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scoundrel [369]
3 years ago
5

Is the gcf of two prime numbers always 1?

Mathematics
1 answer:
Lynna [10]3 years ago
3 0
Yes because they don't have any other factors besides themselves and 1
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Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 cm longer than twice the length of
g100num [7]
STEP 1:
convert meters to centimeters
100 cm= 1 meter

= 100 cm/m * 2.5 m
= 250 cm


STEP 2:
x= length of first shelf
2x+18= length of second shelf
x-12= length of third shelf
x+4= length of fourth shelf

since the whole board has to be used, add lengths of all shelves and set it equal to the whole length of the board (250 cm).

x + (2x+18) + (x-12) + (x+4)= 250 cm
combine like terms
5x + 10= 250
subtract both sides by 10
5x= 240
divide both sides by 5
x= 48


STEP 3:
find length of second shelf
= 2x + 18
= 2(48) + 18
= 114 cm


CHECK:
x + (2x+18) + (x-12) + (x+4)= 250
48 + (2(48)+18) + (48-12) + (48+4)= 250
48 + (96+18) + 36 + 52= 250
48 + 114 + 36 + 52= 250
250= 250


ANSWER: Shelf two is 114 cm.

Hope this helps! :)
8 0
3 years ago
Rachel has a $15,000, three-year loan with an APR of 725%.C. What is the finance charge? ​
Inessa [10]
I think it’s 17% i might be wrong
5 0
2 years ago
Does anyone from 7th grade and higher know this
zepelin [54]
We can combine thos fraction ssince same denomenator
\frac{3y}{7}+ \frac{1}{7}= \frac{3y+1}{7}

so
\frac{3y+1}{7}= \frac{3}{7}

times both sides by 7
3y+1=3
minus 1 both sides
3y=2
divide both sides by 3
y=2/3
6 0
3 years ago
A car is traveling at a constant rate of x miles per hour how many miles will the car travel in y minutes
marin [14]

Answer:

Step-by-step explanation:

1 mile

5 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} }

<h3><u>Find f(x):</u></h3>

Next, we will use  \displaystyle\mathsf{\frac{10}{3}}&#10; 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}.}

<h3>______________________________</h3>

<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
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