Natasha buys 5 bottles of orange juice. She has coupons for $0.65 off the regular price of each bottle of the juice. After using the coupons, the total cost of the orange juice is $6.20. What is your regular price of a bottle of orange juice?

$1.89

Step-by-step explanation:

First we need to do $0.65 times 5 to see how much money the bottles are after the coupons.

0.65 times 5 =3.25

After we subtract this, we get 6.20, which means we have to add 3.25 to 6.20 to find out the total price without the coupon.

You get $9.45.

Now you have to divide this by 5 to get the cost of the regular price per bottle of orange juice.

9.45 divided by 5 is 1.89

Each bottle costs $1.89.

Hope this helped!

x³ - 6·x² + 6·x + 8 = (x - 4) × (x - (1 + √3)) × (x + 1 + √3)

Step-by-step explanation:

From the given graph of the polynomial, x³ - 6·x² + 6·x + 8, we have that one of the zeros of the polynomial, which is one point the graph cuts the x-axis is given as follows;

At a zero, we have, x = 4

∴ x - 4 = 0 is a factor of the polynomial

Dividing the given polynomial by (x - 4), gives;

x² - 2·x - 2

(x³ - 6·x² + 6·x + 8)÷(x - 4)

x³ -4·x²

-2·x² + 6·x + 8

-2·x² + 8·x

-2·x + 8

-2·x + 8

0

∴ (x³ - 6·x² + 6·x + 8)÷(x - 4) = x² - 2·x - 2

∴ (x - 4) × (x² - 2·x - 2) = x³ - 6·x² + 6·x + 8

Factorizing x² - 2·x - 2, gives;

x = (2 ± √((-2)² - 4×1×(-2)))/(2 × 1) =  (2 ± 2·√(3)/(2) = (1 ± √(3)

Therefore, x = 1 + √3, (x - (1 + √3)) = 0 or x = 1 - √3, (x - (1 - √3)) = 0 which gives the factors, after factorizing completely as follows;

x³ - 6·x² + 6·x + 8 = (x - 4) × (x - (1 + √3)) × (x + 1 + √3)