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3 years ago

75% of 48is what number? 22 is what percent of 40?

Mathematics

2 answers:

tigry1 [53]3 years ago

6 0

75%of 48=.75x48=36

40/100=22/x
40 (x)=22 (100)
40x=2200
40/40x=2200/40
x=55%

OlgaM077 [116]3 years ago

4 0

36 is 75% of 48

22 out of 40 is 55%

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2. Seiji and Gavin both worked hard over the summer. Together they earned a total of $425. Gavin earned $25 more than Seiji.

solmaris [256]

Answer:

(A) s + g + ( g + 25) = 425

Step-by-step explanation:

4 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:

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2 years ago

X2+ y2 − 8x + 12y + 27 = 0

snow_lady [41]

Central (4,–6)

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3 years ago

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I'm having trouble understanding this word problem and how they got 6x=44+2x from it.

jenyasd209 [6]

Ok well since it says the product of a number and 6 is 44 more than twice the number. and from this they got 6x=44+2x because it SAYS THE PRODUCT OF A NUMBER U DON'T KKNOW WHAT THE NUMBER IS SO U USE A VARIABLE WHICH IS 6X THEY GOT = 44 FROM THE PRODUCT AND 2X FROM MORE THAN TWICE THE NUMBER AND TWICE IS 2 AND U DON'T KNOW WHAT THE NUMBER IS SO ONCE AGAIN USE A VARIABLE

HOPE THIS HELPED

5 0

3 years ago

Read 2 more answers

Sketch the graph y=−|x−1|+3 and answer the questions:<br> Does it open upward?<br> Yes or No?

Marina CMI [18]

Answer:

1) Please see the required graph created with Microsoft Excel

2) No

Step-by-step explanation:

The given parameters are;

$y= -\left | x - 1 \right | + 3$

From the given equation, we have;

When x > 4, or x -2 <, y < 0, which gives;

y > 0 for -2 < x < 4

Therefore, the graph is opened in the downward direction with the peak at the point with coordinate (1, 3)

The legs of the graphs are straight lines with slopes = -1, and 1 respectively, before and after the maximum point of the graph

The table of values used to sketch the graph with Microsoft Excel is given as follows;

x ${}$ y

-3 -1

-2 0

-1 1

0 2

1 3

2 2

3 1

4 0

5 -1

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3 years ago