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2 years ago

Given that f(x) = 4x + 5 and g(x) = x2 - 2x - 2, find (f + g)(x).

Mathematics

1 answer:

KATRIN_1 [288]2 years ago

4 0

Answer:

Step-by-step explanation:

We are given the two functions:

$f(x)=4x+5\text{ and } g(x)=x^2-2x-2$

And we want to find:

$(f+g)(x)$

This is equivalent to:

$=f(x)+g(x)$

Substitute:

$=(4x+5)+(x^2-2x-2)$

Rearrange:

$=(x^2)+(4x-2x)+(5-2)$

Combine like terms. Hence:

$(f+g)(x)=x^2+2x+3$

Our answer is A.

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Try the numbers 22, 23, 24, 25 in the equation 4/3 = 32/d to test whether any of them is a solution. a. 23 is a solution. c. 24

S_A_V [24]

Answer:

c. 24 is a solution

Step-by-step explanation:

Given equation:

$\frac{4}{3}=\frac{32}{d}$

To test the numbers 22, 23, 24, 25 for the solution.

Solution:

In order to test the given number for the solution, we will plugin each number in the unknown variable $d$ and see if it satisfies the equation.

1) $d=22$

$\frac{4}{3}=\frac{32}{22}$

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

$\frac{4}{3}=\frac{32\div 2}{22\div 2}$

$\frac{4}{3}=\frac{16}{11}$

The above statement can never be true and hence 22 is not a solution.

2) $d=23$

$\frac{4}{3}=\frac{32}{23}$

The fractions can no further be reduced.

The statement can never be true and hence 23 is not a solution.

3) $d=24$

$\frac{4}{3}=\frac{32}{24}$

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

$\frac{4}{3}=\frac{32\div 8}{24\div 8}$

$\frac{4}{3}=\frac{4}{3}$

The above statement is always true and hence 24 is a solution.

4) $d=25$

$\frac{4}{3}=\frac{32}{25}$

The fractions can no further be reduced.

The statement can never be true and hence 25 is not a solution.

4 0

2 years ago

48% of what number is 108? A. 44.4 B. 51.84 C. 225 D. 5184

Ivan

Let the number = x.

48% of x = 108

(48/100)x = 108

x = 108 * 100 /48 = 225 use your calculator.

Answer is option C.

8 0

2 years ago

Read 2 more answers

I need help for this question

Dmitry_Shevchenko [17]

Answer:

Step-by-step explanation:

$12.00 - the total cost of 4 of equally priced gloves

$12.00 : 4 = $3.00 - the cost of 1 glove

The cost per glove is increased by $1.00. Therefore new cost of 1 glove is

$3.00 + $1.00 = $4.00

The total cost of 9 of gloves at the new price:

9 × $4.00 = $36.00

6 0

2 years ago

How much money has to be invested at 2.3% interest compounded continuously to have $41,000 after 17 years?

Llana [10]

For this, we have to calculate how much money has to be invested at 2.3% interest compounded continuously to achieve $41,000 after 17 years

Formula: A= P * ( 1+r)^t
A= $41,000
r=0.023
t= 17
<span>41,000= P * (1+0.023)^17
</span>41,000= P * (1.023)^17
41,000= P * 1.4719
P= 41,000 : 1.4719
P= $27,731.59
Therefore, the answer is C. $27,731.59
I checked by doing the opposite, and I got $41,000.01, which is the closest to the question<span>
</span>

7 0

2 years ago

A flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is

Ainat [17]

Answer:

$15.2~mph$

Step-by-step explanation:

Let the time flown by the flying carpet be $t$ . Then, we have that $(2.4)/t=(1.4)/t+2*4$ .

We multiply both sides of the equation by $t$ to get $2.4=1.4+8t$ .

We subtract $1.4$ from both sides to get $1=8t$ .

We divide both sides of the equation by $t=1/8$ .

We know that the speed of the flying carpet in still wind is the average of the rates of the speed of the flying carpet with the wind and against the wind.

The speed with wind is $(2.4)/(1/8)=19.2$ mph.

The speed against wind is $(1.4)/(1/8)=11.2$ mph.

The speed in still wind is $(19.2+11.2)/2=(30.4)/2=15.2$ .

Therefore, the answer is $\boxed{15.2~mph}$ and we're done!

4 0

2 years ago