The length of a rectangle is 3 m less than the diagonal and the width is 8 m less than the diagonal. if the area is 74 m^2, how long is the diagonal in meters? round your answer to the nearest tenth.

  14.5 m

Step-by-step explanation:

Let x represent the length of the diagonal. Then the length of the rectangle is (x-3) and its width is (x-8). The area is the product of these, so is ...

  (x -3)(x -8) = 74

  x^2 -11x +24 = 74 . . . . eliminate parentheses

  x^2 -11x = 50 . . . . . . . .subtract 24

  x^2 -11x +30.25 = 80.25 . . . . add 30.25 to complete the square

  (x -5.5)^2 = 80.25 . . . . . . write as square

  x - 5.5 = √80.25 ≈ 8.958 . . . . take the square root

  x = 8.958 + 5.5 = 14.458 . . . . .add 5.5

The length of the diagonal is about 14.5 meters.

Step-by-step explanation:

The diagram of the rectangle, ABCD is shown in the attached photo. The diagonal of the rectangle forms a triangle, ABC

Applying Pythagoras theorem,

d^2 = (d - 8)^2 + (d - 3 )^2

d^2 = d^2 - 16d + 64 + d^2 - 6d + 9

d^2 = 2d^2 - 22d + 73

d^2 - 22d + 73 = 0

d^2 = 22d - 73 - - - - - - 1

If the area is 74 m^2, it means that

(d- 8)(d- 3) = 74

d^2 - 11d + 24 = 74

d^2 = 74 - 24 + 11d

d^2 = 50 + 11d - - - - - - - -2

Equating equation 1 and 2, it becomes

22d - 73 = 50 + 11d

22d - 11d = 50 + 73

11d = 123

d = 123/11 = 11.182

diagonal = 11.2 m to the nearest tenth.

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)

the football players are volunteering for the test.

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