The factorization of 8x3 – 125 is (2x – 5)(jx2 + kx + 25). what are the values of j and k? a) j = 6 and k = –10 b) j = 8 and k = 10 c) j = 4 and k = 25 d) j = 4 and k = 10

D

Step-by-step explanation:

8x³ - 125 is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

here 8x³ = (2x)³ ⇒ a = 2x and 125 = 5³ ⇒ b = 5

8x³ - 125 = (2x - 5)((2x)² + (2x × 5) + 5²) = (2x - 5)(4x² + 10x + 25 )

compare the coefficients of like terms with jx² + kx + 25

jx² = 4x² ⇒ j = 4 and kx = 10x ⇒ k = 10 → D

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet