3x – 4y = -5
y = 4x - 2
Is (1, 2) a solution of the system?

Yes, the ordered pair (1, 2) is a solution to the system.

Step-by-step explanation:

The answer can be found quite quickly. Simply substitute the x coordinate of the given pair for x, and the y coordinate of the given pair for y.

The x coordinate is 1 and the y coordinate is 2, so...

3(1) - 4(2) = -5

2=4(1)-2.

Next, simplify:

3-8=-5

This equation is TRUE.

2=4-2

This equation is also TRUE.

Hopefully, this helps in some way!

(a) the volume of the cone is 20/3 in3

hence, option a is correct.

(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