Select the three measurements that could be side lengths that form a right triangle
7cm
11cm
54 cm
60 cm
61 cm
65 cm

The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.

Step-by-step explanation:

The measurements are,

                   7cm, 11cm, 54cm, 60cm, 61cm, 65cm

Step:1

                  To check the right angle triangle, Pythagorean theorem can be used.

                 For a Pythagorean theorem,

                                      ..........................(1)

                The side values are lower than the hypotenuse,

                                                         ...................................(2)

                Where,

                          a,b - side values

                             c - Hypotenuse

                For right angle triangle,  c > a, b

                Alternative : 1

                Take, a = 7cm, b = 11cm

                From eqn (2),

                                                    = = 13.04

               The above value is not equal to the any one of the values of ( 54cm. 60cm, 61cm, 65cm ), So its not an sides of right triangle.

                Alternative : 2

                Take, a = 7cm, b = 54cm

                From eqn (2),

                                                    = = 54.45

               The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.

                Alternative : 3

                Take, a = 7cm, b = 60cm

                From eqn (2),

                                                    = = 60.406

               The above value is not equal to the any one of the values of (61cm, 65cm ), So its not an sides of right triangle.

                Alternative : 4

                Take, a = 7cm, b = 61cm

                From eqn (2),

                                                    = = 61.40

               The above value is not equal to the values of (65cm ), So its not an sides of right triangle.

                  Alternative : 5

                Take, a = 11cm, b = 54cm

                From eqn (2),

                                                    = = 55.1089

               The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.      

                 Alternative : 6

                Take, a = 11cm, b = 60cm

                From eqn (2),

                                                  = = 61

               The above value is equal to the values of (61cm ), So its an sides of right triangle. The three sides are 11, 60 and 61.

Step:2

             Check for solution,

Result:

             The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.                  

4 candies

step-by-step explanation:

7 x 28 = 196

200 - 196 = 4 candies remaining.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b