Drag the tiles to the correct boxes to complete the pairs. Match each hypotenuse length with the leg lengths that will create a right triangle.

√8 ==> 2 units, 2 units

√7 ==> √5 units, √2 units

√5 ==> 1 unit, 2 units

3 ==> >2 units, √5 units

Step-by-step explanation:

To determine which pair of legs that matches a hypotenuse length to create a right triangle, recall the Pythagorean theorem, which holds that, for a right angle triangle, the square of the hypotenuse (c²) = the sum of the square of each leg length (a² + b²)

Using c² = a² + b², let's find the hypotenuse length for each given pairs of leg.

=>√5 units, √2 units

c² = (√5)² + (√2)²

c² = 5 + 2 = 7

c = √7

The hypothenuse length that matches √5 units, √2 units is √7

=>√3 units, 4 units

c² = (√3)² + (4)²

c² = 3 + 16 = 19

c = √19

This given pair of legs doesn't match any given hypotenuse length

=>2 units, √5 units

c² = (2)² + (√5)²

c² = 4 + 5 = 9

c = √9 = 3

legs 2 units, and √5 units matche hypotenuse length of 3

=>2 units, 2 units

c² = 2² + 2² = 4 + 4

c² = 8

c = √8

Legs 2 units, and 2 units matche hypotenuse length of √8

=> 1 unit, 2 units

c² = 1² + 2² = 1 + 4

c² = 5

c = √5

Leg lengths, 1 unit and 2 units match the hypotenuse length, √5

i dont understand

step-by-step explanation:

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)