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).

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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