What is the quotient (3x2 + 4x − 15) ÷ (x + 3)?

a) 3x + 5
b) 3x − 5
c) 3x + 1
d) 3x − 1, r = 1

The correct answer is option B. 3x - 5

Step-by-step explanation:

The given polynomial is 3

x² + 4x - 15

To find the quotient of polynomial division

(x² + 4x - 15)/(x - 3)

                         3x - 5                          

     x-3    | 3x² + 4x - 15

                3x² + 9x        

                       -5x  -15

                      -5x - 15

                             0

Therefore the quotient is 3x - 5

The correct answer is option B). 3x -5

(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

step-by-step explanation:

*calories burned = (weight)(calorie factor)*

calories burned = 180 (0.65)

calories burned = 117

the calories he used up is 117, which is 65% of his weight.