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3 years ago

If f(x) = 3x + 2 and

Mathematics

1 answer:

WARRIOR [948]3 years ago

5 0

Answer:

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) = 3x + 2, g(x) = 2x - 2.

Substitute:

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

<em>combine like terms</em>

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

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Solve the system of equations:

Sophie [7]

The solution of the system of equations is (6 , -7)

Step-by-step explanation:

There are two method to solve the system of equations

Elimination method: we make the coefficients of one variable in the two equations have same values and different signs, then we add the two equations to eliminate this variable and have an equation of other variable, we solve it to find the other variable, then substitute the value of this variable in one of the two equations to find the first variable
Substitution method: We use one of the two equations to find one variable in terms of the other, then substitute it in the second equation to have an equation of the other variable, we solve it to find the other variable, then substitute the value of this variable in the equation of the first variable

Let us use the elimination method with your problem

∵ 3x + 2y = 4 ⇒ (1)

∵ 3x + 6y = -24 ⇒ (2)

- Multiply equation (1) by -1 to eliminate x ⇒ to make the coefficients of x in the two equations have same values and different signs

∵ -3x - 2y = -4 ⇒ (3)

- Add equations (2) and (3)

∴ 4y = -28

- Divide both sides by 4

∴ y = -7

Substitute value of y in equations (1) OR (2) to find x

∵ 3x + 2(-7) = 4

∴ 3x - 14 = 4

- Add 14 for both sides

∴ 3x = 18

- Divide both sides by 3

∴ x = 6

The solution of the system of equations is (6 , -7)

<em>I hope this explanation help you</em>

Learn more:

You can learn more about the system of linear equations in brainly.com/question/6075514

#LearnwithBrainly

3 0

3 years ago

Which are the numbers that are common multiples of 6 and 8. 12 18 24 30 40 48

snow_lady [41]

12 and 24.
Because
6=2*3
8=2*4

And 12=2*3*4
24=2*3*4*2
General rule: Try to find the factors of given numbers and multiply them in various cominations to get results.

5 0

3 years ago

Describe the end behavior of the following exponential function.

oee [108]

Answer:

C. As the x-values increase, the function increases towards positive infinity.

Step-by-step explanation:

4 0

3 years ago

Julie and her family go to the movies. They buy 2 adult tickets and 3 child tickets. An adult ticket costs $3.50 more than a chi

EastWind [94]

Answer:

$9.25

Step-by-step explanation:

let x = the cost of a child ticket

3(x)+2(x+3.50)=35.75

3x+2x+7=35.75

5x=28.75

x=5.75 cost of child ticket

5.75+3.50= 9.25

7 0

3 years ago

Read 2 more answers

ace bike rentals rents bikes for $28 per day. Renters can keep the bike for 8 hours. Bart's bikes rents bikes for $30 per day. R

lyudmila [28]

Bart company charges a lower rate. It is lower by rate $ 0.5 per hour

<h3><u>Solution:</u></h3>

Given that Ace bike rentals rents bikes for $28 per day. Renters can keep the bike for 8 hours

Also given that Bart's bikes rents bikes for $30 per day. Renters can keep the bike for 10 hours

To find: company that charges lower rate

Let us find the hourly rate of Ace and Bart

$\text {hourly rate }=\frac{\text { Rental price }}{\text { total time in a day }}$

<em><u>Hourly rate of Ace company:</u></em>

Rental price = $28

total time in a day 8 hours

$\text {hourly rate }=\frac{28}{8}=3.5$

So the hourly rate of Ace company is $ 3.5 per hour

<em><u>Hourly rate of Bart company:</u></em>

Rental price = $ 30

total time in a day 10 hours

$\text {hourly rate }=\frac{30}{10}=3$

So the hourly rate of Bart company is $ 3 per hour

<em><u>Comparing hourly rate of both companies</u></em>

Ace company is $ 3.5 per hour

Bart company is $ 3 per hour

Bart company < Ace company

3 < 3.5

Thus bart company charges a lower rate

<h3><em><u>How much lower?</u></em></h3>

hourly rate of Ace company - hourly rate of Bart company = 3.5 - 3 = 0.5

So, it is lower by rate $0.5 per hour

6 0

3 years ago