A right triangle has a hypotenuse that is 24 yd long and one leg that is 14 yd long. Find the
length of the other leg.

Step-by-step explanation:

a^2+b^2=c^2 is the formula for area of a triangle.

The hypotenuse (c) is 24. 24*24 is equivalent is 576.

As we are given one side of the triangle we can find a or b, any works, it doesn't effect the answer.

14*14 is 196.

Now we are left with, 196+b^2=576. Then we subtract 196 from both sides so both sides of the equation remain equivalent. Even if you do not use the equation, the hypotenuse of a triangle is always its largest size, so we must subtract a^2 from c^2. 576-196 is 380. The answer is  or the square root of 380. This can be simplified to as 4 is a perfect square and a factor of 380. Hope this helps!!

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.