2 - 6k = 5 - 3k - 12 k =

k = 3

Step-by-step explanation:

2 - 6k = 5 - 3k -12

Add like terms at RHS

2 - 6k = -3k - 7

Add 6k to both sides

2 - 6k + 6k = -3k - 7 + 6k

2 = 3k - 7

Add 7 to both sides

2 +7 = 3k

9 = 3k

Divide both sides by 3

9/3 = 3k/3

3 = k

k  = 3

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

(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.