4. You sketch a right triangle that has a hypotenuse of 12 centimeters, and one leg
that is 7 centimeters. How many centimeters
Is the other leg?

√95 cm

Step-by-step explanation:

To solve, you need to use the pythagorean theorem, or a^2 + b^2 = c^2

The hypotenuse is the c and let one leg be b. You can write:

a^2 + 7^2 = 12^2

a^2 + 49 = 144

Now, you need to solve for a:

a^2 = 144 - 49

a^2 = 95

a = √95 cm, or about 9.75cm

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.