Mathematics , 21.06.2019 12:40 hma9153

Match each function with the corresponding function formula when h(x)=5-3x and g(x)=-3+5

Answers: 1

Show answers

Answers

Answer from: PLSsHELPMEH

k(x) = (3g + 5h)(x) ⇒ (1)

k(x) = (5h - 3g)(x) ⇒ (3)

k(x) = (h - g)(x) ⇒ (2)

k(x) = (g + h)(x) ⇒ (4)

k(x) = (5g + 3h)(x) ⇒ (5)

k(x) = (3h - 5g)(x) ⇒ (6)

Step-by-step explanation:

* To solve this problem we will substitute h(x) and g(x) in k(x) in the

right column to find the corresponding function formula in the

left column

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

- Lets start with the right column

# k(x) = (3g + 5h)(x)

∵ g(x) = -3^x + 5

∵ 3g(x) = 3[-3^x + 5] = [3 × -3^x + 3 × 5]

- Lets simplify 3 × -3^x

take the negative out -(3 × 3^x), and use the rule a^n × a^m = a^(n+m)

∴ -3(3 × 3^x) = -(3^x+1)

∴ 3g(x) = -3^x+1 + 15

∵ h(x) = 5 - 3x

∵ 5h(x) = 5[5 - 3x] = [5 × 5 - 5 × 3x] = 25 - 15x

- Now substitute 3g(x) and 5h(x) in k(x)

∵ k(x) = (3g + 5h)(x)

∴ k(x) = -3^x+1 + 15 + 25 - 15x ⇒ simplify

∴ k(x) = 40 - 3^x+1 - 15x

∴ k(x) = 40 - 3^x+1 - 15x ⇒ k(x) = (3g + 5h)(x)

* k(x) = (3g + 5h)(x) ⇒ (1)

# k(x) = (5h - 3g)(x)

∵ 5h(x) = 25 - 15x

∵ 3g(x) = -3^x+1 + 15

∵ k(x) = (5h - 3g)(x)

∴ k(x) = 25 - 15x - (-3^x+1 + 15) = 25 -15x + 3^x+1 - 15 ⇒ simplify

∴ k(x) = 10 + 3^x+1 - 15x

∴ k(x) = 10 + 3^x+1 - 15x ⇒ k(x) = (5h - 3g)(x)

* k(x) = (5h - 3g)(x) ⇒ (3)

# k(x) = (h - g)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (h - g)(x)

∴ k(x) = 5 - 3x - (-3^x + 5) = 5 - 3x + 3^x - 5 ⇒ simplify

∴ k(x) = 3^x - 3x

∴ k(x)= 3^x - 3x ⇒ k(x) = (h - g)(x)

* k(x) = (h - g)(x) ⇒ (2)

# k(x) = (g + h)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (g + h)(x)

∴ k(x) = -3^x + 5 + 5 - 3x ⇒ simplify

∴ k(x) = 10 - 3^x - 3x

∴ k(x)= 10 - 3^x - 3x ⇒ k(x) = (g + h)(x)

* k(x) = (g + h)(x) ⇒ (4)

# k(x) = (5g + 3h)(x)

∵ g(x) = -3^x + 5

∵ 5g(x) = 5[-3^x + 5] = [5 × -3^x + 5 × 5] = 5(-3^x) + 25

∴ 5g(x) = -5(3^x) + 25

∵ h(x) = 5 - 3x

∵ 3h(x) = 3[5 - 3x] = [3 × 5 - 3 × 3x] = 15 - 9x

- Now substitute 5g(x) and 3h(x) in k(x)

∵ k(x) = (5g + 3h)(x)

∴ k(x) = -5(3^x) + 25 + 15 - 9x ⇒ simplify

∴ k(x) = 40 - 5(3^x) - 9x

∴ k(x) = 40 - 5(3^x) - 9x ⇒ k(x) = (5g + 3h)(x)

* k(x) = (5g + 3h)(x) ⇒ (5)

# k(x) = (3h - 5g)(x)

∵ 3h(x) = 15 - 9x

∵ 5g(x) = -5(3^x) + 25

∵ k(x) = (3h - 5g)(x)

∴ k(x) = 15 - 9x - [-5(3^x) + 25] = 15 - 9x + 5(3^x) - 25 ⇒ simplify

∴ k(x) = 5(3^x) - 9x - 10

∴ k(x) = 5(3^x) - 9x - 10 ⇒ k(x) = (3h - 5g)(x)

* k(x) = (3h - 5g)(x) ⇒ (6)

Answer from: brendamillan05

I hope this helps

Step-by-step explanation:

1) g=h−k

2)g=−h+k

3) g=h−k/2

4)g=−h+k/2

5) g=2h−k/2

6)g=h+k

Answer from: Aerial14

1 - 3, 2 - 5, 3 - 4, 4 - 6, 5 - 1, 6 - 2.

Step-by-step explanation:

We have,

h(x) = 5-3x and

So, according to the options, we have,

1. k(x) = (5g + 3h)(x)

Now,

i.e.

2. k(x) = (3h - 5g)(x)

Now,

i.e.

3. k(x) = (3g + 5h)(x)

Now,

i.e.

4. k(x) = (5h - 3g)(x)

Now,

i.e.

5. k(x) = (h - g)(x)

Now,

i.e.

6. k(x) = (g + h)(x)

Now,

i.e.

Thus, we have the matches as,

1. k(x) = (5g + 3h)(x) ---------------- 5. k(x)=40-5(3^x)-9x

2. k(x) = (3h - 5g)(x) ---------------- 6. k(x)=5(3^x)-9x-10

3. k(x) = (3g + 5h)(x) ---------------- 1. k(x)=40-3^x+1-15x

4. k(x) = (5h - 3g)(x) ----------------- 3. k(x)=10+3^x+1-15x

5. k(x) = (h - g)(x) ----------------- 2. k(x)=3^x-3x

6. k(x) = (g + h)(x) ----------------- 4. k(x)=10-3^x-3x

Answer from: richdakid26

1 -> f

2 -> a

3 -> d

4 -> b

5 -> e

6 -> c

Step-by-step explanation:

We are given:

h(x) = 2 - 2x and g(x) = -2^x+2

a) k(x)= (g-h)(x) = g(x) - h(x)

= -2^x+2 - (2 - 2x)

= -2^x+2 - 2 + 2x

= -2^x+2x or 2x-2^x

k(x) = 2x-2^x = (g-h)(x)

So, 2 matches with a

b) k(x)= (g+h)(x) = g(x) + h(x)

= -2^x+2 + (2 - 2x)

= -2^x+2 + 2 - 2x

= -2^x+4-2x or 4 - 2^x -2x

So, k(x) = 4 - 2^x -2x = (g+h)(x)

So, 4 matches with b

c) k(x)= (2h - 2g)(x) = 2h(x) - 2g(x)

= 2(2 - 2x)-2(-2^x+2)

= 4 - 4x+2.2^x-4

= -4x+2^x+1 or 2^x+1-4x

So, k(x) = 2^x+1-4x = (2h - 2g)(x)

So, 6 matches with c

d) k(x) = (h-2g)(x) = h(x) - 2g(x)

= (2 - 2x)-2(-2^x+2)

= 2 - 2x+2.2^x-4

= -2-2x+2^x+1

= 2^x+1-2x-2

So, k(x) = 2^x+1-2x-2 = (h-2g)(x)

So, 3 matches with d

e) k(x) = (h-g)(x) = h(x) - g(x)

= (2 - 2x)-(-2^x+2)

= 2 - 2x+2^x-2

= -2x+2^x or 2^x-2x

So, k(x) = 2^x-2x = (h-g)(x)

So, 5 matches with e

f) k(x) = (2g+h)(x) = 2g(x)+h(x)

= 2(-2^x+2) + (2 - 2x)

= -2.2^x+4 + 2 - 2x

= -2^x+1+6-2x or 6 - 2^x+1-2x

So, k(x) = 6 - 2^x+1-2x = (2g+h)(x)

So, 1 matches with f

Answer from: jsh65bsbs

1) 6 - 2^(x + 1) - 2x = (2g - h)(x)

2) 2x - 2^x = (g - h)(x)

3) 2^(x + 1) - 2x - 2 = (h - 2g)(x)

4) 4 - 2^x - 2x = (g + h)(x)

5) 2^x - 2x = (h - g)(x)

6) 2^(x + 1) - 4x = (2h - 2g)(x)

Step-by-step explanation:

* Lets use right column to find the corresponding function in the

left column

∵ h(x) = 2 - 2x

∵ g(x) = -2^x + 2

# k(x) = (g - h)(x)

∵ k(x) = g(x) - h(x)

∴ k(x) = -2^x + 2 - (2 - 2x) ⇒ multiply the -ve sign by the bracket

- Remember -ve × +ve = -ve and -ve × -ve = +ve

∴ k(x) = -2^x + 2 - 2 + 2x

∴ k(x) = -2^x + 2x ⇒ (2)

∴ k(x) = (g - h)(x) ⇒ (2)

* 2x - 2^x = (g - h)(x)

# k(x) = (g + h)(x)

∵ k(x) = g(x) + h(x)

∴ k(x) = -2^x + 2 + (2 - 2x) ⇒ simplify

∴ k(x) = -2^x + 2 + 2 - 2x

∴ k(x) = -2^x + 4 - 2x ⇒ (4)

∴ k(x) = (g + h)(x) ⇒ (4)

* 4 - 2^x - 2x = (g + h)(x)

# k(x) = (2h - 2g)(x)

∵ k(x) = 2h(x) - 2g(x)

- Lets find 2h(x) and 2g(x)

∵ 2h(x) = 2[2 - 2x] = 2(2) - 2(2x) = 4 - 4x

∵ 2g(x) = 2[-2^x + 2] = 2(-2^x) + 2(2)

- Remember a^n × a^m = a^(n + m)

∴ 2g(x) = 2(-2^x) + 4 = - (2 × 2^x) + 4 = - 2^(x + 1) + 4

∴ k(x) = 4 - 4x - [-2^(x + 1) + 4] ⇒ simplify

∴ k(x) = 4 - 4x + 2^(x + 1) - 4

∴ k(x) = 2^(x + 1) - 4x ⇒ (6)

∴ k(x) = (2h - 2g)(x) ⇒ (6)

* 2^(x + 1) - 4x = (2h - 2g)(x)

# k(x) = (h - 2g)(x)

∵ k(x) = h(x) - 2g(x)

∵ h(x) = 2 - 2x =

∴ 2g(x) = - 2^(x + 1) + 4

∴ k(x) = 2 - 2x - [-2^(x + 1) + 4] ⇒ simplify

∴ k(x) = 2 - 2x + 2^(x + 1) - 4

∴ k(x) = 2^(x + 1) - 2x - 2 ⇒ (3)

∴ k(x) = (h - 2g)(x) ⇒ (3)

* 2^(x + 1) - 2x - 2 = (h - 2g)(x)

# k(x) = (h - g)(x)

∵ k(x) = h(x) - g(x)

∴ k(x) = 2 - 2x - [-2^x + 2] ⇒ multiply the -ve sign by the bracket

- Remember -ve × +ve = -ve and -ve × -ve = +ve

∴ k(x) = 2 - 2x + 2^x - 2

∴ k(x) = 2^x - 2x ⇒ (5)

∴ k(x) = (h - g)(x) ⇒ (5)

* 2^x - 2x = (h - g)(x)

# k(x) = (2g + h)(x)

∵ k(x) = 2g(x) + h(x)

∵ h(x) = 2 - 2x =

∴ 2g(x) = - 2^(x + 1) + 4

∴ k(x) = -2^(x + 1) + 4 + 2 - 2x ⇒ simplify

∴ k(x) = -2^(x + 1) - 2x + 6

∴ k(x) = 6 - 2^(x + 1) - 2x ⇒ (1)

∴ k(x) = (2g + h)(x) ⇒ (1)

* 6 - 2^(x + 1) - 2x = (2g - h)(x)

Answer from: edandjill24

1.k(x) = (3g + 5h)(x) = -24x+40

2.k(x) = (h - g)(x) = 0

3.k(x) = (g + h)(x) = -6x+10

4.k(x) = (5g + 3h)(x) = -24x+40

5.k(x) = (3h - 5g)(x) = 6x-10

6.k(x) = (5h - 3g)(x) = 10-6x

Step-by-step explanation:

Given

h(x) = 5 - 3x

and

g(x) = -3 x + 5

1. k(x) = (3g + 5h)(x)

3*g(x) = 3(-3 x + 5)

=> -9x+15

5*h(x) = 5(5 - 3x)

=>25-15x

(3g + 5h)(x)=3*g(x)+5*h(x)

= -9x+15+25-15x

=-9x-15x+15+25

=-24x+40

2. k(x) = (h - g)(x)

(h - g)(x) = h(x) - g(x)

= 5 - 3x -(-3 x + 5)

=5-3x+3x-5

= 0

3. k(x) = (g + h)(x)

(g+h)x = g(x) + h(x)

= -3 x + 5 + 5 - 3x

= -6x+10

4. k(x) = (5g + 3h)(x)

5*g(x) = 5(-3 x + 5)

=-15x+25

3*h(x) = 3(5 - 3x)

=15-9x

(5g + 3h)(x) = 5*g(x) + 3*h(x)

= -15x+25+15-9x

= -15x-9x+25+15

=-24x+40

5. k(x) = (3h - 5g)(x)

(3h - 5g)(x) = 3*h(x)-5*g(x)

=15-9x-(-15x+25)

=15-9x+15x-25

=-9x+15x+15-25

=6x-10

6. k(x) = (5h - 3g)(x)

5*h(x)-3*g(x) = 25-15x - (-9x+15)

= 25-15x+9x-15

= 25-15-15x+9x

=10-6x

Answer from: jadetaull19

funtions: a, b, c...

formulas: 1, 2, 3...

A and 5, F and 2, B and 4, D and 1, C and 3, E and 6

Answer from: raconteuraki

k(x) = (h – g)(x) k(x) = 2x - 2^x

k(x) = (g + h)(x) k(x) = 4 - 2^x - 2x

k(x) = (h – 2g)(x) k(x) = 2^x+1 - 2x - 2

k(x) = (2g + h)(x) k(x) = 6 - 2 ^x+1 - 2x

k(x) = (2h – 2g)(x) k(x) = 2^x+1 - 4x

k(x) = (g – h)(x) k(x) = 2x - 2^x

Answer from: hawleyemily

the correct functions are

h(x) = 3x + 2

g(x) = 2^x

proceed to calculate the different values of K (x)

case 1) k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + 2]> is the option 4.k(x) = 2^(3x + 2 )

case 2) k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+2> is the option 1.) k(x) = 2^x + 3x + 4

case 3)k(x) = g(x) - h(x)

k(x) = [2^x]-[3x + 2]=2^x-3x-2> is the option 2.) k(x) = 2^x - 3x - 2

Answer from: itscheesycheedar

To match each functions with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3 x + 5.

1. k(x) = (3h - 5g)(x)

= = 3(5 - 3x)-5(-3 x + 5)

= = 15 - 9x + 15x - 25

K(x) = -10 + 6x

2. k(x) = (h - g)(x)

= = (5 - 3x) - (-3 x + 5)

= = 0

k(x) = 0

3. k(x) = (5g + 3h)(x)

= = 5(-3 x + 5)+3(5 - 3x)

= = -15x + 25 + 15 - 9x

k(x) = - 24x +40

4. k(x) = (3g + 5h)(x)

= = 3 (-3 x + 5) + 5(5 - 3x)

= = -9x + 15 +25 -15x

k(x) = -24x + 40

5. k(x) = (g + h)(x)

= = (-3 x + 5) + (5 - 3x)

k(x) = -6x + 10

6. k(x) = (5h - 3g)(x)

= = 5(5 - 3x) - 3(-3 x + 5)

= =25 - 15x + 9x - 15

k(x) = 10 - 6x

Another question on Mathematics

Mathematics, 21.06.2019 15:40

Need ! discuss how to convert the standard form of the equation of a circle to the general form. 50 points

Answers: 1

Answer

Mathematics, 21.06.2019 16:00

Which segments are congruent? o jn and ln o jn and nm o in and nk onk and nm

Answers: 3

Answer

Mathematics, 21.06.2019 17:00

According to modern science, earth is about 4.5 billion years old and written human history extends back about 10,000 years. suppose the entire history of earth is represented with a 10-meter-long timeline, with the birth of earth on one end and today at the other end.

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

X+ y = 5 ; x - y =3 solve using linear combination

Answers: 2

Answer

You know the right answer?

Match each function with the corresponding function formula when h(x)=5-3x and g(x)=-3+5
...

Questions

Biology, 15.11.2019 20:31

Why do organisms need both processes?...

Mathematics, 15.11.2019 20:31

George works in an office as a cleaner he earns a total of $25 for five hours of cleaning later that year he earned $30 for six hours how much money d...

Social Studies, 15.11.2019 20:31

The average annual rainfall for boston is 43.76 inches. one year, a weather station measured the city’s actual rainfall to be 33.45 inches. from this...

Mathematics, 15.11.2019 20:31

Which graph could represent y, the amount owed on a car loan, as regular payments are made each month, x?

Mathematics, 15.11.2019 20:31

Given a sequence is defined by the explicit definition t_n= n^2+nt n = n 2 + n, find the 4th term of the sequence. (i. e. t_4t 4) a. 4

Mathematics, 15.11.2019 20:31

Which best describes the function on the graph? direct variation; k = direct variation; k = 4 inverse variation; k = inverse variation; k = 4...

Business, 15.11.2019 20:31

Give and take in the marketplace always determines the...

Chemistry, 15.11.2019 20:31

What coefficient is assumed if no coefficient written before a formula in a chemical equation...

Mathematics, 15.11.2019 20:31

Amovie theater charged $10. 50 per ticket and 5$ per bucket of popcorn. you never buy the popcorn because it’s too expensive. is the total price you p...

Business, 15.11.2019 20:31

Asequence arranged from highest to lowest is . a. field b. access c. ascending d. descending...

History, 15.11.2019 20:31

How did the atlantic slave trade benefit the africans?...

History, 15.11.2019 20:31

Was a british philosopher who is credited with proposing the idea of natural rights and the social contract theory....

Mathematics, 15.11.2019 20:31

An interior decorator buys a curtain for a customer's rectangular living room window. the window measures 5 feet and 2 inches tall by 3 feet and 11 in...

History, 15.11.2019 20:31

How was the declaration of independence diferent from previous documents prepared by colonists? it committed the colonies to being independent....

Social Studies, 15.11.2019 20:31

Our freedom began at the end of the civil war. that was thirty years ago. we started with a few quilts, pumpkins and chickens. today we make ne...

History, 15.11.2019 20:31

What conflict is know for the death of general george custer and as custers last stand...

Mathematics, 15.11.2019 20:31

Will mark you as brainliest! i need the answer as soon as possible!

Mathematics, 15.11.2019 20:31

Eur/usd = 1.11706 how much usd is 300 eur?...

Biology, 15.11.2019 20:31

Which molecule is not found in dna?...

English, 15.11.2019 20:31

Which of the following choices contains indirect characterization? group of answer choices selma kept her eyes glued to the g...

More questions: Mathematics Another questions