For what value of x, the triangle having the sides x, x+7,x+8 is a right angled triangle

x = 5

Step-by-step explanation:

Using Pythagoras' identity.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

Here the longest side, the hypotenuse is x + 8, thus

x² + (x + 7)² = (x + 8)² ← expand factors using FOIL

x² + x² + 14x + 49 = x² + 16x + 64

2x² + 14x + 49 = x² + 16x + 64 ← subtract terms on right side from both sides

x² - 2x - 15 = 0 ← in standard form

(x - 5)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 3 = 0 ⇒ x = - 3

However x > 0 , thus x = 5

The sides of the right triangle are 5, 12, 13

answer: the answer is 23

step-by-step explanation:

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,