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topjm [15]
3 years ago
7

For the functions f(x) = 2x + 2 and g(x) = 7x + 1, which composition produces the greatest output?

Mathematics
2 answers:
Nesterboy [21]3 years ago
7 0

The answer is the fourth option "g(f(x)) produces the greatest output."

How:

  • (f o g)(x) = [2(7x + 1) + 2] = (14x + 2 + 2) = 14x + 4
  • (g o f)(x) = [7(2x + 2) + 1] = (14x + 14 + 1) = 14x + 15

Looking at both equations you would see that (g o f)(x) > (f o g)(x) so the answer is the fourth option!

Hope this helps!

stepan [7]3 years ago
7 0
First we have to find <span>(f o g)(x):
</span>(f o g)(x) = [2(7x + 1) + 2] = (14x + 2 + 2) = 14x + 4 
Then we have to find (g o f)(x):
(g o f)(x) = [7(2x + 2) + 1] = (14x + 14 + 1) = 14x + 15 
Comparing both the results:

(g o f)(x) > (f o g)(x)
According to above explanation,
D.<span>g(f(x)) produces the greatest output, is the correct answer.</span>
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2x squared minus 17 equals 183 <br> what is the value of x
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A carpenter uses 10 1/2 ft of cedar for every 12 1/3 ft of redwood for a construction project. If the carpenter uses 5 1/4 ft of
motikmotik

Answer: 6 1/6

Step-by-step explanation:

1) First divide 10 1/2 = 5 1/4.

2) Then, since we divide 10 1/2 then we need to divide 12 1/3.

3) 12 1/3 divided by 2 = 6 1/6.

And there is your answer; 6 1/6

8 0
3 years ago
You are taking a trip at the same time as another
Valentin [98]

Answer:

My family is traveling faster, since it is traveling at the rate of 950 miles per day, while the other family travels at 900 miles per day.

Step-by-step explanation:

Since I am taking a trip at the same time as another family, and my family traveled 1,900 miles in 2 days, while their family traveled 2,700 miles in 3 days, to determine who is traveling faster the following calculation must be performed:

1,900 / 2 = 950

2,700 / 3 = 900

Thus, my family is traveling faster, since it is traveling at the rate of 950 miles per day, while the other family travels at 900 miles per day.

4 0
3 years ago
Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.
kozerog [31]

Answer:

6.75g

Step-by-step explanation:

The first step is converting everything to grams, by rules of three. Then we add.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

First step: 0.0025kg to g

Each kg has 1000g, so:

1kg - 1000g

0.0025kg - xg

x = 1000*0.0025 = 2.5g

0.0025kg = 2.5g

Second step:  1750 mg

Each g has 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

x = \frac{1750}{1000}

x = 1.75g

1750 mg = 1.75g

2.25g - OK

Third step: 825,000 μg to g

Each g has 1,000,000 ug, so:

1g - 1,000,000 ug

xg - 825,000 ug

1,000,000x = 825,000

x = \frac{825,000}{1,000,000}

x = 0.25g

825,000 μg = 0.25g

Final step: adding everyting

0.25g + 2.25g + 1.75g + 2.50g = 6.75g

5 0
3 years ago
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