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3 years ago

5

Write each of the following in completely factored form. These will involve slightly more difficult final trinomial expressions

15x^2-110x+120

2 answers:

777dan777 [17]3 years ago

7 0

Answer:

5⋅(x−6)⋅(3x−4)

Step-by-step explanation:

OLEGan [10]3 years ago

6 0

Answer: 5⋅(x−6)⋅(3x−4)

Hope this helps!

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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:

<u>Question 8</u>

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:

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

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

The function is <u>undefined</u> when the <u>denominator equals zero</u>:

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

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

Therefore, there are <u>vertical asymptotes</u> at x = -15 and x = -5.

<u>Domain</u>: set of all possible input values (x-values)

Therefore, the <u>domain of the given rational function</u> is:

(-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

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

<u>Question 9</u>

Given function:

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

<u>Domain</u>: set of all possible input values (x-values)

As the <u>square root of a negative number</u> is <u>undefined</u>:

$\implies 13x-7\geq 0$

$\implies 13x\geq 7$

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

Therefore, the <u>domain of the given function</u> is:

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

<u>Range</u>: set of all possible output values (y-values)

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

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

Therefore, the <u>range of the given function</u> is:

[1, ∞)

8 0

2 years ago

it takes Patty 1/3 of an hour to wash your car and half the time to dry it off how long will it take to get to wash and dry six

AnnyKZ [126]

It would take 20 min to wash so 20 times 6 120 then u add 60 bc there is 6 cars and it takes 10 min to dry each of them off

6 0

3 years ago

Debora [2.8K]

6x^8−10x^2+8x^2

option C

hope it helps...!!!

6 0

1 year ago

How can we describe the relationships that exist between circles and lines?

Lunna [17]

circles are 360⁰ and lines are 180⁰

5 0

2 years ago

Please help my son asked me for this and I don't understand it.

Tasya [4]

Answer:

y = 2x + 3

Step-by-step explanation:

In the slope-intercept form of the equation of a line,

y = mx + b,

m = slope, and b = y-intercept.

Let's look at Adriana's equation and understand the parts:

y = 2x + 4

y = mx + b

m = slope = 2; b = y-intercept = 4

Now let's look at the description of Henry's equation.

He has the same slope as Adriana, so for Henry, m = 2 also.

His y-intercept is 1 less than Adriana's, so it is 1 less than 4. Henry's y-intercept is 3.

Now that we know that for Henry, m = 2, and b = 3, we can write his equation.

y = mx + b

y = 2x + 3

Answer: y = 2x + 3

7 0

2 years ago

Read 2 more answers