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3 years ago

Find the intersection point for the following linear functions. f(x) = 2x + 3 g(x) = -4x − 27

Mathematics

1 answer:

Ratling [72]3 years ago

3 0

Answer:

(- 5, - 7 )

Step-by-step explanation:

Equate f(x) and g(x), that is

2x + 3 = - 4x - 27 ( add 4x to both sides )

6x + 3 = - 27 ( subtract 3 from both sides )

6x = - 30 ( divide both sides by 6 )

x = - 5

Substitute x = - 5 into either of the 2 functions for y- coordinate

Substituting into f(x)

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

Thus point of intersection = (- 5, - 7 )

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3 years ago

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aliya0001 [1]

Answer:

Step-by-step explanation:

In the base we have the right triangle. Use the Pythagorean theorem for to calculate the hypotenuse:

$h^2=4^2+3^2\\\\h^2=16+9\\\\h^=25\to h=\sqrt{25}\\\\h=5\ ft$

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$4\ ft\ \times\ 2\ ft\to A_1=(4)(2)=8\ ft^2\\\\3\ ft\ \times\ 2\ ft\to A_2=(3)(2)=6\ ft^2\\\\5\ ft\ \times\ 2\ \ft\to A_3=(5)(2)=10\ ft^2$

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3 years ago

annual sales for a company are $149,999 and are increasing at a rate of 6% per year. write an exponential growth function to mod

elixir [45]

Answer:

S(t) = 149999(1.06)^t
$225543

Step-by-step explanation:

Initial value is $149999
Increase rate is 6% per year = 1.06 times

The model of the growth is:

S(t) = 149999(1.06)^t, where S- amount of annual sales, t- time in years, 1.06- growth rate per year

Annual sales after 7 years:

S(7) = 149999(1.06)^7 = $225543

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3 years ago

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ZanzabumX [31]

Answer:

Step-by-step explanation:

f-1(x) is the inverse of f(x)

to find the inverse let’s set the equation up like this

y = 4x -2

now we’ll switch x and y

x = 4y -2

and solve for y

x + 2 = 4y

x/4 + 2/4 = y

the inverse is

y = x/4 + 1/2

this equation is written in y = mx + b form

where b = y intercept

so the y intercept is 1/2

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3 years ago