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Question
\newline
What is the length of the hypotenuse in the triangle shown below?
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Math Problems
Algebra 1
Rational functions: asymptotes and excluded values
Full solution
Q.
Question
\newline
What is the length of the hypotenuse in the triangle shown below?
Identify triangle and sides:
Identify the right triangle and the sides given. Assume the sides are
3
cm
3\,\text{cm}
3
cm
and
4
cm
4\,\text{cm}
4
cm
as the legs of the triangle.
Apply Pythagorean theorem:
Apply the Pythagorean theorem, which states
a
2
+
b
2
=
c
2
a^2 + b^2 = c^2
a
2
+
b
2
=
c
2
, where
c
c
c
is the hypotenuse. Here,
a
=
3
a = 3
a
=
3
cm and
b
=
4
b = 4
b
=
4
cm.
Calculate squares:
Calculate the square of each side:
3
2
=
9
3^2 = 9
3
2
=
9
and
4
2
=
16
4^2 = 16
4
2
=
16
.
Add squares:
Add the squares of the legs:
9
+
16
=
25
9 + 16 = 25
9
+
16
=
25
.
Find hypotenuse length:
Find the square root of
25
25
25
to get the length of the hypotenuse:
25
=
5
\sqrt{25} = 5
25
=
5
cm.
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Evaluate the expression for
t
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t = -4.4
t
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Write your answer in simplest form.
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Simplify. Express your answer as a single fraction in simplest form.
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Solve for
h
h
h
.
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−
5
h
−
2
=
−
4
h
−
3
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h
−
2
−
5
=
h
−
3
−
4
\newline
There may be
1
1
1
or
2
2
2
solutions.
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h
=
h =
h
=
_____ or
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Question
What is the equation of the vertical asymptote of
y
=
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y
=
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+
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? _____
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Question
What is the excluded value for
y
=
1
x
−
9
−
9
y = \frac{1}{x - 9} - 9
y
=
x
−
9
1
−
9
?
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______
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Posted 2 months ago
Question
Simplify. Write your answer using whole numbers and variables.
\newline
9
k
+
4
9
k
2
+
4
k
\frac{9k + 4}{9k^2 + 4k}
9
k
2
+
4
k
9
k
+
4
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______
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Posted 2 months ago
Question
Divide. Write your answer in simplest form.
\newline
g
−
1
10
g
3
+
25
g
2
÷
(
g
−
1
)
\frac{g- 1}{10g^3 + 25g^2} \div (g- 1)
10
g
3
+
25
g
2
g
−
1
÷
(
g
−
1
)
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Question
Simplify. Express your answer as a single fraction in simplest form.
\newline
5
−
3
t
3
1
\frac{5 - \frac{3}{t^3}}{1}
1
5
−
t
3
3
\newline
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