Match the addition and subtraction problems to their solutions:

we conclude that:

5/7 - 3/7:     B 2/7

1/6+3/6:      C 2/3

1/2+1/4:       E 3/4

1/5+1/2:       D 7/10

1/6-1/8:       A 1/24

Step-by-step explanation:

1)

Given the expression

Apply the fraction rule:  

Add the numbers:  

2)

Given the expression

Apply the fraction rule:  

Add the numbers:  

Cancel 4/6: 2/3

3)

Given the expression

Lease common multiplier of 2, 4: 4

Adjust fractions based on LCM

Apply the fraction rule:  

Add the numbers:  

4)

Lease common multiplier of 5, 2: 10

Adjust fractions based on LCM

Apply the fraction rule:  

Add the numbers: 2+5 = 7

5)

Given the expression

Lease common multiplier of 6, 8: 24

Adjust fractions based on LCM

Apply the fraction rule:  

Therefore, we conclude that:

5/7 - 3/7:     B 2/7

1/6+3/6:      C 2/3

1/2+1/4:       E 3/4

1/5+1/2:       D 7/10

1/6-1/8:       A 1/24

47 - 90 = 43

43 - 180 = x

x = 137

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.