Two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.
Which functions could be the result of the combinations? Select two options.
16x - 12
17x - 12
72x? - 96x
72x2 - 108
72x2 - 204x + 144

Answers

Answer 1
Final answer:

Adding two linear functions results in a linear function, which could be represented as '16 x - 12' or '17 x - 12'. Multiplying two linear functions results in a quadratic function, which could be represented as '72 x² - 204 x + 144'.

Explanation:

In this scenario, when the two linear functions are being combined by addition and multiplication, it results in an expression that could be either linear or quadratic. When you add two linear functions together: f(x) = ax + b and g(x) = cx + d, the result is also a linear function: h(x) = (a+c)x + (b+d). Therefore, both 16 x - 12 and 17 x - 12 could be the result of an addition of two linear functions.

However, when you multiply two linear functions, you get a quadratic function: i(x) = (ax + b)(cx + d) = acx^2 + (ad+bc)x + bd. So 72 x² - 204 x + 144 could be the result of a multiplication of two linear functions.

Learn more about Combining Functions here:

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Related Questions

It takes Jill 2 hours to run 14.5 miles, At this rate, how far could she run in 3 hours? Btw, I am giving a lot of points if you get it correct!

Answers

Answer:

21.75

Step-by-step explanation:

To find how long she can run in a single mile, divide 14.5 by 2, giving you 7.25. If she runs three of those, (3 times 7.25), she runs 21.75 miles.

Answer: 21.75miles

Step-by-step explanation:

Let the number of miles for 3 hours be represented as x

If 2 hours = 14.5 miles

Then, 3 hours = x

We Cross multiply

2x = 14.5 × 3

2x = 43.5

Divide both sides by 2

x = 43.5/2

x = 21.75

In 3 hours, Jill will be able to run 21.75miles. I hope this helps.

15) Yanni received her monthly credit card statement in the mail, the summary of which is shown below. When she
calculated the new balance for the month, she arrived at a different amount than the credit card company. What
should be the correct new balance?
SUMMARY
Previous
Balance
$3,589
Payments
Credits
$130.00
Transactions
$275,00
Late
Charge
$0.00
Average
Daily
Balance
$3,558.71
Finance
Charge
$82.28
Days
in Billing
Cycle
Now
Balance
$3,796.28
Minimum
Payment
$100.00
Monthly
Periodic
Rate
1.75%
Total Credit Line
Total Available Credit
$ 10.000.00
$6,203.72
APR
21%
$3,576.28
$3,676.28
B.
C. $3,766.28
D. $3,776.28

Answers

Answer:

  D.  $3,776.28

Step-by-step explanation:

The finance charge should be ...

  $3558.71 × 1.75% = $62.28 . . . . . . not $82.28

The new balance should be $20 less than what is shown, so should be ...

  $3,776.28

Answer:

I believe the answer is D

Step-by-step explanation:

Joyce is thinking of a 3 - digit number. Her number has the digits 8,4, and 6. To the nearest hundred, it rounds to 600. What is the number?

Answers

Answer:

684 :)

Step-by-step explanation:

Joyce's number is 648.

To determine Joyce's number, we need to use the information that it has the digits 8, 4, and 6, and it rounds to 600 to the nearest hundred. Here's how we can approach this:

The number must round to 600, so it must be closer to 600 than to 500 or 700. This means it must be in the range 550 to 649.We need to form numbers using the digits 8, 4, and 6: 486, 468, 846, 864, 684, and 648.Comparing these numbers, only 648 falls within the range of 550 to 649.

Therefore, Joyce's number is 648.

he solid shown has two square faces and four rectangular faces. A plane intersects the solid at vertices R, S, T, and U. What is the shape of this plane?

A. square

B. rectangle
C. right triangle
D. scalene triangle

Answers

I think the answer is D.

Answer:

hi idiot its b

not d

Step-by-step explanation:

Translate this sentence into an equation. 153 is the product of Greg’s score and 9. Use the variable g to represent Greg’s score

Answers

Answer:

9g = 153

Step-by-step explanation:

Product means multiplication.

"the product of Greg’s score and 9" translates to 9g

"is" means "is equal to"

9g = 153

Mike, Chris, and John decided to go running. Mike can run 4 miles per hour, Chris
can run 6 miles per hour, and John can run 5 miles per hour. Mike ran for 1 hour
and 45 minutes, Chris ran 70 minutes, and John ran for 90 minutes. What was
the total amount of miles that they combined to run?

1. 25.5 miles
2. 25 miles
3. 21 miles
4. 21.5 miles
5. 22.5 miles

Answers

Answer:

21.5 miles total

Step-by-step explanation:

First, identify what you know:

1) Mike can run 4 mph, and runs a total of 1 hour, and 45 minutes (105 min)

2) Chris can run 6 mph, and runs a total of 70 minutes.

3) John can run 5 mph, and runs a total of 1 hour, and 30 minutes (90 min)

We need to calculate how many miles each person ran, and then add the miles ran, to find the total!

Mike: 1 hour and 45 minutes it equal to 1.75! So, in one hour, Mike ran 4 miles. He ran 3/4 of 4 mph, in 3/4 of an hour! Thus, Mike ran 7 miles. Simply multiply 1.75 by 4, to get 7 mph.

Chris: Chris ran 6 mph for 70 minutes. 6 mph, means that Chris can run one mile per every ten minutes! In 70 minutes, he'll have run 7 miles.

John: If john ran 90 minutes, that means he ran 1.5 hours! Simply multiply 1.5 by 5 mph, to get 7.5 miles!

Now, all we need to do, is add the totals!

7 + 7 + 7.5 = 21.5

In total, Mike, Chris, and John ran 21.5 miles!

Hope this helps! :)

The total amount of miles they ran was 21.5 miles

Which is bigger 2/3 1/8 or 3/4

Answers

Answer:

3/4

Step-by-step explanation:

2/3= 0.6

1/8= 0.125

3/4= 0.75

I convert the fractions into decimals the decimal with the highest number in the tenths place is the biggest

Hope This Helps!

Answer:

3/4

Step-by-step explanation:

if you convert them all to have the same denominator you find that 3/4 has the biggest numerator.

2/3 = 16/24

1/8 = 3/24

3/4 = 18/24 ← has the greatest numerator so it's the greatest

Ronaldo is carving a sculpture is made up of two figures, a rectangular prism and a square prism

Answers

Answer:

84 cubic

Step-by-step explanation:

Answer:

Step-by-step explanation: 361 1/2

20 POINTS!!! PLEASE ANSWER CORRECTLY!
Olivia is buying juice boxes for a party. She is comparing two brands to determine the best price. A case of All Natural Juice costs $2.80 and has 8 boxes of juice. A case of Just Juice costs $1.98 and has 6 boxes of juice.

(a) What is the unit price (cost per box) for All Natural Juice?

(b) What is the unit price (cost per box) for Just Juice?


(c) She spends $8.40 on several cases of All Natural Juice. She wants to buy the same number of boxes of Just Juice. How many cases of Just Juice will she need to buy?

(d) How much will the cases of Just Juice from problem (c) cost?

Answers

Answer:

a) $0.35

b) $0.33

c) 4 cases

d) $7.92

Step-by-step explanation:

a) 2.80/8 = $0.35

b) 1.98/6 = $0.33

c) 8.40/2.4 = 3

3 cases = 3×8 = 24 boxes

24/6 = 6 cases of Just Juice

d) 4 × 1.98 = $7.92

1458+3. Use multiplication to check answer. Show work?

Answers

1458+ 3 = 1461 just add three

Answer:

1461

Step-by-step explanation:

1458 + 3 = 1461

1458 + 3

3(486 + 1)

3(487)

1461

Paula leaned a 10 ft ladder against a building as shown below. if Paula wants the top of the ladder to reac
h exactly 5 feet up in the building, what is x the distance between the building and the base of the ladder, in feet?

Answers

The distance between the building and the base of the ladder is 5√3 feet.

Step-by-step explanation:

Consider a right angle triangle,

Hypotenuse = Paula leaned a 10 ft ladder against a building.Height = the top of the ladder is exactly 5 feet up in the building.Base = 'x' ft, distance between the building and the base of the ladder.

From the Pythagorean theorem,

Base, x = [tex]\sqrt{hypotenuse^{2}-height^{2} }[/tex]

⇒ x = [tex]\sqrt{10^{2} -5^{2} }[/tex]

⇒ x = [tex]\sqrt{100-25}[/tex]

⇒ x = [tex]\sqrt{75}[/tex]

x = 5√3

The distance between the building and the base of the ladder is 5√3 feet.

Can I get help please ?

Answers

Answer:

8

Step-by-step explanation:

1) let’s take the original number as “x”

So

3x=28-0.5x

Lol don’t worry I’ll show you how I got that

So it says 3 times a number. That tells me my number, X is multiplied by 3 so I have

3x so far

Next it says “is equal to”, this tells me my number 3x is equal to something so I have this now:

3x=

After that it says “half of a number” so I know I will have 0.5x subtracted from 28. Since it says subtracted from 28 that means my number will be subtracted from 28, not the other way around so

3x=28-0.5X

Now I can solve this by bringing “-0.5” to the left.

3x+0.5x=28

3.5x=28

Divide both sides by 3.5 and

X=8

what is the volume of a sphere with a radius of 5 meters rounded to the nearest square meter.
560m
314m
340m
524m

Answers

Step-by-step explanation:

V = 4/3 π r³

V = 4/3 π (5 m)³

V = 524 m³

Final answer:

The volume of a sphere with a radius of 5 meters rounded to the nearest whole number is 524 cubic meters, calculated using the formula V = (4/3)πr³.

Explanation:

The question is asking for the volume of a sphere with a radius of 5 meters. To find the volume of a sphere, we use the formula V = (4/3)πr³, where V is the volume and r is the radius of the sphere. In this case, the radius r is given as 5 meters.

Plugging in the values, we get:
V = (4/3)π(5³) = (4/3)π(125) = 523.6 cubic meters.
When we round to the nearest whole number, we get 524 cubic meters.

Therefore, the correct answer from the options provided is 524m³.

y=-5x - 1 What is the slope?​

Answers

Answer:

Slope is -5

Step-by-step explanation:

The slope is the number attached to the x.

In this problem:  y = -5x - 1, the slope is -5 because it is the number attached to the x

Example:  y = -23/5x + 6

In this case, the slope is -23/5 because it is the number attached to the x.

Answer:  Slope is -5

choose yes or no for each question will mark brainlist :) !!

Answers

Answer:

1. No

2. Yes

3. No

4. Yes

Step-by-step explanation:

Hope this helped!

what is 15/21 subtracted by 5/7 equal ?

Answers

Answer:

0

Step-by-step explanation:

Step 1:  Make common denominators

What is the LCM of 21 and 7:  7

So, we need to convert both fractions into a 21 denominator.

15/21 * 1/1 = 15/21

5/7 * 3/3 = 15/21

Step 2:  Subtract the numbers

15/21 - 5/7 is same as 15/21 - 15/21

15/21 - 15/21

0

Answer:  0

Answer:

10 over 7 is the answer

Step-by-step explanation:

(-45-24v^2+v^4-22v-6v^3)/(v-9)

Answers

Answer:

If my 15 year old brain has functioned correctly, the answer is v^3+3v^2+3v+5

Step-by-step explanation:


Will y’all help me on num 9!

Answers

Answer:

Option C, Ryder owed his mom $2.50.  He babysits his sister and makes $8.75

Step-by-step explanation:

Since it starts at 0 and goes to -2.5, that means that he owes $2.50

Since it goes from -2.5 to 6.25, that means that he ears $8.75

Answer:  Option C, Ryder owed his mom $2.50.  He babysits his sister and makes $8.75


A company launches two new products. The market price, in dollars, of the two products after a different number of years, x, is shown in the following table:


Product Function Year 1
(dollars) Year 2
(dollars) Year 3
(dollars)
Product 1 g(x) = x2 + 11 12 15 20
Product 2 h(x) = 4x 4 16 64


Based on the data in the table, for which product does the price eventually exceed all others, and why?
Product 1, because it has a greater start value
Product 1, because the function is exponential
Product 2, because it has a higher Year 3 value
Product 2, because the function is exponential

Answers

Answer: I believe the answer is D) Product 2, because the function is exponential!!!!!!!

From the question that we have the period that would have the price that would exceed others would be Product 2, because the function is exponential.

What is an exponential function?

This is the type of function that is raised to a power of a constant. An exponential function is of the type f ( x ) = a^x.

x is a variable in the function while a is referred to as the constant of the equation.

Read more on exponential equation here:

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why are we still here?

Answers

Answer:

like why are we still alive or why are we still on the site?

Step-by-step explanation:

Due to our superior intelligence, we have managed to survive through history. It is still unknown what primates originally descended from and why we are smarter than other organisms. With our superiority, many have realized that there is no point in living. That’s where religion comes into play. Religion is the justification for our meaningless existence. No one can prove whether any religion is completely valid, we can only trust it and keep living on. In conclusion, you can blame everyone’s existence on religion and our superiority.

not sure how to do thisss,,, help!

Answers

Answer:

4 and 13

Step-by-step explanation:

(a)

To evaluate f(3) substitute x = 3 into f(x), that is

f(3) = 3 + 1 = 4

(b)

To evaluate gf(3) substitute f(3) = 4 into g(x), that is

g(4) = 4² - 3 = 16 - 3 = 13

A construction company built bleachers that can hold a 149,227 pounds. How many 169-pound people can the bleachers hold?

Answers

Answer: 883 people

Step-by-step explanation: If the bleachers can hold 149,227 pounds and each person weighs 169 pounds, then you would do 149,227 divided by 169 to get 883.

149,227 ÷ 169 = 883

Answer:

883 people

Step-by-step explanation:

This is a division problem.

(149,227 lb)/(169 lb) = 883

Answer: 883 people.

Second time asking plz help. Linear or exponential. plz help me :(​

Answers

Answer:

Exponential

Step-by-step explanation:

The change isn't constant for the volume, so it must be exponential.

Using quadratic regression, the equation is:

[tex]y=\frac{19}{63}x^{2}-\frac{968}{105}x+\frac{3312}{35}[/tex]

Answer:

I agree it's exponential, but it's so much simpler than you guys make it out to be. An easy way to check is to measure the distance in the x and y values to see if they change at a constant rate.

for instance; 1) abs(0-3) =3  95-69= 26  

2) abs(3-6) = 3     59-50= 19 ...

It's easier, faster, and less to memorize

1. Find the next term in the sequence.
9, 15, 21, 27,..

Answers

It’s would be 33 that the next sequence

Answer:

33

Step-by-step explanation:

9+6=15

15+6=21

21+6=27

27+6=33

33

PLS HELP HURRY!!Its ten points​

Answers

Answer:

12in long and 10in wide

Step-by-step explanation:

If he were to trim the edges of the photographs to [tex]12\frac{1}{2}[/tex] and [tex]10\frac{1}{2}[/tex], the edges of the photographs from Russ's vacation would be too long and wide to fit inside of the photo album.

If you convert the fractions into decimals, you can easily discern that the vacation photos would be too large to fit inside of the photo album.

Photo Album:

[tex]12\frac{1}{8}[/tex] = 12.1 inches •Original

[tex]10\frac{1}{8}[/tex] = 10.1 inches •Original

• Too large:

[tex]12\frac{1}{2}[/tex] = 12.5 inches > 12.1 - 12.5 = -0.4 •Too large

[tex]10\frac{1}{2}[/tex] = 10.5 inches > 10.1 - 10.5 = -0.4 •Too large

• Just right:

10 = 10 inches > 10.1 - 10 = 0.1 •Space left

12 = 12 inches > 12.1 - 12 = 0.1 •Space left

How many times can 1/6 go into 4

Answers

Final answer:

To determine how many times 1/6 can be contained in 4, we multiply 4 by the reciprocal of 1/6, which is 6. The answer is 24.

Explanation:

To find out how many times 1/6 can go into 4, we need to perform a division operation. We are essentially asking how many sixths are there in 4 wholes. This can be written as a division expression:

4 ÷ (1/6)

To divide by a fraction, you multiply by its reciprocal. For the fraction 1/6, the reciprocal is 6, so you multiply 4 by 6 to find the answer:

4 × 6 = 24

Therefore, 1/6 can go into 4 a total of 24 times.

Solve (x + 5 < 4) ∩ (x - 3 > -6)

Answers

Answer:

∅ i.e empty

Step-by-step explanation:

(x + 5 < 4) ∩ (x - 3 > -6)

Let A represent the set (x + 5 < 4)

Let B represent the set (x - 3 > -6)

For set A:

x + 5 < 4

subtract 5 from both side

x < 4 —5

x < —9

Possible values of x are - 10, - 11, - 12,...

A = {- 10, - 11, - 12,...}

For set B:

x - 3 > -6

Add 3 to both side

x > -6 + 3

x > - 3

Possible values of x are - 2, - 1, 0,...

B = {- 2, - 1, 0,...}

A= {- 10, - 11, - 12,...}

A ∩ B = ∅ i.e empty

Therefore, (x + 5 < 4) ∩ (x - 3 > -6) is ∅ i.e empty

What is the LCM of 12 46

Answers

Answer:

To get the Least Common Multiple (LCM) of 12 and 46 we need to factor each value first and then we choose all the factors which appear in any column and multiply them:  

12:    

2

2

3

 

46:    

2

 

 

23

LCM:    

2

2

3

23

The Least Common Multiple (LCM) is:   2 x 2 x 3 x 23 = 276

Step-by-step explanation:

Step-by-step explanation:

12=1× 2×2×3

46=1×2×23

LCM=1×2×2×3×23

= 276

Ana bought a 15.5-pound turkey at the grocery
store this month. The equation p-15.5 = 2.5
gives the weight p, in pounds, of the turkey
she bought last month. What is the solution
of the equation?

Answers

Answer:

18

Step-by-step explanation:

Question 2 of 10
2 Points
What is the measure of XYZ?
O A. 1740
O B. 96
O C. 186°
O D. 93°
SUBMIT

Answers

Answer:

Question is not clear.

Step-by-step explanation:

But i think so 186degree

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