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3 years ago

Triangle CEN is congruent to Triangle CED. What property is shown by line segment CE being congruent to line segment CE?

Mathematics

1 answer:

agasfer [191]3 years ago

4 0

Answer:

C. Reflexive property

Step-by-step explanation:

When a line segment is congruent or the same as itself, it is considered to have a property known as reflexive property.

This means line segment CE is a mirror image of itself. Therefore, line segment CE is congruent to line segment CE.

Line segment CE is what divides the figure given into two equal halves, making both parts congruent to each other.

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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:

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8 0

2 years ago

Solve and show your work for each question.

Harlamova29_29 [7]

Answer:

9/20

Step-by-step explanation:

You set the fraction up at first as 45/100. Then you know that 5 goes into each so you divide by 5 $\frac{45}{100} /5$

45/5=9

100/5=20

You get 9/20, and this is in simplest form.

4 0

3 years ago

Read 2 more answers

How do you find the area of a triangle

Anna007 [38]

Salutations!

How do you find the area of a triangle

To find the area of a triangle, you need to know the formula of the triangle to work it out. The following is the formula of the triangle:

$hb/2$

H - height

B- Base

You need to multiply the base and height and divide it by 2.

Lets solve a question!

Find the area of a triangle with a base of 32mm and a height $32 * 35$ of 35mm

Area = $hb/2$

= $32* 35$

= $1120$

= $1120/2$

= $56cm^2$

Hope I helped (:

Have a great day!

3 0

3 years ago

What is an equation of the line that passes through the point (-6,-4)(−6,−4) and is parallel to the line x+6y=12x+6y=12?

masya89 [10]

Answer:

x + 6y + 30 = 0

Step-by-step explanation:

x + 6y = 12

6y = -x + 12

y = -⅙x + 2

Slope: -⅙

y - (-4) = -⅙(x - (-6))

y + 4 = -⅙(x + 6)

-6y - 24 = x + 6

x + 6y + 30 = 0

4 0

4 years ago

What is the first step needed to solve x-3 =-18? O Add 3 to both sides O Subtract 18 from both sides O Multiply both sides by 3

aev [14]

Answer:

Add 3 to both sides

6 0

4 years ago

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