Can somebody help me with (a) and (b)? Thanks! :D

PART A:

Line m: 1/2x + 6

Line n: 1/2x - 3

PART B:

The slope is the same in both lines

see explanation

Step-by-step explanation:

Since the lines are parallel they have the same slopes

Calculate the slope of line m using the slope formula

m =

with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (2, 7) ← 2 points on the line

m = =

Note the line crosses the y- axis at (0, 6) ⇒ b = 6

Thus

y = x + 6 ← equation of line m

Note for line n the line crosses the y- axis at (0, - 3) ⇒ b = - 3

Thus

y = x - 3 ← equation of line n

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.

(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.