Solve the following equation using the zero prouduct property (x+9)(4x-1)=0

-9

1

Distribute

x

(

4

x

−

1

)

+

9

(

4

x

−

1

)

=

0

x(4x−1)+9(4x−1)=0



2

Distribute

4

x

2

−

x

+

9

(

4

x

−

1

)

=

0

4x

2

−x+9(4x−1)=0



3

Distribute

4

x

2

−

x

+

36

x

−

9

=

0

4x

2

−x+36x−9=0



4

Combine like terms

4

x

2

+

35

x

−

9

=

0

4x

2

+35x−9=0



5

Use the quadratic formula

x

=

−

35

±

35

2

−

4

⋅

4

(

−

9

)

2

⋅

4

x=

2⋅4

−35±

35

2

−4⋅4(−9)

​

​



6

Simplify

x

=

−

35

±

37

8

x=

8

−35±37

​



7

Separate the equations

x

=

−

35

+

37

8

x

=

−

35

−

37

8

x=

8

−35+37

​

x=

8

−35−37

​



8

Solve

x

=

1

4

x

=

−

9

x=

4

1

​

x=−9

(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.