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posledela
2 years ago
7

Given that f(x) = x2 + 5x + 6 and g(x) = x + 2, find (fºg)(x) and

Mathematics
1 answer:
PolarNik [594]2 years ago
7 0

Answer:

(f\circ g)(x)=x^2+9x+20

Step-by-step explanation:

We have the two functions:

f(x)=x^2+5x+6\text{ and } g(x)=x+2

And we want to find:

(f\circ g)(x)

This is equivalent to:

(f\circ g)(x)=f(g(x))

Therefore, we will have:

f(x+2)

By substitution:

f(x+2)=(x+2)^2+5(x+2)+6

Simplify. Square and distribute:

f(x+2)=(x^2+4x+4)+(5x+10)+6

Rearrange:

f(x+2)=(x^2)+(4x+5x)+(4+10+6)

Combine like terms:

f(x+2)=(f\circ g)(x)=x^2+9x+20

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List all two-digit positive integers that satisfy both of the following :
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The two-digit positive integers that tens and ones digits are consecutive numbers include 12, 23, 34, 45, 56, 67, 78, and 89.

<h3>What are integers?</h3>

It should be noted that integers are the whole numbers that can be either positive, negative, or zero.

The two-digit positive integers that the integer is the product of two consecutive numbers will be:

3 × 4 = 12

7 × 8 = 56

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2 years ago
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Nolan Walker decided to buy a used snowmobile since his credit union was offering such low interest rates. He borrowed $2,700 at
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<h3>How to calculate simple interest amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R % annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

I = \dfrac{P \times R \times T}{100}

The given data in the problem is;

The principal is,P=$2700

The rate of interest = 3.5%

The total time interval is,T

The total time interval is;

\rm T= 5+365+31+21\ days

The simple interest is found as;

\rm SI = P \times R \times T \\\\ \rm SI = 2700 \times 0.0035 \times 1.172222 \\\\ SI=111.0375

Hence, he pays in interest of $111.0375.

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2 years ago
3x - 4y = -16<br> 2x - 4y = -8<br> what is x and y
FinnZ [79.3K]

Answer:

x = -8 , y = -2

Step-by-step explanation:

Solve the following system:

{3 x - 4 y = -16 | (equation 1)

2 x - 4 y = -8 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:

{3 x - 4 y = -16 | (equation 1)

0 x - (4 y)/3 = 8/3 | (equation 2)

Multiply equation 2 by 3/4:

{3 x - 4 y = -16 | (equation 1)

0 x - y = 2 | (equation 2)

Multiply equation 2 by -1:

{3 x - 4 y = -16 | (equation 1)

0 x+y = -2 | (equation 2)

Add 4 × (equation 2) to equation 1:

{3 x+0 y = -24 | (equation 1)

0 x+y = -2 | (equation 2)

Divide equation 1 by 3:

{x+0 y = -8 | (equation 1)

0 x+y = -2 | (equation 2)

Collect results:

Answer: {x = -8 , y = -2

4 0
2 years ago
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