8. Subtact (7x – 10) – (-6x – 8).

13x - 2

Step-by-step explanation:

7x - -6x = 7x + 6x = 13x.

-10 - -8 = -10 + 8 = -2

13x - 2

13x - 2

Step-by-step explanation:

( 7x - 10 ) - ( -6x - 8 )

First, distribute the minus sign outside of the second parenthesis. Multiply each term within the second parenthesis by the minus sign.

( 7x - 10 ) + ( (-1)(-6x) + (-1)( -8))

Simplify,

( 7x - 10 ) + ( 6x + 8 )

Remove parenthesis,

7x - 10 + 6x + 8

Simplify, combine like terms,

7x - 10 + 6x + 8

13x - 2

(w – 2.5)(w + 2.5)

(–4v – 9)(–4v + 9)

step-by-step explanation:

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.