What is the value of the expression below?

1 3/4 divided by 1/2 minus (1 1/2)^3

1/8

Step-by-step explanation:

Simplify the following:

(1 + 3/4)/(1/2) - (1/2 + 1)^3

Hint: | Write (1 + 3/4)/(1/2) as a single fraction.

Multiply the numerator of (1 + 3/4)/(1/2) by the reciprocal of the denominator. (1 + 3/4)/(1/2) = ((1 + 3/4)×2)/1:

(3/4 + 1) 2 - (1/2 + 1)^3

Hint: | Put the fractions in 1 + 1/2 over a common denominator.

Put 1 + 1/2 over the common denominator 2. 1 + 1/2 = 2/2 + 1/2:

(1 + 3/4) 2 - (2/2 + 1/2)^3

Hint: | Add the fractions over a common denominator to a single fraction.

2/2 + 1/2 = (2 + 1)/2:

(1 + 3/4) 2 - ((2 + 1)/2)^3

Hint: | Evaluate 2 + 1.

2 + 1 = 3:

(1 + 3/4) 2 - (3/2)^3

Hint: | Put the fractions in 1 + 3/4 over a common denominator.

Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:

4/4 + 3/4 2 - (3/2)^3

Hint: | Add the fractions over a common denominator to a single fraction.

4/4 + 3/4 = (4 + 3)/4:

(4 + 3)/4×2 - (3/2)^3

Hint: | Evaluate 4 + 3.

4 + 3 = 7:

7/4×2 - (3/2)^3

Hint: | Express 7/4×2 as a single fraction.

7/4×2 = (7×2)/4:

(7×2)/4 - (3/2)^3

Hint: | In (7×2)/4, divide 4 in the denominator by 2 in the numerator.

2/4 = 2/(2×2) = 1/2:

7/2 - (3/2)^3

Hint: | Simplify (3/2)^3 using the rule (p/q)^n = p^n/q^n.

(3/2)^3 = 3^3/2^3:

7/2 - 3^3/2^3

Hint: | In order to evaluate 3^3 express 3^3 as 3×3^2.

3^3 = 3×3^2:

7/2 - (3×3^2)/2^3

Hint: | In order to evaluate 2^3 express 2^3 as 2×2^2.

2^3 = 2×2^2:

7/2 - (3×3^2)/(2×2^2)

Hint: | Evaluate 2^2.

2^2 = 4:

7/2 - (3×3^2)/(2×4)

Hint: | Evaluate 3^2.

3^2 = 9:

7/2 - (3×9)/(2×4)

Hint: | Multiply 2 and 4 together.

2×4 = 8:

7/2 - (3×9)/8

Hint: | Multiply 3 and 9 together.

3×9 = 27:

7/2 - 27/8

Hint: | Put the fractions in 7/2 - 27/8 over a common denominator.

Put 7/2 - 27/8 over the common denominator 8. 7/2 - 27/8 = (4×7)/8 - 27/8:

(4×7)/8 - 27/8

Hint: | Multiply 4 and 7 together.

4×7 = 28:

28/8 - 27/8

Hint: | Subtract the fractions over a common denominator to a single fraction.

28/8 - 27/8 = (28 - 27)/8:

(28 - 27)/8

Hint: | Subtract 27 from 28.

| 2 | 8

- | 2 | 7

| 0 | 1:

1/8

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b