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4 years ago

Can someone please help me?

Mathematics

1 answer:

Eddi Din [679]4 years ago

5 0

To solve these types of problems, we need to break it down and see what each part represents.

(11) 3m
(12) j-10
(13) d+4
(14) 4p

All we must do is understand some basic keywords, such as times which represents multiplication, less which represents subtraction, and more which can represent addition or multiplication.<span />

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How do I do this this is all new to me please show work so I can learn

Natali5045456 [20]

≅Answer:

See below.

Step-by-step explanation:

If we rotate the shape on the right 90 degrees counterclockwise we see they fit together, because they are congruent. They are exactly equal in size and shape - that's what congruent means.

So the following angles are equal in measure:

m < A = m < R

m < B = m < S

m < C = m < P

m < D = m < Q.

Corresponding sides are also equal in length:

Sides AB = RS

BC = SP

CD = PQ

AD = RQ.

Note: in the US the symbol ≅ is used for equality of sides. I think it means 'is congruent to'. (I'm from the UK).

8 0

3 years ago

Which situation is best modeled by the inequality g ≤ 13?

Olin [163]

Answer:

You must be no older than 13 to play a game.

Step-by-step explanation:

≤ this sign means equal to or less than in this case it is 13

8 0

4 years ago

It took Fabian 40 minutes to dig 5 post holes. If he continues at this rate, how long will it take him to dig 20 post holes?

Artyom0805 [142]

Answer:

13.33 hours

Step-by-step explanation:

plz give brainliest

7 0

3 years ago

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

Can i get help? Don’t really understand.

Rufina [12.5K]

First option: correct. This is because angles WOX and XOZ are supplementary, so

$m\angle WOX=180^\circ-104^\circ=76^\circ$

Second option: correct. By the inscribed angles theorem, we have

$m\angle XWZ=m\angle XYZ=\dfrac{113^\circ}2=56.5^\circ$

Angles WOX and YOZ are congruent because they form a vertical pair; they both have measure 76 degrees. This means angles WXY and WZY are also congruent, since the interior angles of any triangle sum to 180 degrees in measure. Therefore triangles WXO and YZO form a side-side-side pair, and all SSS triangles are similar.

Third option: not correct. There is a theorem (not sure what the name is) regarding intersecting chords that asserts the average of the measures of arcs WY and XZ is the same as the measure of angle XOZ. This means

$\dfrac{m\widehat{WY}+113^\circ}2=104^\circ\implies m\widehat{WY}=95^\circ$

Fourth option: not correct. This is because arcs WX and XZ are not "supplementary" in the sense that they do not form a semicircle and their measures do not add to 180 degrees. We know this because it's clear that point O is not the center of the circle. If it was, then angle XOZ would be a central angle and its measure would be the same as the arc XZ it subtends.

Fifth option: correct. The theorem mentioned in the assessment of the third option makes itself useful here. We have

$\dfrac{m\widehat{WX}+m\widehat{YZ}}2=m\angle WOX\implies m\widehat{WX}+m\widehat{YZ}=2\cdot76^\circ=152^\circ$

4 0

3 years ago