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3 years ago

Determine the vertical asymptote for the rational function f(x) = x - 4 over 2x + 3.

Mathematics

1 answer:

mr_godi [17]3 years ago

3 0

Vertical asymptotes happen at x=a if the function is undefined at x=a.

This is a rational functions, and rational functions are not defined when the denominator is zero, since you can't divide by zero.

In this case, the denominator is zero if

$2x+3=0 \iff 2x=-3 \iff x=-\drac{3}{2}$

And thus the function has a vertical asymptote at x= -3/2

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Brandi needs to wrap a birthday present for her friend's party. Each side length is 16.7 in. What is the minimum amount of paper

tester [92]

A box has 6 sides so you multiply 16.7 and 6 and you’ll get 100.2
ANSWER IS 100.2in

3 0

3 years ago

A gardener makes a new circular flower bed. The bed is teen feet in diameter. Calculate the circumference and the area of the ci

KATRIN_1 [288]

Answer:

I. Circumference of circular flower bed = 31.42 ft.

II. Area of circular flower bed = 78.55 ft²

Step-by-step explanation:

Given the following data;

Diameter = 10 ft

Radius = diameter/2

Radius = 10/2

Radius, r = 5 ft

I. To find the circumference of the circular flower bed;

Circumference of circle = 2πr

Substituting into the formula, we have

Circumference of circular flower bed = 2*3.142*5

Circumference of circular flower bed = 31.42 ft

II. To find the area;

Area of circle = πr²

Substituting into the formula, we have;

Area of circular flower bed = 3.142*5²

Area of circular flower bed = 3.142*25

Area of circular flower bed = 78.55 ft²

8 0

3 years ago

Joe's annual income has been increasing each year by the same dollar amount. The first year his income was $17 comma 90017,900

Vedmedyk [2.9K]

Answer:

In 17th year, his income was $30,700.

Step-by-step explanation:

It is given that the income has been increasing each year by the same dollar amount. It means it is linear function.

Income in first year = $17,900

Income in 4th year = $20,300

Let y be the income at x year.

It means the line passes through the point (1,17900) and (4,20300).

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ , then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of line is

$y-17900=\frac{20300-17900}{4-1}(x-1)$

$y-17900=\frac{2400}{3}(x-1)$

$y-17900=800(x-1)$

$y-17900=800x-800$

Add 17900 on both sides.

$y=800x-800+17900$

$y=800x+17100$

The income equation is y=800x+17100.

Substitute y=30,700 in the above equation.

$30700=800x+17100$

Subtract 17100 from both sides.

$30700-17100=800x$

$13600=800x$

Divide both sides by 800.

$\frac{13600}{800}=x$

$17=x$

Therefore, in 17th year his income was $30,700.

5 0

4 years ago

In ΔJKL, the measure of ∠L=90°, LJ = 2.8 feet, and JK = 9.3 feet. Find the measure of ∠J to the nearest tenth of a degree.

Inga [223]

Answer:72.5

Step-by-step explanation:

On delta

8 0

3 years ago

Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that

Thepotemich [5.8K]

Answer:

$6750 in the bank account and $20,250 in the stock fund

Step-by-step explanation:

If B is the money they put in the bank and S is the amount they put in the stock fund, then:

B + S = 27000

1.024 B + 1.072 S = 1.06 × 27000

Solving the system of equations:

1.024 (27000 − S) + 1.072 S = 28620

27648 − 1.024 S + 1.072 S = 28620

0.048 S = 972

S = 20250

B = 27000 − S

B = 6750

They should put $6750 in the bank account and $20,250 in the stock fund.

6 0

3 years ago