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3 years ago

Precalc help needed convert y = x^2 − x −6 to vertex form

Mathematics

2 answers:

Nadya [2.5K]3 years ago

5 0

I think it would it be -6,-4

statuscvo [17]3 years ago

3 0

Rewrite in standard form and use this form to find the vertex (h,k)
(1/2, -25/4)

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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

2 years ago

Consider the procedure used below to solve the given equation.

slavikrds [6]

Answer is D you can plug it in to check it as well

5 0

3 years ago

Find X and the measure of each angle

Taya2010 [7]

Answer:

x = 68

Step-by-step explanation:

sum of interior angles of 5-sided figure is 3(180°) or 540°

5x + 200 = 540

5x = 340

x = 68

5 0

3 years ago

What is an expression equivalent to 5x+10 using the distributive property?

Crank

Answer:

5x + 10

Step-by-step explanation:

I did the math and checked. :)

5 0

3 years ago

The estimated product of two numbers that are not multiples of 10 is 2800. what is the question?

Nitella [24]

You need to find the 2 numbers that will estimate to the nearest hundred.
here is your answer 13 x 213

4 0

3 years ago