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
Sphinxa [80]
3 years ago
7

Which expression is equal to f(x) + g(x)?

Mathematics
1 answer:
eimsori [14]3 years ago
7 0

Answer:

\frac{2x-20}{x^2+6x-40}

Step-by-step explanation:

f(x)+g(x)

\frac{x-16}{x^2+6x-40}+\frac{1}{x+10}

I'm going to factor that quadratic in the first fraction's denominator to figure out what I need to multiply top and bottom of the other fraction or this fraction so that I have a common denominator.

I want a common denominator so I can write as a single fraction.

So since the leading coefficient is 1, all we have to do is find two numbers that multiply to be c and at the same thing add up to be b.

c=-40

b=6

We need to find two numbers that multiply to be -40 and add to be 6.

These numbers are 10 and -4 since (10)(-4)=-40 and 10+-4=6.

So the factored form of x^2+6x-40 is (x+10)(x-4).

So the way the bottoms will be the same is if I multiply top and bottom of my second fraction by (x-4).

This will give me the following sum so far:

\frac{x-16}{x^2+6x-40}+\frac{x-4}{x^2+6x-40}

Now that the bottoms are the same we just need to add the tops and then we are truly done:

\frac{(x-16)+(x-4)}{x^2+6x-40}

\frac{x+x-16-4}{x^2+6x-40}

\frac{2x-20}{x^2+6x-40}

You might be interested in
Disruptive properties<br> 5(4 + 7x)
Gnesinka [82]

Answer:

It is 35x+20

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A cylinder has a base radius of 4m and a height of 6m. What is its volume in cubic m,
BlackZzzverrR [31]

Answer:

301.4

Step-by-step explanation:

Volume of a cylinder=pi*r^{2}*h.  Assuming you want 3.14 for pi, we can substitue the 4m for r, 6 for h and 3.14 for pi.

V=3.14*4^{2}*6

V=301.44

Since you want to round to nearest tenths, the answer is 301.4

8 0
3 years ago
49 POINTS! PLEASE HELP!
SSSSS [86.1K]

Answer:

B (2, 2)

Step-by-step explanation:

Given the graphs of a system of equations then the solution is at the point of intersection of the 2 lines.

That is (2,2) ← is the solution → B

5 0
3 years ago
Read 2 more answers
12) Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}
never [62]

Answer:

<em>Part a) </em>Domain of f : {-3, -2, -1, 0, 1, 2, 3}

<em>Part b) </em>Domain of g : {-1, 0, 1, 2, 3, 4}

<em>Part c)  </em>Domain of f+g = {-1, 0, 1, 2, 3}

<em>Part d) </em>Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Step-by-step explanation:

<em>Part a) Determining the domain of f </em>

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

<em>Part b) Determining the domain of g</em>

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

As domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of g : {-1, 0, 1, 2, 3, 4}

<em>Part c) Determining the domain of f+g</em>

<em>When there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains.</em>

<em>As,</em>

<em>      </em>Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

      Domain of f : {-3, -2, -1, 0, 1, 2, 3}

and,

      Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

       Domain of g : {-1, 0, 1, 2, 3, 4}

<em>As</em> when <em>there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains</em>

So, the domain of f+g = {-1, 0, 1, 2, 3}

<em>Part d) List the ordered pairs of f-g</em>

As

    f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

and

    g = {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

For f - g, we must focus on subtracting the second (y) coordinates of both function that correspond to the same element in the domain (x)

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

(f - g)(x) = f(-1) - g(-1)  = 14 - 4 = 10

(f - g)(x) = f(0) - g(0)  = 7 - 5 = 2

(f - g)(x) = f(1) - g(1)  = 4 - 6 = -2

(f - g)(x) = f(2) - g(2)  = 5 - 1 = 4

(f - g)(x) = f(3) - g(3)  = 7 - (-16) = 23

So,

Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Keywords:  domain, function, f+g, f-g

Learn more about domain, and ordered pairs from brainly.com/question/11422136

#learnwithBrainly

7 0
3 years ago
The Polygons below are similar. Find the value of x. A. 4.5 B. 7.5 C. 12 D. 16
koban [17]
I'm pretty sure that it is C. 12 
3 0
3 years ago
Other questions:
  • A scientist was studying a population of elephants. the first year, he counted a population of 80. over the next eight years, th
    10·2 answers
  • An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the ref
    6·1 answer
  • A builder needs three pipes of different lengths. The pipes are 6√96 feet long, 12√150 feet long, and 2√294 feet long. How many
    5·2 answers
  • Algebra question, please help me i am in need.
    10·1 answer
  • Plz answer these questions need help
    10·1 answer
  • Amy ran 3/4 mile. which decimal shows how many miles she ran?
    11·2 answers
  • <img src="https://tex.z-dn.net/?f=5%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20%20%5Cfrac%7B3%7D%7B8%7D%20" id="TexFormula1" title=
    14·1 answer
  • A pyramid has a horizontal square base of 12cm. the vertex of the pyramid is 7cm vertically above the base. calculate, correct t
    7·1 answer
  • Find the distance between the two given points H(-3,6) and C(-3,-3)
    6·1 answer
  • Can someone find the volume to thisssss
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!