Which graph represents a function?

Mathematics

2 answers:

VMariaS [17]2 years ago

8 0

Answer:

Step-by-step explanation:

AVprozaik [17]2 years ago

5 0

Answer:

b and c

Step-by-step explanation:

vertical line test

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Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id

Thepotemich [5.8K]

$\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

Explanation

$\frac{1}{a+bi}=c+di$

Step 1

multiplicate by the conjugate

$\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}$

notice that

$\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\ \end{gathered}$ $\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

I hope this helsp you

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1 year ago

A square has a perimeter of 36 ft. What is the length of each side?

Yanka [14]

9 ft is the answer because a square has four sides, so 36 divided by 4 is 9

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3 years ago

If 5x-7=13x+17, what is 6(x-4)?

Luba_88 [7]

30 I believe, sorry if I am wrong, I am bad at math and history.

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