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3 years ago

What is the answer to this queation for my maths homework 3a+7=13

Mathematics

1 answer:

borishaifa [10]3 years ago

5 0

3a+7=13
3a+7-7=13-7
3a=6
$\frac{3a}{3}$ = $\frac{6}{3}$
a=2

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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, ∞)

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1 year ago

A rectangular prism is a three-dimensional geometric figure, hollow or solid, contained by six rectangular sides that meet at ri

jenyasd209 [6]

Answer:B. C. D.

Step-by-step explanation:

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2 years ago

The measure of an angle is nine times the measure of its complement. find the measure of each angle.

andrew11 [14]

Two angles are complementary when they add up to 90 degrees

smaller angle = x
larger angle = 9x

x + 9x = 90
10x = 90
x = 90/10
x = 9° ← smaller angle

larger angle = 9x = 9 * 9 = 81°

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3 years ago

EAST MATH PLS HELP ASAP PLEASE PLEASE

serious [3.7K]

4(x+7)=8x-20

4x+28=8x-20

28=4x-20

48=4x

x=12

7 0

3 years ago

Cameron said that the Y intercept of a quadratic function always tells the maximum value of the function. explain Cameron's erro

Leno4ka [110]

Answer:

We can have two cases.

A quadratic function where the leading coefficient is larger than zero, in this case the arms of the graph will open up, and it will continue forever, so the maximum in this case is infinite.

A quadratic function where the leading coefficient is negative. In this case the arms of the graph will open down, then the maximum of the quadratic function coincides with the vertex of the function.

Where for a generic function:

y(x) = a*x^2 + b*x + c

The vertex is at:

x = -a/2b

and the maximum value is:

y(-a/2b)

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3 years ago