Find and simplify the function (f +g) (10), given that f(x) = x + 4 and g(x) = x² +2.

116

Step-by-step explanation:

note that (f + g)(x) = f(x) + g(x)

f(x) + g(x) = x + 4 + x² + 2 = x² + x + 6

To evaluate (f + g)(10) substitute x = 10 into f(x) + g(x), that is

x² + x + 6 = 10² + 10 + 6 = 100 + 10 + 6 = 116

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answer: d.) the total number of protons and neutrons is 15

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simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .