1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
viktelen [127]
3 years ago
11

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

Mathematics
1 answer:
Grace [21]3 years ago
4 0

Answer:

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)

You might be interested in
. A fair coin and then a die with 6 sides are tosses find the probabilities of the six events occurring respectively a. P(Tails)
Dvinal [7]

Answer:

F

Step-by-step explanation:

7 0
3 years ago
15=7-|2x|<br> Solve for x in this absolute value equation.
ivann1987 [24]
7-|2x|=15\ \ \ \ |subtract\ 7\ from\ both\ sides\\\\-|2x|=8\\\\|2x|=-8-FALSE\\\\x\in\O\ because\ |a|\geq0\ for\ each\ a\in\mathbb{R}

6 0
3 years ago
Read 2 more answers
Which of the following represents fifth root of x to the fourth power in exponential form? (6 points) a 4x5 b 5x4 c x to the fiv
sleet_krkn [62]

Answer:

B) 5x4

one its not A nor its C

its either B or D but i would go with B because D doesn't make sense all because D is saying x4^5 but its 5x^4

3 0
3 years ago
Read 2 more answers
2-(-2)= asaapaappaappap pleaseee help
IRINA_888 [86]

Answer:

Four is the final answer (4)

Step-by-step explanation: Have a brilliant day of learning!

7 0
3 years ago
the function of y= x^2 - 4x + 8 approximates the height y, of a bird and its horizontal distance, x as it flies from one fence p
Vika [28.1K]
Rewrite the given equation as 
y=x^2-4x+8=x^2-4x+4+4=(x-2)^2+4.
Since (x-2)^2\ge 0, you can conclude that the imimum value of y will be gained for the minimum value of (x-2)^2. The minimum value of (x-2)^2 is 0 for x=2. 
So, y(2)=0+4=4.
Answer: minimum value of y is 4, when x=2.


7 0
3 years ago
Read 2 more answers
Other questions:
  • What is 3/5 of 12? Please answer!
    9·1 answer
  • Two parallel lines are crossed by a transversal. Parallel lines x and y are cut by transversal w. On line x where it intersects
    14·2 answers
  • What is the ratio of wings to beaks in a flock of birds
    13·2 answers
  • describe how you can tell by lookin at a graph of a function which variable is the input variable and which is the output variab
    15·1 answer
  • Which inequality can be used to determine the amount of money the family still needs to save?
    8·1 answer
  • Max is saving $10 a month for a summer vacation. If he also has $50 from his grandmother, how many months will Max need to save
    15·2 answers
  • I WILL GIVE BRAINLIEST!! I WILL ALSO GIVE 20+ POINTS!! HELP ASAP, NO LINKS! &lt;3
    11·2 answers
  • 140 is what percent less than 160
    7·1 answer
  • Help, i dont know any of this lol
    9·1 answer
  • Kim buys a dress for $65 and some shirts for $15 each. Linda buys some shoes for $50 and some shirts for $20. If the girls spend
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!