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3 years ago

5

The table below shows four systems of equations:

1 answer:

fredd [130]3 years ago

5 0

<span>System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1

This is the correct answer because not only is it true but it also follows the property of solving systems of equations with adding the equations. To prove that it is true:

2nd equation in system #2 = 1st equation in system #1 + 2(2nd equation in system #1)

</span>10x − 7y = 18 == 4x − 5y = 2 + 2(<span>3x − y = 8)
10x - 7y = 18 == 4x - 5y = 2 + 6x - 2y = 16
10x = 7y = 18 == 10x - 7y = 18</span>

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Drag each tile to the correct box.

Natasha_Volkova [10]

Answer:

1) Function h

interval [3, 5]

rate of change 6

2) Function f

interval [3, 6]

rate of change 8.33

3) Function g

interval [2, 3]

rate of change 9.6

Step-by-step explanation:

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

$\frac{f(b)-f(a)}{b-a}$

step 1

Find the average rate of change of function h(x) over interval [3,5]

Looking at the third picture (table)

$f(a)=h(3)=4$

$f(b)=h(5)=16$

$a=3$

$b=5$

Substitute

$\frac{16-4}{5-3}=6$

step 2

Find the average rate of change of function f(x) over interval [3,6]

Looking at the graph

$f(a)=f(3)=10$

$f(b)=f(6)=35$

$a=3$

$b=6$

Substitute

$\frac{35-10}{6-3}=8.33$

step 3

Find the average rate of change of function g(x) over interval [2,3]

we have

$g(x)=\frac{1}{5}(4)^x$

$f(a)=g(2)=\frac{1}{5}(4)^2=\frac{16}{5}$

$f(b)=g(3)=\frac{1}{5}(4)^3=\frac{64}{5}$

$a=2$

$b=3$

Substitute

$\frac{\frac{64}{5}-\frac{16}{5}}{3-2}=9.6$

therefore

In order from least to greatest according to their average rates of change over those intervals

1) Function h

interval [3, 5]

rate of change 6

2) Function f

interval [3, 6]

rate of change 8.33

3) Function g

interval [2, 3]

rate of change 9.6

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