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3 years ago

Find the intersection point for the following liner function f(x)= 2x+3 g(x)=-4x-27

Mathematics

1 answer:

Leona [35]3 years ago

5 0

Answer:

( -5,-7)

Step-by-step explanation:

f(x)= 2x+3 g(x)=-4x-27

Set the two functions equal

2x+3 = -4x-27

Add 4x to each side

2x+3+4x = -4x-27+4x

6x+3 = -27

Subtract 3

6x+3 - 3 = -27-3

6x = -30

Divide each side by 6

6x/6 = -30/6

x =-5

Now we need to find the output

f(-5) = 2(-5) +3 = -10+3 = -7

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What is the total floor area in inches of a rectangular floor 8ft. by 6ft.?

Anestetic [448]

Answer:the answeer is

= 72 ft³

Step-by-step explanation:

Multiply the width of the wall by its height. So one of the walls is 80 square feet (10 feet wide x 8 feet high) and the other is 96 square feet (12 feet x 8 feet). If you need the total square footage of the walls - for figuring paint or wallpaper for example - you can simplify the calculation by first adding all the wall lengths together, then multiplying by the height (10 + 12 + 10 + 12 = 44 x 8 = 352 square feet of total wall area).

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3 years ago

A television screen, length is 16 1/2 inches, width is w inches, and area is 462 square inches. Select all THREE equations that

tatiyna

Answer:

it's B, C, and D

Step-by-step explanation:

A. w ⋅ 462 = 16 1/2

not A

w * a ≠ l

B. 16 1/2 ⋅ w = 462

is B

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C. 462 ÷ 16 1/2 = w

is C

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D. 462 ÷ w = 16 1/2

is D

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2 years ago

What is the probability that both spinners land on red or orange?

yawa3891 [41]

Answer:

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Step-by-step explanation:

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3 years ago

Find the radius of convergence, r, of the series. ? n2xn 7 · 14 · 21 · ? · (7n) n = 1

defon

I'm guessing the series is supposed to be

$\displaystyle\sum_{n=1}^\infty\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}$

By the ratio test, the series converges if the following limit is less than 1.

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7\cdot14\cdot21\cdot\cdots\cdot(7n)\cdot(7(n+1))}}{\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}}\right|$

The first $n$ terms in the numerator's denominator cancel with the denominator's denominator:

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7(n+1)}}{n^2x^n}\right|$

$|x^n|$ also cancels out and the remaining factor of $|x|$ can be pulled out of the limit (as it doesn't depend on $n$ ).

$\displaystyle|x|\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2}{7(n+1)}}{n^2}\right|=|x|\lim_{n\to\infty}\frac{|n+1|}{7n^2}=0$

which means the series converges everywhere (independently of $x$ ), and so the radius of convergence is infinite.

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3 years ago