Solve the equation. round to the nearest hundredth. show work.

The value of x = 0.41

Step-by-step explanation:

∵

Let

∴

∴ 6y² - 5y = 6

∴ 6y² - 5y - 6 = 0 ⇒ factorize

∴ (3y + 2)(2y - 3) = 0

∴ 3y + 2 = 0 ⇒ 3y = -2 ⇒ y = -2/3

∴ 2y - 3 = 0 ⇒ 2y = 3 ⇒ y = 3/2

∵

∴ ⇒ refused

  (never gives -ve values)

∵ ⇒ insert ln in both sides

∵ ⇒ ln(e) = 1

∴

∴ x = ln(3/2) = 0.41

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.