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3 years ago

Which inequality is NOT satisfied by this table of values?

Mathematics

1 answer:

klasskru [66]3 years ago

4 0

Answer: y < -2x-4

Step-by-step explanation:

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Given f(x)=x^2+2x+3 and g(x)=x+4/3 solve for f(g(x)) when x=2

Makovka662 [10]

Answer:

$\displaystyle\mathsf{f(g(2)) \:=\:\frac{187}{9}}$

Step-by-step explanation:

We are provided with the following functions:

f(x) = x² + 2x + 3

$\displaystyle\mathsf{ g(x)\:=\:x+\frac{4}{3} }$

The given problem also requires to find the Composition of Functions, f(g(x)) when x = 2.

The <u>Composition of Function</u> <em>f</em> with function <em>g</em> can be expressed as ( <em>f ° g </em>)(x) = f(g(x)). In solving for the composition of functions, we must first evaluate the <em>innermost</em> function, g(x), then use the output as an input for f(x).

<h2>Solve for f(g(x)) when x = 2:</h2><h3><u>Find g(x):</u></h3>

Starting with g(x), we will use x = 2 as an <u>input</u> value into the function:

$\displaystyle\mathsf{ g(x)\:=\:x+\frac{4}{3} }$

$\displaystyle\mathsf{ g(2)\:=\:(2)+\frac{4}{3} }$

Transform the first term, x = 2, into a fraction with a denominator of 3 to combine with 4/3:

$\displaystyle\mathsf{ g(2)\:=\:\frac{2\: \times\ 3}{3}+\frac{4}{3} }$

$\displaystyle\mathsf{ g(2)\:=\:\frac{6}{3}+\frac{4}{3}\:=\:\frac{6+4}{3}}$

$\displaystyle\mathsf{ g(2)\:=\:\frac{10}{3} }$

$\displaystyle\mathsf{Therefore,\:\: g(2)\:=\:\frac{10}{3} }$

Next, we will use $\displaystyle\mathsf{\frac{10}{3}}
$ as input for the function, f(x) = x² + 2x + 3:

f(x) = x² + 2x + 3

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg)\:=\:x^2 \:+ 2x\:+\:3}$

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{10}{3}\Bigg)^{2}\:+ 2\Bigg(\frac{10}{3}\Bigg) \:+\:3}$

Use the <u>Quotient-to-Power Rule of Exponents</u> onto the <em>leading term </em>(x²):

$\displaystyle\mathsf{Quotient-to-Power\:\:Rule:\:\: \Bigg(\frac{a}{b}\Bigg)^m\:=\:\frac{a^m}{b^m} }$

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{10\:^2}{3\:^2}\Bigg)\:+ 2\Bigg(\frac{10}{3}\Bigg) \:+\:3}$

Multiply the numerator (10) of the middle term by 2:

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{100}{9}\Bigg)\:+ \Bigg(\frac{20}{3}\Bigg) \:+\:\frac{3}{1}}$

Determine the <u>least common multiple (LCM)</u> of the denominators from the previous step: 9, 3, and 1 (which is 9).
Then, transform the denominators of 20/3 and 3/1 on the <u>right-hand side</u> of the equation into like-fractions:

$\displaystyle\mathsf{\frac{20}{3}\Rightarrow \:\frac{20\:\times\ 3}{3\:\times\ 3} =\:\frac{60}{9}}$

$\displaystyle\mathsf{\frac{3}{1}\Rightarrow \:\frac{3\:\times\ 9}{1\:\times\ 9} =\:\frac{27}{9}}$

Finally, add the three fractions on the right-hand side of the equation:

$\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{100}{9}\Bigg)\:+ \Bigg(\frac{60}{9}\Bigg) \:+\:\frac{27}{9}\:=\:\frac{187}{9}}$

<h2>Final Answer:</h2>

$\displaystyle\mathsf{Therefore,\:\:f(g(2)) \:=\:\frac{187}{9}.}$

<em>Keywords:</em>

Composition of functions

f o g

f (g(x))

____________________________________

Learn more about <u><em>Composition of Functions</em></u> here:

brainly.com/question/11388036

8 0

2 years ago

A large brine tank containing a solution of salt and water is being diluted with fresh water. The relationship between the elaps

rewona [7]

Answer:

41.04

Step-by-step explanation:

thats the answer on khan academy :3 i hope this helps

6 0

3 years ago

Plz help ASAP!! Explain your answer! I will mark at brainliest!!!

SSSSS [86.1K]

Cylinder: First you need to find the radius. To do that, you need to divide the diameter by 2

Then, you multiply it by itself

After that, you multiply it by the height

And finally multiply it by pi

Cone: First, you need to find the radius dividing the diameter by 2

Then, multiply it by itself

After that, divide the height by 3

Finally, multiply the radius times the height and then multiply it by pi

The answer to the cylinder is 251.2 and the answer to the cone is 251.2

The processes are the following:

Cylinder

D:8

R:4

V:π4^2*5

V:π16*5

V:80π

V:251.2

Cone

D:8

R:4

V:π4^2 15/3

V:π16*5

V:80π

V:251.2

5 0

3 years ago

Ethan has has 3/4 of a box of cereal. He gives 1/8 of the box to his little brother and Ethan eats 1/4 of the box, himself. What

nalin [4]

Answer:

Step-by-step explanation:

3/4 - 1/4 = 2/4

2/4 - 1/4

get the same denominators

2/4 /2= 1/8

1/8 - 1/8= 0

There is nothing left in the cereal box.

6 0

4 years ago

The width of Maya’s poster is 2 inches shorter than the length. The graph models the possible area (y) of Maya’s poster determin

sp2606 [1]

Width = Length - 2
Area = L x W
y = x * ( x - 2 )
If the point is ( 2, 0 ): x = 2, y = 0
y = 2 * ( 2 - 2 ) = 2 * 0 = 0 ( area )
Answer:
B ) The area is 0 if the length is 2.

3 0

3 years ago

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