If a square television has a 32-inch diagonal viewing screen, what are the approximate dimensions of the screen? Round to the nearest inch. inches by ? ?inches

The dimensions are 23 inch by 23 inches

Step-by-step explanation:

We can use the Pythagorean theorem

a^2+b^2 = c^2

We know the diagonal  is 32 and since it is square each side is x

x^2+x^2 = 32^2

2x^2 = 32^2

2x^2 =1024

Divide by2

x^2 =512

Take the square root of each side

sqrt(x^2) = sqrt( 512)

x =22.627417

To the nearest inch

x = 23

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)