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3 years ago

For f(x) = 3x +1 and g(x) = x2 – 6, find (f- g)(x).

Mathematics

1 answer:

Fiesta28 [93]3 years ago

8 0

Answer:

$\boxed{\sf (f-g)(x) = -{x}^{2} + 3x + 7}$

Given:

$\sf f(x) = 3x + 1 \\ \sf g(x) = {x}^{2} - 6$

To find:

$\sf (f - g)(x) = f(x) - g(x)$

Step-by-step explanation:

$\sf \implies(f - g)x = f(x) - g(x) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) - ( {x}^{2} - 6) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) + (- {x}^{2} + 6) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3x + 1 - {x}^{2} + 6 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - {x}^{2} + 3x + 1 + 6 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = -{x}^{2} + 3x + 7$

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The length of a rectangular mailing label is

trasher [3.6K]

P = 2(L + W)
P = 22
L = 2W - 4

22 = 2(2W - 4 + W)
22 = 2(3W - 4)
22 = 6W - 8
22 + 8 = 6W
30 = 6W
30/6 = W
5 = W.....width is 5 cm

L = 2W - 4
L = 2(5) - 4
L = 10 - 4
L = 6....length is 6 cm

3 0

2 years ago

Gina works at a diner.She earns 6$ each hour plus tips.In one week,She worksed 37 hours a week and earned 434$ in tips.How much

finlep [7]

False.

6(x)+434=?
x= number of hours so problem can be rewritten as
6(37)+434
———
222+434=
656

3 0

2 years ago

There are three consecutive even integers. If twice the first integer added to the second is 268, 244 find all three integers.

Rudik [331]

Answer:

The numbers would be 89,414 , 89,416, and 89,418

Step-by-step explanation:

In order to find this, start by setting the lowest number as x. Then we can determine that the next two even integers are x + 2 and x + 4. From this we can write the following equation.

2(x) + x + 2 = 268,244

3x + 2 = 268,244

3x = 268,242

x = 89,414

Since the first number is 89,414, we know the next two are 89,416 and 89,418.

6 0

2 years ago

Sabena invests $250 in an account that earns 2.4% interest per year compounded continuously. How many years will it take the acc

g100num [7]

Answer:

It'll take 7.5967 years to have $300 on that account.

Step-by-step explanation:

This problem involves a compounded interest compounded continuously, so in order to solve it we must use the formula for those cases as shown below:

M = C*e^(i*t)

Where M is the final value, C is the initial capital, i is the interest rate and t is the total time. We have:

300 = 250*e^(0.024*t)

e^(0.024*t) = 300/250

e^(0.024*t) = 1.2

0.024*t = ln(1.2)

t = ln(1.2)/0.024 = 7.5967

It'll take 7.5967 years to have $300 on that account.

6 0

2 years ago

What is the rate of change of the linear relationship modeled in the table?

Lisa [10]

The correct answer is 3/2.

Slope = Rate Of Change

Slope Formula: y₂ - y₁ 5 - 2 3
-------------- = ---------- = -----
x₂ - x₁ 3 - 1 2

I hope that this helps you!

Btw, ₁ and ₂ are subscripts, they do not have anything to do with the actual working of the problem.

7 0

3 years ago