The length of the hypotenuse of a right triangle is three times the length of the shorter leg. The length of the longer leg is 12. What is the length of the shorter leg. Question 12 options: 2√3, √14.4, 6√2, 3√2

D

Step-by-step explanation:

Say the short leg is x and the hypotenuse is y. Then, y = 3x (because "The length of the hypotenuse of a right triangle is three times the length of the shorter leg.")

Use the Pythagorean Theorem: a^2 + b^2 = c^2 (where a and b are the legs and c is the hypotenuse). Here, we can say a = x and b = 12 and c = y. So:

x^2 + 12^2 = y^2

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

x^2 + 144 = 9x^2

8x^2 = 144

x^2 = 18

x =

The answer is D.

Hope this helps!

Last one: 3√2

Step-by-step explanation:

Let the shorter length be S

Then,

The hypotenuse would be: 3S

Using pythagoras theorem,

(3S)² = S² + 12²

9S² = S² + 144

8S² = 144

S² = 18

S = sqrt(18)

S = 3sqrt(2)

-50/3 is the final answer! : )

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3