Let f(x) = -20x2 + 14x + 12 and g(x) = 5x - 6. find f/g and state its domain. –4x – 2; all real numbers 5x - 6; all real numbers except x = 6/5 –4x – 2; all real numbers except x = 6/5 5x - 6; all real numbers

Solution

f(x) = -20 +14x + 12 and g(x) = 5x - 6.

(f/g)(x) =

(f/g)(x) =

Step 1: Now we have to factorize the numerator.

f(x) = -20x^2 + 14x + 12

Factor out -2, we get

= -2 (10x^2 - 7x - 6)

Now we can factorize 10x^2 - 7x - 6                  

f(x) = -2(2x + 1) (5x - 6)

Step 2: Plug in the factors

(f/g)(x) =

Step 3: Cancel out the common factor (5x - 6) from the numerator and the denominator, we get

(f/g)(x) = -2(2x +1) = -4x -2

Since -4x -2 is linear expression, the domain is all the real numbers.

Therefore, the answer is –4x – 2; all real numbers

Thank you :)

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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