Afarmer wants to plant peas and carrots on no more than 200 acres of his farm. if x represents the number of acres of peas and y represents the number of acres of carrots for solution (x, y), then which is a viable solution?
a.(−50, 160)
b.(80, 160)
c.(75, −200)
d.(60, 135)

Option D.(60, 135)

Step-by-step explanation:

Let

x -----> the number of acres of peas

y ----> the number of acres of carrots

we know that

The inequality that represent the problem is equal to

so

Verify each case

case A) (-50,160)

substitute the value of x and the value of y in the inequality and then compare the result

----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case B) (80,160)

substitute the value of x and the value of y in the inequality and then compare the result

----> is not true

therefore

The point is not a solution

case C) (75,-200)

substitute the value of x and the value of y in the inequality and then compare the result

----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case D) (60,135)

substitute the value of x and the value of y in the inequality and then compare the result

----> is true

therefore

The point is a viable solution

(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.