Ask question

Ask question

All categories

3 years ago

15

The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an air

plane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.

1 answer:

tensa zangetsu [6.8K]3 years ago

6 0

The total time taken for round trip will be: (f+g)(x) = 14x+11

Step-by-step explanation:

Given

$f(x) = 4x+13\\g(x) = 10x-2$

In order to find the round-trip time, we have to add both functions to represent the time taken to travel east and the time taken to travel to west.

$(f+g)(x) = f(x)+g(x)\\= (4x+13)+(10x-2)\\=4x+13+10x-2\\=4x+10x+13-2\\=14x+11$

Hence,

The total time taken for round trip will be: (f+g)(x) = 14x+11

Keywords: Functions, variables

Learn more about functions at:

#LearnwithBrainly

You might be interested in

Fine length of BC on the following photo.

MrMuchimi

Answer:

$BC=4\sqrt{5}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

$AC^2=16^2+8^2$

$AC^2=320$

$AC=\sqrt{320}\ units$

simplify

$AC=8\sqrt{5}\ units$

step 2

In the right triangle ACD

Find the cosine of angle CAD

$cos(\angle CAD)=\frac{AD}{AC}$

substitute the given values

$cos(\angle CAD)=\frac{16}{8\sqrt{5}}$

$cos(\angle CAD)=\frac{2}{\sqrt{5}}$ ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

so

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

$BC^2=8^2+4^2$

$BC^2=80$

$BC=\sqrt{80}\ units$

simplify

$BC=4\sqrt{5}\ units$

7 0

3 years ago

Helpppppp fasttttttttttt

bija089 [108]

Answer:

60 wpm

Step-by-step explanation:

5 0

3 years ago

Identify the frequency of the graph

olya-2409 [2.1K]

ANSWER

$\frac{1}{2}$

EXPLANATION

The frequency of a wave function refers to the number of times the graph repeats its cycle within the interval [0,2π]

We can observe explicitly from the graph that the frequency is half.

The period of the given function is 4π

$\frac{2\pi}{b} = 4\pi$

$b = \frac{2\pi}{4\pi} = \frac{1}{2}$

Hence the frequency is half.

4 0

3 years ago

You have already traveled 25 miles. If you continue driving at the same speed, x miles per hour, for 5 more hours, you will trav

Fiesta28 [93]

Answer:1

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The policy of the Kauderman's pawnshop is to lend up to 30% of the value of borrower's collateral. Tommy wants to use a pair of

lubasha [3.4K]

Answer:

30/100×$1500 = $450

Step-by-step explanation:

Tommy needs total capital of $1500 and he wants to lend 30% of loan from kaunderman, which is calculated as above.

8 0

3 years ago