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cricket20 [7]
3 years ago
6

What is the domain (in interval notation) of the following functions?

Mathematics
1 answer:
alexgriva [62]3 years ago
4 0
1.\\g(x)=\frac{3}{5x-4}\\\\D:5x-4\neq0\to5x\neq4\ \ \ /:5\to x\neq\frac{4}{5}\to x\in\mathbb{R}\ \backslash\ \{\frac{4}{5}\}\\\\2.\\h(x)=\frac{\sqrt{x}}{x-5}\\\\D:x\geq0\ \wedge\ x-5\neq0\to x\geq0\ \wedge\ x\neq5\to x\in\left

3.\\f(x)=\frac{\sqrt{x}}{x^2-5x}\\\\D:x\geq0\ \wedge\ x^2-5x\neq0\to x\geq0\ \wedge\ x(x-5)\neq0\\\\\to x\geq0\ \wedge\ x\neq0\ \wedge\ x\neq5\to x\in\mathbb{R^+}\ \backslash\ \{5\}\\\\4.\\g(x)=\frac{\sqrt{x}+5}{x^2-x-20}\\\\D:x\geq0\ \wedge\ x^2-x-20\neq0\to x\geq0\ \wedge\ (x+4)(x-5)\neq0\\\\\to x\geq0\ \wedge\ x\neq-4\ \wedge\ x\neq5\to x\in\left

5.\\h(x)=\frac{3}{x^2+1}\\\\D:x^2+1\neq0\to x^2\neq-1\to x\in\mathbb{R}\\\\6.\\f(x)=\frac{\sqrt{x-2}}{x+1}\\\\D:x-2\geq0\ \wedge\ x+1\neq0\to x\geq2\ \wedge\ x\neq-1\to x\in\left

7.\\g(x)=\frac{x^2}{3x^2-x-2}\\\\D:3x^2-x-2\neq0\to (3x+2)(x-1)\neq0\to x\neq-\frac{2}{3}\ \wedge\ x\neq1\\\\\to x\in\mathbb{R}\ \backslash\ \{-\frac{2}{3};\ 1\}\\\\8.\\h(x)=3(x-4)^2-7\\\\D:x\in\mathbb{R}
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1-58. Mr. Wright was making a table to figure out how much it costs to send a certain numt
Drupady [299]

A table of values can be used to represent variables that are directly proportional.

The complete table of proportions is:

\left[\begin{array}{ccccccccc}Letters&10&2&[150 ]&7&1&500&[420] \\Cost&0.45&0.90&6.75&[0.315]&[0.045 ]&[22.5 ] & 18.90\end{array}\right]

Given that

\left[\begin{array}{ccccccccc}Letters&10&2&[\ ]&7&1&500&[\ ] \\Cost&0.45&0.90&6.75&[\ ]&[\ ]&[\ ] & 18.90\end{array}\right]

Let:

<em />L \to<em> Letters</em>

<em />C \to<em> Cost</em>

<em />

Using proportional reasoning, we have:

C  = kL

Where

<em />k \to<em> ratio of proportion</em>

For the first values of C and L, we have:

C  = kL

0.45 = k \times 10

Divide both sides by 10

k = 0.045

So, the equation of proportion is:

C = 0.045L

<u>When C = 6.75, we have:</u>

C = 0.045L

6.75 = 0.045L

Solve for L

L = \frac{6.75}{0.045}

L = 150

<u>When L = 7, we have:</u>

C = 0.045L

C = 0.045 \times 7

C = 0.315

<u>When L = 1, we have:</u>

C = 0.045L

C = 0.045 \times 1

C = 0.045

<u>When L = 500, we have:</u>

C =0.045L\\

C =0.045 \times 500

C =22.5

<u>When C = 18.90, we have:</u>

C = 0.045L

18.90 = 0.045L

Solve for L

L=\frac{18.90}{0.045}

L=420

Hence, the complete table is:

\left[\begin{array}{ccccccccc}Letters&10&2&[150 ]&7&1&500&[420] \\Cost&0.45&0.90&6.75&[0.315]&[0.045 ]&[22.5 ] & 18.90\end{array}\right]

Read more about proportions at:

brainly.com/question/21126582

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2 years ago
What is the absolute value of –27? <br><br> A.<br> –27<br><br> B.<br> 27
Serga [27]
Absolute value makes it positive
answe is 27
the answer is B

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3 years ago
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$1800 at 6.5% for 30 months
nasty-shy [4]
1800×6.5%×30=b
b-1800=a

a) $1,710

b) $3,510
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25 because you would just get rid of the 2/3

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How many solutions are there to the equation below 9x+16=4x
Lina20 [59]

Answer:

one solution

Step-by-step explanation:

9x+16=4x

16=4x-9x

16/-5=x

x=-3.2

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