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2 years ago

I NEED HELP! If f(x)= 5x^2-3 and g(x)=x^2-4x-8, find (f-g)(x).

Mathematics

1 answer:

yaroslaw [1]2 years ago

5 0

Answer:

(f - g)(x) = 4x² + 4x + 5

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Combining Like Terms

Step-by-step explanation:

Step 1: Define

f(x) = 5x² - 3

g(x) = x² - 4x - 8

(f - g)(x) is f(x) - g(x)

Step 2: Find (f - g)(x)

Substitute: (f - g)(x) = 5x² - 3 - (x² - 4x - 8)
Distribute -1: (f - g)(x) = 5x² - 3 - x² + 4x + 8
Combine like terms: (f - g)(x) = 4x² + 4x + 5

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On a coordinate plane, a line goes through (negative 12, negative 2) and (0, negative 4). A point is at (0, 6).

mariarad [96]

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st

Step-by-step explanation:

Parallel lines have:

Same slopes
Different y-intercepts

The formula of the slope of a line which passes through points $(x_{1},y_{1})$ and $(x_{1},y_{1})$ is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ The given line passes through points (-12 , -2) and (0 , -4)

∴ $x_{1}$ = -12 , $x_{2}$ = 0

∴ $y_{1}$ = -2 , $y_{2}$ = -4

- Use the formula of the slope above to find the slope of the given line

∵ $m=\frac{-4-(-2)}{0-(-12)}=\frac{-4+2}{12}=\frac{-2}{12}=\frac{-1}{6}$

∴ The slope of the given line is $\frac{-1}{6}$

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = $\frac{-1}{6}$

∵ The parallel line passes through point (0 , 6)

- The form of the linear equation is y = mx + b, where m is the slope

and b is the y-intercept (y when x = 0)

∵ m = $\frac{-1}{6}$ and b = 6

∴ The equation of the parallel line is y = $\frac{-1}{6}$ x + 6

Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line

Point (-12 , 8)

∵ x = -12 and y = 8

∵ y = $\frac{-1}{6}$ (-12) + 6

∴ y = 2 + 6 = 8

- The value of y is equal the y-coordinate of the point

∴ Point (-12 , 8) is on the line

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/9527422

#LearnwithBrainly

4 0

3 years ago

Read 2 more answers

PLEASE NO LINKS, I will report you.

FromTheMoon [43]

Answer:

for 18 x is 6 and for 20 it is 11

Step-by-step explanation:

For 18, since -1+2x and 5+x is the same thing, set up and equation. WE can simplify to -1+x=5 and then we get x=6

For 20, 18 is 11 since 18=-4+2x. If we simplify we get 22=2x then we can use algebra to say that x=11

Hope this helps :)

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2 years ago

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daser333 [38]

Answer:

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Step-by-step explanation:

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Paha777 [63]

Answer:

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Step-by-step explanation:

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