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Math Problems
Algebra 1
Properties of matrices
Matt solved the equation
3
(
z
+
1
)
−
2
=
4
z
−
z
−
1
3(z + 1) - 2 = 4z - z - 1
3
(
z
+
1
)
−
2
=
4
z
−
z
−
1
. Here are his last two steps:
\newline
3
z
+
1
=
3
z
−
1
3z + 1 = 3z - 1
3
z
+
1
=
3
z
−
1
\newline
1
=
−
1
1 = -1
1
=
−
1
\newline
Which statement is true about the equation?
\newline
(A) The solution is
z
=
−
1
z = -1
z
=
−
1
.
\newline
(B) There is no solution because
1
=
−
1
1 = -1
1
=
−
1
is a false equation.
\newline
(C) There are infinitely many solutions because
1
=
−
1
1 = -1
1
=
−
1
is a false equation.
\newline
(D) The solution is
(
1
,
−
1
)
(1, -1)
(
1
,
−
1
)
.
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已知
\newline
△
A
B
C
\triangle ABC
△
A
BC
中,
\newline
A
C
=
8
AC=8
A
C
=
8
,
A
B
=
41
AB=\sqrt{41}
A
B
=
41
,
B
C
BC
BC
边上的高
\newline
A
G
=
5
AG=5
A
G
=
5
,
D
D
D
为线段
\newline
A
C
AC
A
C
上的动点, 在
\newline
B
C
BC
BC
上截取
\newline
C
E
=
A
D
CE=AD
CE
=
A
D
, 连接
\newline
A
E
,
B
D
AE,BD
A
E
,
B
D
, 则
\newline
A
C
=
8
AC=8
A
C
=
8
0
0
0
的最小值为
\newline
A
C
=
8
AC=8
A
C
=
8
1
1
1
题图
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h
(
t
)
=
−
4.9
t
2
+
9.8
t
+
39.2
h(t)=-4.9 t^{2}+9.8 t+39.2
h
(
t
)
=
−
4.9
t
2
+
9.8
t
+
39.2
\newline
Kaia throws a stone vertically upward from a bridge. The height, in meters, of the stone above the water
t
t
t
seconds after the throw can be modeled by the quadratic function given. How many seconds after the throw does the stone hit the water?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
2
2
2
\newline
(C)
4
4
4
\newline
(D)
8
8
8
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2
(
x
−
1
3
)
−
3
2
(
y
−
1
6
)
=
0
3
(
y
−
1
2
)
+
8
3
(
x
−
1
6
)
=
0
\begin{aligned} 2 \left( x - \dfrac{1}{3} \right) - \dfrac{3}{2} \left( y - \dfrac{1}{6} \right) &= 0\ 3 \left(y - \dfrac{1}{2} \right) + \dfrac{8}{3} \left( x - \dfrac{1}{6} \right) &= 0 \end{aligned}
2
(
x
−
3
1
)
−
2
3
(
y
−
6
1
)
=
0
3
(
y
−
2
1
)
+
3
8
(
x
−
6
1
)
=
0
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7
x
+
10
y
=
60
7
x
−
2
y
=
240
\begin{aligned} 7x+10y&=60 \ 7x-2y&=240 \end{aligned}
7
x
+
10
y
=
60
7
x
−
2
y
=
240
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Answer the following True or False.
\newline
If
∫
a
b
f
(
x
)
d
x
\int_{a}^{b} f(x) \, dx
∫
a
b
f
(
x
)
d
x
converges and
a
<
c
<
b
a < c < b
a
<
c
<
b
, then
∫
a
c
f
(
x
)
d
x
\int_{a}^{c} f(x) \, dx
∫
a
c
f
(
x
)
d
x
also converges.
\newline
True
\newline
False
\newline
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Given the functions
f
(
x
)
=
4
x
3
f(x)=4 x^{3}
f
(
x
)
=
4
x
3
and
g
(
x
)
=
4
⋅
3
x
g(x)=4 \cdot 3^{x}
g
(
x
)
=
4
⋅
3
x
, which of the following statements is true?
\newline
f
(
3
)
=
g
(
3
)
f(3)=g(3)
f
(
3
)
=
g
(
3
)
\newline
f
(
3
)
>
g
(
3
)
f(3)>g(3)
f
(
3
)
>
g
(
3
)
\newline
f
(
3
)
<
g
(
3
)
f(3)<g(3)
f
(
3
)
<
g
(
3
)
Get tutor help
Given the functions
f
(
x
)
=
5
x
4
f(x)=5 x^{4}
f
(
x
)
=
5
x
4
and
g
(
x
)
=
4
⋅
3
x
g(x)=4 \cdot 3^{x}
g
(
x
)
=
4
⋅
3
x
, which of the following statements is true?
\newline
f
(
3
)
=
g
(
3
)
f(3)=g(3)
f
(
3
)
=
g
(
3
)
\newline
f
(
3
)
<
g
(
3
)
f(3)<g(3)
f
(
3
)
<
g
(
3
)
\newline
f
(
3
)
>
g
(
3
)
f(3)>g(3)
f
(
3
)
>
g
(
3
)
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Question
17
17
17
\newline
2
2
2
pts
\newline
True or False. Determine whether the statement is correct.
5
5
5
is included as a solution in the solution set for
[
8
,
∞
[8, \infty
[
8
,
∞
)
\newline
True
\newline
False
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True or False. Determine whether the statement is correct. ＂
X
X
X
is greater than or equal to
9
9
9
can be represented
x
≤
9
x \leq 9
x
≤
9
.＂
\newline
True
\newline
False
\newline
4
4
4
. Previous
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True or False. Determine whether the statement is correct.
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True or False. Determine whether the statement is correct.
{
x
∣
x
≥
5
}
\{x\mid x \geq 5\}
{
x
∣
x
≥
5
}
means that
8
8
8
can be a value for
x
x
x
.
\newline
True
\newline
False
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Answer the following True or False.
\newline
∫
8
x
d
x
=
8
x
+
C
ln
8
\int 8^x \, dx = \frac{8^x + C}{\ln 8}
∫
8
x
d
x
=
l
n
8
8
x
+
C
\newline
True
\newline
False
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Answer the following True or False. For all
1
<
a
<
b
1 < a < b
1
<
a
<
b
,
∫
a
b
x
2
d
x
>
∫
a
b
x
d
x
\int_{a}^{b} x^{2} \, dx > \int_{a}^{b} x \, dx
∫
a
b
x
2
d
x
>
∫
a
b
x
d
x
.
\newline
True
\newline
False
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Answer the following True or False.
\newline
Since
d
d
x
3
x
1
3
=
x
−
2
3
\frac{d}{dx}3x^{\frac{1}{3}}=x^{-\frac{2}{3}}
d
x
d
3
x
3
1
=
x
−
3
2
, the fundamental theorem of calculus tells us that
∫
−
1
1
x
−
2
3
d
x
=
3
(
1
1
3
)
−
3
(
−
1
)
1
3
=
6
\int_{-1}^{1}x^{-\frac{2}{3}}dx=3(1^{\frac{1}{3}})-3(-1)^{\frac{1}{3}}=6
∫
−
1
1
x
−
3
2
d
x
=
3
(
1
3
1
)
−
3
(
−
1
)
3
1
=
6
.
\newline
True
\newline
False
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Answer the following True or False.
\newline
∫
−
a
a
(
3
x
3
+
9
x
)
d
x
=
0
\int_{-a}^{a}(3x^{3}+9x)dx=0
∫
−
a
a
(
3
x
3
+
9
x
)
d
x
=
0
\newline
True
\newline
False
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Answer the following True or False.
\newline
Suppose
a
a
a
and
b
b
b
are both positive real numbers. Then
∫
a
b
1
x
2
d
x
=
∫
−
b
−
a
1
x
2
d
x
.
\int_{a}^{b}\frac{1}{x^{2}}dx=\int_{-b}^{-a}\frac{1}{x^{2}}dx.
∫
a
b
x
2
1
d
x
=
∫
−
b
−
a
x
2
1
d
x
.
\newline
True
\newline
False
\newline
Next Question
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Answer the following True or False.
\newline
∫
1
sec
x
d
x
=
ln
(
sec
x
)
+
C
\int \frac{1}{\sec x}\,dx = \ln(\sec x) + C
∫
s
e
c
x
1
d
x
=
ln
(
sec
x
)
+
C
\newline
True
\newline
False
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Answer the following True or False.
\newline
∫
3
x
d
x
=
3
x
+
C
ln
3
\int 3^{x}\,dx = \frac{3^{x} + C}{\ln 3}
∫
3
x
d
x
=
l
n
3
3
x
+
C
\newline
True
\newline
False
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