Given the function h(x) = 3(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.Part A: Find the average rate of change of each section. (4 points)

Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)

(10 points)

Answers

Answer 1

Answer:

Answer:

Part A) The average rate of change of section A is 6 and the average rate of change of section B is 24

Part B) The average rate of change of Section B is 4 times greater than the average rate of change of Section A. see the explanation

Step-by-step explanation:

Part A) Find the average rate of change of each section

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change is equal to

$(f(b)-f(a))/(b-a)$

In this problem we have

Section A

$a=1$

$b=2$

$f(a)=f(1)=3(2)^1=6$

$f(b)=f(2)=3(2)^2=12$

Substitute

$(12-6)/(2-1)=6$

Section B

$a=3$

$b=4$

$f(a)=f(3)=3(2)^3=24$

$f(b)=f(4)=3(2)^4=48$

Substitute

$(48-24)/(4-3)=24$

Part B) How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other

Divide the average rate of change section B by the average rate of change of Section B

$(Section\ B)/(Section\ A)=(24)/(6)$

$(Section\ B)/(Section\ A)=4$

$Section\ B=(4)*Section\ A$

The average rate of change of Section B is 4 times greater than the average rate of change of Section A.

One rate of change is greater than the other, because it is an exponential function and the slope grows bigger.

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Answers

a b/c is a mixed number, we can turn a mixed number into its simplest form in this way:
a b/c= a + b/c=(a*c+b)/c

In this case:
7 5/6=7+ 5/6=(7*6+5)/6=(42+5)/6=47/6

Therefore: 7 5/6 =47/6

Convert 7 5/6 to decimal form...

The fractional part of this number is what needs the focus. The whole number is 7, so we know that the decimal will lie somewhere between 7 and 8 (it will be 7 point something). All we have to do is convert 5/6 To decimal and attach it to the 7...

To find the decimal just do the math described by the fraction. 5/6 literally reads 5 ÷ 6. Set up the division and the result is .8333

So the decimal form of
7 5/6 is 7.8333

Alternatively you can set it up as a ratio then solve for x.

5/6 = x/100

Cross multiply

6x = 500

divide each side by 6

x = 83

83/100 = .83

7 5/6 = 7.83

Kara buys 24 bagels. Ten are whole wheat. What fraction of the bagels are wheat? Write in simplest form.

Answers

since 10 is whole wheat, the fraction is 10/24
in the simplest form 5/12

First the default fracton: 24 over 10 bagels.
So 24 over ten simplified (made into smallest form) 12 over 5.

Your answer is 12
__

5

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Answers

Answer:

We can conclude that Δ GHI ≅ Δ JKL by SAS postulate.

Step-by-step explanation:

Δ GHI and Δ JKL are congruents because:

1. Their sides GH and JK are equal (9 units = 9 units)

2. Their included angles ∠G and ∠J are equal (62° = 62°)

3. Their sides GI and JL are equal (17 units = 17 units)

Now, we can conclude that Δ GHI ≅ Δ JKL by SAS postulate.

Write a word problem that can be solved by finding the numbers that have 4 as a factor

Answers

Answer:

'There are 7 rocks in 4 boxes, How many rocks are there in total.'

Step-by-step explanation:

We are given to form a word problem having solution which has 4 as a factor.

Now, if we take the following statement,

'There are 7 rocks in 4 boxes, How many rocks are there in total.'

Its solution is given by,

As there are 4 boxes in total and each box has 7 rocks.

Thus, total number of rocks will be 4 × 7 = 28.

We can see that 4 is a factor of 28.

Hence, the word problem could be 'There are 7 rocks in 4 boxes, How many rocks are there in total.'

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Answers

I have already answered it

We first divide the big shape into smaller shapes

We get a trapezium and a triangle

We add the areas of the trapezium and the triangle together to get the total area of the big shape
It would be:

Area = area of trapezium + Area of triangle
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Answers

28 because 7 times 5 is 35 and 2 times 5 is ten so you have 35-10 which is 25 plus 3 which is 28

7x-2x+3x
Plug in the 5
7(5)-2(5)+3(5)
35-10+15
25+15
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