Factor completely. 2x^2y + 2xy + 4x + 4 a. (2x + 4)(xy + 1) b. (2x + 4y)(x + 1) c. 2(xy + 2)(x + 1) d. (2xy + 4)(x + 1)

2(xy + 2)(x + 1)   (C)

Step-by-step explanation:

2x^2y + 2xy + 4x + 4

= 2xy(x + 1) + 4(x + 1)

= (2xy + 4)(x + 1)

=  2(xy + 2)(x + 1)

76%

step-by-step explanation:

24% are dogs and the remaining is 76% because 100-24=76

(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.