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3 years ago

How many solutions are in this equation?

Mathematics

2 answers:

Serjik [45]3 years ago

4 0

There are no solutions to this!

vfiekz [6]3 years ago

3 0

9(x-4)=9x-33

9x-36=9x-33

No solution so b =0

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8. What is the domain of <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bx%5E%7B2%7D%20%2B20x%2B75%7D" id="TexFormula1" title

antiseptic1488 [7]

Answer:

8. Domain: (-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

9. Domain: [7/13, ∞)

Range: [1, ∞)

Step-by-step explanation:

Question 8

Given rational function:

$f(x)=\dfrac{x}{x^2+20x+75}$

Factor the denominator of the given rational function:

$\implies x^2+20x+75$

$\implies x^2+5x+15x+75$

$\implies x(x+5)+15(x+5)$

$\implies (x+15)(x+5)$

Therefore:

$f(x)=\dfrac{x}{(x+15)(x+5)}$

Asymptote: a line that the curve gets infinitely close to, but never touches.

The function is undefined when the denominator equals zero:

$x+15=0 \implies x=-15$

$x+5=0 \implies x=-5$

Therefore, there are vertical asymptotes at x = -15 and x = -5.

Domain: set of all possible input values (x-values)

Therefore, the domain of the given rational function is:

(-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

---------------------------------------------------------------------------------

Question 9

Given function:

$f(x)=\sqrt{13x-7}+1$

Domain: set of all possible input values (x-values)

As the square root of a negative number is undefined:

$\implies 13x-7\geq 0$

$\implies 13x\geq 7$

$\implies x\geq \dfrac{7}{13}$

Therefore, the domain of the given function is:

$\left[\dfrac{7}{13},\infty\right)$

Range: set of all possible output values (y-values)

$\textsf{As }\:\sqrt{13x-7}\geq 0$

$\implies \sqrt{13x-7}+1\geq 1$

Therefore, the range of the given function is:

[1, ∞)

8 0

1 year ago

Operations with Complex Numbers Simplify. 1) 1 + 6i 3) 3i + i 5) -1 – 8i- 4 - i

kogti [31]

1. The answer is already in its simplest form.
3. 3i + i is equal to 4i.
5. Combining like terms results in -5 - 9i.

7 0

3 years ago

A plumber charges $80 for a house call and $25 per hour for his services. Which of the following is a linear model of his charge

blsea [12.9K]

Answer:bals

Step-by-step explanation:25(number of hours worked) +80$ for initial charge

6 0

2 years ago

Read 2 more answers

A number cube is rolled 25 times. A number less than four comes up 20 times. What is the experimental probability that a number

laiz [17]

It would be 20 because the highest number is 25

4 0

2 years ago

Seven more than double a number one is equal to five less than triple that number. What is that number?

Inga [223]

Answer:

$-\frac{2}{5}$

Step-by-step explanation:

$7+2n=5-3n$

$2n+3n=5-7\\5n=-2\\n=-\frac{2}{5}$

6 0

2 years ago