In a right triangle, the hypotenuse is three inches more than twice the length of one leg. if the other leg is 12 inches, what is the lengths of the other leg and hypotenuse?

Length of hypothenuse = 13 inches

Length of other leg = 5 inches

Step-by-step explanation:

A triangle has three sides and three angles. A right angle triangle has 90 degrees as one of the angles. The remaining two angles are complimentary. This means that the sum if the other two angles is 90 degrees.

The longest side is the hypotenuse. The shorter sides are the opposite and adjacent.

In this triangle, the hypotenuse is three inches more than twice the length of one leg. Let the length of one leg be x inches.

Hypothenuse = 2x + 3

The other leg is 12 inches.

The diagram is illustrated in the attached photo.

Applying Pythagoras theorem,

Hypothenuse ^2 = adjacent^2 + opposite ^2

(2x+3)^2 = 12^2 + x^2

(2x+3)(2x+3)= 144 + x^2

4x^2 + 6x + 6x + 9 = 144 + x^2

4x^2 - x^2 + 6x + 6x + 9 - 144 = 0

3x^2 +12x - 135 = 0

3x^2 +27x - 15x - 135 = 0

3x(x+9)-15(x+9)=0

(3x -15)(x+9) = 0

3x -15 = 0 or x+9= 0

3x = 15 or x = -9

x = 15/3 = 5

x = 5inches because it cannot be negative.

Length of hypothenuse = 2x + 3

= 2×5 + 3 = 10 + 3 = 13 inches

which of the following can speed up the rate at which the liver breaks  

down alcohol?

question 1 options:

carbohydrates  

coffee  

nothing  

high-protein meals  

step-by-step explanation:

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.