A chemistry student was asked to make 100 L of 48% alcohol solution by mixing a 40% alcohol solution and a 60% alcohol solution. If x is the required amount (L) of the 40% solution and y is required amount (L) of the 60% solution, which of the following linear systems would best model this situation?

A) x + y = 100

40x + 60y = 48

B) x + y = 0.48

0.4 x + 0.6 y = 100

C) x+ y = 100

0.4 x + 0.6 y = 0.48

D) x + y = 100

0.4x + 0.6y = 0.48(100)

E) x + y = 100

0.4x + 0.6y = 0.48

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

step-by-step explanation:

mnkjn

step-by-step explanation:

(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.