F(x)=3/2x-3 g(x)=5x+4 determine where f(x)=g(x)

x = -2

Step-by-step explanation:

I am not sure you typed this correctly.

the way you wrote this, it says

f(x) = (3/2)x - 3

but I suspect you mean

f(x) = 3/(2x) - 3

our even

f(x) = 3/(2x - 3)

I assume the last one.

3/(2x - 3) = 5x + 4

that is what is meant by f(x)=g(x) : find out the value(s) of x for which the y/result values of both functions are the same.

so, then we can transform

3 = (5x + 4)×(2x - 3)

3 = 10x² -15x + 8x - 12

10x² - 7x - 15 = 0

and this can be solved by the solution squared equations :

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case here

a = 10

b = -7

c = -15

so,

x = (7 ± sqrt(49 - 4×10×-15))/20 = (7 ± sqrt(49+600))/20 =

≈ (7 ± 25.48)/20

x1 = -18.48/20

x2 = 32.48/20

these are really not nice numbers for a homework or such.

so, let's try the next interpretation of what you wrote.

f(x) = 3/(2x) - 3

3/(2x) - 3 = 5x + 4

3/(2x) = 5x + 7

3 = 10x² + 14x

10x² + 14x - 3 = 0

a = 10

b = 14

c = -3

x = (-14 ± sqrt(196 - 4×10×-3))/20 =

= (-14 ± sqrt(196 + 120))/20 = (-14 ± 17.78)/20

that did not give any good numbers either.

so, next attempt :

f(x) = (3/2)x - 3 = 3x/2 - 3

3x/2 - 3 = 5x + 4

3x/2 = 5x + 7

3x = 10x + 14

7x = -14

x = -2

ok, so it seems the first, original interpretation was correct. sorry.

but just in case, please use the other 2 approaches if and as needed.

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.

unless if u could do my questions, if not i wouldn't want to