Factor the expressions.
x2 + 22x + 120 =

(x + 10 and (x + 12)

Step-by-step explanation:

x^2 + 22x + 120 = ( ? )( ? )

We need to find two constants whose product is 120 and whose sum is 22.

Let the two constants be a and b.  Then:

a*b = 120 and a + b = 22.

It's a bit easier to find a and b such that a + b = 22:  2 and 20, 4 and 18, 6 and 16, and so on.  Note that 6 + 16 = 22 (correct) but that 6*16 = 96 (not correct).  Try 8 and 14, 10 and 12.  Note that 10 + 12 = 22 and that 10*12 = 120.  So the desired roots are {10, 12} and the desired factors are (x + 10 and (x + 12).

Check:  Does (x + 10)(x + 12) work out to x^2 + 22x + 120?

                       x^2 + 12x + 10x + 120 = x^2 + 22x + 120?  YES

The factors are (x + 10 and (x + 12).

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

395.84

step-by-step explanation:

2πrh+2πr²

2 (pie)(radius)(height)+2(pie)(radius)^2