|-4|+|19|=? Helpppppppppp

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

2 years ago

What is the respond for 4(b-6)+19

vlabodo [156]

So I think you’re asking for the solution to the equation mentioned.

The answer would be 4b-5

Explanation:
Steps:

4(b-6)+19

4b-24+19

4b-5 (Answer)

4 0

3 years ago

Anyone know how to do this? I need an answer fast show work please it’s 11:19 for me in California in 40 minutes I won’t need th

Anarel [89]

Answer:

Answer is 30.25

hope it helps u

5 0

2 years ago

Read 2 more answers

The radius of a sphere and of a cylinder are the same. The diameter of the sphere and the height of the cylinder are also the sa

emmasim [6.3K]

First we have to know the formula of the volume f each of the solids,

V of sphere = 4/3 pi r^3
Volume of Cylinder = pi r^2(2r)=2pi r^3
Volume of cone = 1/3 pi r^2(r)=1/3 pi r^3

The surest and easiest way we can answer this is actually assigning values. We first assign values to r hence we would get the volume of the sphere and rest of the solids (cylinder and cone). You then compare your answers to that of the sphere, and you should get your answer.

4 0

3 years ago

A triangular prism has base edges 4cm, 5cm, and 6cm long. Its lateral area is 300 cm2. What's the height if the prism?

almond37 [142]

Answer: For your specific problem, h = 300 / (4 + 5 + 6) = 300 / 15 = 20

Step-by-step explanation:

4 0

3 years ago