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Math Problems
Algebra 2
Find the constant of variation
Sketch an angle
θ
\theta
θ
in standard position such that
θ
\theta
θ
has the least possible positive measure, and the point
(
−
7
,
−
24
)
(-7,-24)
(
−
7
,
−
24
)
is on the terminal side of
θ
\theta
θ
. Then find the values of the six trigonometric functions for the angle. Rationalize denominators when applicable. Do not use a calculator.
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a
y
=
2
x
+
1
ay=2x+1
a
y
=
2
x
+
1
\newline
y
=
2
x
+
2
y=2x+2
y
=
2
x
+
2
\newline
Consider the system of equations, where
a
a
a
is a constant. For what value of
a
a
a
are there no
(
x
,
y
)
(x,y)
(
x
,
y
)
solutions?
\newline
□
\square
□
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10
+
7
x
=
4
x
+
2
+
b
x
10+7 x=4 x+2+b x
10
+
7
x
=
4
x
+
2
+
b
x
\newline
In the equation shown,
b
b
b
is a constant. For what value of
b
b
b
does the equation have no solutions?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
3
3
\newline
(B)
5
5
5
\newline
(C)
6
6
6
\newline
(D)
7
7
7
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х +
6
6
6
у = r -
2
2
2
х
\newline
2
2
2
(x+
4
4
4
) +
2
2
2
y =
11
11
11
+ \frac{
1
1
1
}{
2
2
2
}(
16
16
16
+
2
2
2
x)
\newline
In the system of equations, r is a constant. For what value of r does the system of linear equations have infinitely many solutions?
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The quantity
z
z
z
varies directly with
y
y
y
and inversely with
w
w
w
and
x
x
x
. When
y
=
12
y = 12
y
=
12
,
w
=
8
w = 8
w
=
8
, and
x
=
–
5
x = –5
x
=
–5
,
z
=
–
3
z = –3
z
=
–3
. What is the value of
k
k
k
, the constant of variation?
\newline
Write your answer in the form
A
A
A
or
(
A
)
(
B
)
\frac {(A)}{(B)}
(
B
)
(
A
)
, where
A
A
A
and
B
B
B
are constants or variable expressions.
\newline
____
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