two number are on the ratio 2:3.if 12 is added to both the numbers, ratio becomes 5:6.find the numbers

The numbers are: 8 , 12

Step-by-step explanation:

Ratio of two numbers = 2:3

Two numbers are : 2x , 3x

Cross multiply,

6*(2x + 12) = 5*(3x+12)

6*2x +6*12 = 5*3x + 5*12

12x + 72 = 15x + 60

72 - 60 = 15x - 12x

12 = 3x

3x = 12

x = 12/3

x = 4

2x = 2*4 = 8

3x = 3*4 = 12

The numbers are: 8 , 12

y = 0.77(x)

step-by-step explanation:

the jacket retains this value after 23% cut or retains 77% of original value. plug original 87 jacket price for x and the remaining value should be y.

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.