Let f(x)=-4x+7 and g(x)=10x-6. Find f(g(x))

Answers

Answer 1

Answer: $\bf \begin{cases}f(x)=-4x+7\ng(x)=10x-6\end{cases}\qquad \qquad f(~~g(x)~~)=-4[g(x)]+7\n\n\nf(~~g(x)~~)=-4[10x-6]+7\implies f(~~g(x)~~)=-40x+24+7\n\n\nf(~~g(x)~~)=-40x+31$

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A 65.0 gram sample of some unknown metal at 100.0° C is added to 100.8 grams of water at 22.0° C. The temperature of the water rises to 27.0° C. If the specific heat capacity of liquid water is 4.18 J/ (°C × g), what is the specific heat of the metal?2.25 J/ (°C × g).
1.75 J/ (°C × g).
0.444 J/ (°C × g).
0.324 J/ (°C × g).

Answers

heat gained by the metal = heat lost by the water
65.0* Cs * (100.0°C - 27.0°C) = 100.8 g * 4.18 J/(°Cxg) * (27.0°C - 22.0°C)

Cs = 100.8 * 4.18 * 5.0 / (65.0 * 73) J/(°Cxg) = 0.444J/(°Cxg)

Answer: the fhird option, 0.444 J/(°Cxg)

Monica is 2 years older than Liam. Emmett is 34. Brittany is 5 years older than Emmett and 4 years older than Liam. How old is Liam?

Answers

Answer:

She is 30

Explanation:

Because if you read it right it says "Emmett is 4 years older than Liam." Also you had a grammar error in it.

Ernie deposited $4000 between two savings accounts. One account paid 4% simple interest and the other paid 2%. At the end of one year, Ernie had earned $140 in interest for both accounts. How much money did Ernie deposit in the account that paid 4% interest?A) $2000
B) $2500
C) $2800
D) $3000

Answers

D) 3000
4000
-140
=3000

Consider the function f(x)=6x+5
(A) find it’s average rate of change by changing x=1 to x=5

Answers

Answer: I really don’t know

Step-by-step explanation: I need help with this as well. I’m really sorry if you were looking for a real answer

Final answer:

The average rate of change of the function f(x) = 6x +5 over the interval x = 1 to x = 5 is calculated with the formula Δf/Δx and is found to be 6.

Explanation:

In the given function, f(x) = 6x + 5, the average rate of change is calculated by the formula Δf/Δx, which refers to the change in the function value over the change in the x-value. Plugging in the given values, we have:

Δf = f(5) - f(1) = [6(5) + 5] - [6(1) + 5]

Δx = 5 - 1

So, the average rate of change is Δf/Δx = [30 + 5 - 6 - 5]/(5 - 1) = 24/4 = 6.

Learn more about Rate of Change here:

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The area of the trapezoid is 108 in2.

What is the height of the trapezoid?

Answers

The area of the trapezoid is given by the formula A= (a+b)/ 2 * h

in this question a= 8, b= 10, A= 108 inches², and h is what we have to find, substitute what we have got into the formula and you will have:

108= (8+10) /2 *h

108= 9 *h

h= 108/9

h= 12 inches

area for a trapezoid is A= a+b/2 times h (a and b are the bases which are 8 and 10

so 108=8+10/2 x h 8+10 divided by 2 equals 9 so now we have 108=9 x h

now we must divide both sides by 9 to solve for the height 108/9 equals 12 so the height of the trapezoid is 12

Stephanie took a science exam that had two parts. Part 1: She got 16 questions correct, which was 45 of the number of part 1 questions. Part 2: She got 16 questions correct, which was 23 of the number of part 2 questions. What was the total number of questions on Stephanie's exam?

Answers

Given :

Stephanie took a science exam that had two parts. Part 1: She got 16 questions correct, which was 4/5 of the number of part 1 questions. Part 2: She got 16 questions correct, which was 2/3 of the number of part 2 questions.

To Find :

The total number of questions on Stephanie's exam.

Solution :

Let, number of questions in Part 1 is x :

$16=(4)/(5)x\n\nx=20$

Let, number of questions in Part 2 is y :

$16=(2)/(3)y\n\ny=24$

Therefore, total number of questions on Stephanie's exam are 20 + 40 = 60.

Hence, this is the required solution.

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