The number of girls, g, in a room is four more than two times the number of boys, b. half of the number of girls in the room minus the number of boys is 2. the equations below represent the situation. g=4+2b 1/2 g-b=2

The given equations to the above question are :

g=4+2b and

We need to solve for g and b.

We write the equations in the form ax+by=c.

The first equation is g=4+2b

Subtracting 2b both sides :

g-2b=4.

This is of the form ax+by=c.

The second equation is :

Multiplying both sides by 2 to get rid of the denominator 2 the equation reduces to

g-2b=4.This is of the form ax+by=c.

Both the equations are same .This implies the system of equations has infinite number of solutions.

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240