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Math Problems
Precalculus
Find the magnitude of a vector scalar multiple
In the equation
y
=
c
x
−
10
,
c
y=c x-10, c
y
=
c
x
−
10
,
c
is a constant. If the graph of this equation in the
x
y
x y
x
y
-plane passes through the point
(
1
,
−
3
)
(1,-3)
(
1
,
−
3
)
, what is the value of
c
c
c
?
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Each of
a
a
a
and
b
b
b
can take values
1
1
1
or
2
2
2
with equal probabilty. The probability that the equation
a
x
2
+
b
x
+
1
=
0
ax^2+bx+1=0
a
x
2
+
b
x
+
1
=
0
has real roots, is equal to
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(
2
x
−
3
)
(
x
+
4
)
=
0
(2x-3)(x+4)=0
(
2
x
−
3
)
(
x
+
4
)
=
0
\newline
Let
x
=
a
x=a
x
=
a
and
x
=
b
x=b
x
=
b
be unique solutions to the given equation. What is the value of
−
a
−
b
-a-b
−
a
−
b
?
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Consider the system of equations. If
(
x
,
y
)
(x, y)
(
x
,
y
)
is the solution to the system, what is the value of the sum of
x
x
x
and
y
y
y
?
\newline
2
(
x
−
1
3
)
−
3
2
(
y
−
1
6
)
=
0
2(x-\frac{1}{3})-\frac{3}{2}(y-\frac{1}{6})=0
2
(
x
−
3
1
)
−
2
3
(
y
−
6
1
)
=
0
\newline
3
(
y
−
1
2
)
+
8
3
(
x
−
1
6
)
=
0
3(y-\frac{1}{2})+\frac{8}{3}(x-\frac{1}{6})=0
3
(
y
−
2
1
)
+
3
8
(
x
−
6
1
)
=
0
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Given
g
(
x
)
=
−
x
+
2
g(x)=-x+2
g
(
x
)
=
−
x
+
2
, solve for
x
x
x
when
g
(
x
)
=
−
4
g(x)=-4
g
(
x
)
=
−
4
.
\newline
Answer:
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Given
h
(
x
)
=
−
x
−
4
h(x)=-x-4
h
(
x
)
=
−
x
−
4
, solve for
x
x
x
when
h
(
x
)
=
4
h(x)=4
h
(
x
)
=
4
.
\newline
Answer:
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Given
f
(
x
)
=
2
x
+
2
f(x)=2 x+2
f
(
x
)
=
2
x
+
2
, solve for
x
x
x
when
f
(
x
)
=
−
4
f(x)=-4
f
(
x
)
=
−
4
.
\newline
Answer:
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Given
f
(
x
)
=
−
x
−
4
f(x)=-x-4
f
(
x
)
=
−
x
−
4
, solve for
x
x
x
when
f
(
x
)
=
−
1
f(x)=-1
f
(
x
)
=
−
1
.
\newline
Answer:
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Given
f
(
x
)
=
−
x
+
3
f(x)=-x+3
f
(
x
)
=
−
x
+
3
, solve for
x
x
x
when
f
(
x
)
=
4
f(x)=4
f
(
x
)
=
4
.
\newline
Answer:
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Given
f
(
x
)
=
2
x
−
2
f(x)=2 x-2
f
(
x
)
=
2
x
−
2
, solve for
x
x
x
when
f
(
x
)
=
−
2
f(x)=-2
f
(
x
)
=
−
2
.
\newline
Answer:
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Given
h
(
x
)
=
−
x
+
4
h(x)=-x+4
h
(
x
)
=
−
x
+
4
, solve for
x
x
x
when
h
(
x
)
=
−
8
h(x)=-8
h
(
x
)
=
−
8
.
\newline
Answer:
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Given
h
(
x
)
=
−
x
+
1
h(x)=-x+1
h
(
x
)
=
−
x
+
1
, solve for
x
x
x
when
h
(
x
)
=
6
h(x)=6
h
(
x
)
=
6
.
\newline
Answer:
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Given
f
(
x
)
=
−
x
−
2
f(x)=-x-2
f
(
x
)
=
−
x
−
2
, find
f
(
−
1
)
f(-1)
f
(
−
1
)
.
\newline
Answer:
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Given
f
(
x
)
=
−
x
−
3
f(x)=-x-3
f
(
x
)
=
−
x
−
3
, find
f
(
−
1
)
f(-1)
f
(
−
1
)
.
\newline
Answer:
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The sum of a number and
18
18
18
is
−
29
-29
−
29
\newline
The equation is
□
\square
□
. (Do not simplify.)
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y
=
x
(
x
−
3
)
(
x
−
2
)
y = x(x - 3)(x - 2)
y
=
x
(
x
−
3
)
(
x
−
2
)
what is the value of
y
y
y
when
x
=
3
x = 3
x
=
3
?
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