The volume of a prism which has an altitude of 10 units and has a right triangle base with a hypotenuse of 13 units and a leg of 12 units is:

The volume of the prism = 300 units³

Step-by-step explanation:

* Lets study the triangular prism

- The triangular prism has 6 faces

- Two right triangular bases

- Four rectangular side faces

- The volume of the prism = area of its base × its height (altitude)

* Now lets solve the problem

∵ The base is a right triangle with a hypotenuse of 13 units and

   a leg of 12 units

∵ The area of the right triangle = 1/2 × leg1 × leg2

- You can find the length of other leg by using Pythagoras theorem

∵ (hypotenuse)² = (leg1)² + (leg2)²

∵ hypotenuse = 13 units

∵ leg1 = 12 units

∴ (13)² = (12)² + (leg2)²

∴ 169 = 144 +  (leg2)² ⇒ subtract 144 from both sides

∴ 25 =  (leg2)² ⇒ take √ for both sides

∴ leg2 = 5 units

- The area of the right triangle = 1/2 × leg1 × leg2

∴ The area of the base = 1/2 × 12 × 5 = 30 units²

∴ The volume of the prism = 30 × 10 = 300 units³

i believe your answer is 99.7% of 7-year-old children are between 46.6 inches and 49.5 inches tall.

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)