
\newline
Choose
1
1
1
answer:
\newline
(A)
64
3
\frac{64}{3}
3
64
\newline
(B)
160
160
160
\newline
(C)
320
3
\frac{320}{3}
3
320
\newline
(D)
128
128
128
Get tutor help
What is the area of the region between the graphs of
f
(
x
)
=
2
x
2
+
5
x
f(x)=2 x^{2}+5 x
f
(
x
)
=
2
x
2
+
5
x
and
g
(
x
)
=
−
x
2
−
6
x
+
4
g(x)=-x^{2}-6 x+4
g
(
x
)
=
−
x
2
−
6
x
+
4
from
x
=
−
4
x=-4
x
=
−
4
to
x
=
0
x=0
x
=
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
40
40
40
\newline
(B)
355
12
\frac{355}{12}
12
355
\newline
(C)
8
8
8
\newline
(D)
128
3
\frac{128}{3}
3
128
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Let
g
(
x
)
=
3
x
4
+
8
x
3
+
4
g(x)=3 x^{4}+8 x^{3}+4
g
(
x
)
=
3
x
4
+
8
x
3
+
4
.
\newline
What is the absolute maximum value of
g
g
g
?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
\newline
(B)
36
36
36
\newline
(C)
116
116
116
\newline
(D)
g
g
g
has no maximum value
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The differentiable functions
x
x
x
and
y
y
y
are related by the following equation:
\newline
x
y
=
4
x y=4
x
y
=
4
\newline
We are also given that
d
y
d
t
=
1
\frac{d y}{d t}=1
d
t
d
y
=
1
.
\newline
Find
d
x
d
t
\frac{d x}{d t}
d
t
d
x
when
y
=
0.5
y=0.5
y
=
0.5
.
Get tutor help
Let
f
(
x
)
=
x
−
1
−
2
x
−
5
f(x)=\frac{\sqrt{x-1}-2}{x-5}
f
(
x
)
=
x
−
5
x
−
1
−
2
when
x
≠
5
x \neq 5
x
=
5
.
\newline
f
f
f
is continuous for all
x
>
1
x>1
x
>
1
.
\newline
Find
f
(
5
)
f(5)
f
(
5
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
\frac{1}{2}
2
1
\newline
(B)
1
4
\frac{1}{4}
4
1
\newline
(C)
1
1
1
\newline
(D)
1
10
\frac{1}{10}
10
1
Get tutor help
Let
h
(
x
)
=
{
x
+
26
−
5
x
+
1
for
x
≥
−
26
,
x
≠
−
1
k
for
x
=
−
1
h(x)=\left\{\begin{array}{ll}\frac{\sqrt{x+26}-5}{x+1} & \text { for } x \geq-26, x \neq-1 \\ k & \text { for } x=-1\end{array}\right.
h
(
x
)
=
{
x
+
1
x
+
26
−
5
k
for
x
≥
−
26
,
x
=
−
1
for
x
=
−
1
\newline
h
h
h
is continuous for all
x
>
−
26
x>-26
x
>
−
26
.
\newline
What is the value of
k
k
k
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
5
-\frac{1}{5}
−
5
1
\newline
(B)
1
1
1
\newline
(C)
1
10
\frac{1}{10}
10
1
\newline
(D)
0
0
0
Get tutor help
f
(
x
)
=
{
sin
(
x
⋅
π
)
for
−
8
<
x
<
0
x
5
for
0
≤
x
≤
10
f(x)=\left\{\begin{array}{ll} \sin (x \cdot \pi) & \text { for }-8<x<0 \\ \frac{x}{5} & \text { for } 0 \leq x \leq 10 \end{array}\right.
f
(
x
)
=
{
sin
(
x
⋅
π
)
5
x
for
−
8
<
x
<
0
for
0
≤
x
≤
10
\newline
Find
lim
x
→
−
5
f
(
x
)
\lim _{x \rightarrow-5} f(x)
lim
x
→
−
5
f
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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