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IrinaK [193]
3 years ago
12

Solve for x using common denominators. 4/7 (x+6) = x/(x+6)​

Mathematics
1 answer:
artcher [175]3 years ago
5 0

Answer:

The value of x = 4/7

Step-by-step explanation:

Given the expression

\frac{4}{7\left(x+6\right)}=\frac{x}{x+6}

\frac{4}{7\left(x+6\right)}-\frac{x}{x+6}=0

Multiply the numerator and denominator of \frac{x}{x+6} by 7

\frac{4}{7\left(x+6\right)}-\frac{7x}{7\left(x+6\right)}=0

Now taking the denominator \frac{1}{7\left(x+6\right)} as common

\frac{1}{7\left(x+6\right)}\left(4-7x\right)=0

\frac{4-7x}{7\left(x+6\right)}=0

\frac{f\left(x\right)}{g\left(x\right)}=0\quad \Rightarrow \quad f\left(x\right)=0

4-7x=0

Subtract 4 from both sides

4-7x-4=0-4

Simplify

-7x=-4

Divide both sides by -7

\frac{-7x}{-7}=\frac{-4}{-7}

Simplify

x=\frac{4}{7}

Therefore,

The value of x = 4/7

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Answer:

Since Darcie wants to crochet a minimum of 3 blankets and she crochets at a rate of 1/5 blanket per day, we can determine how many days she will need to crochet a minimum of 3 blankets following the next steps:

- Finding the number of days needed to crochet one (1) blanket:

\begin{gathered}1=\frac{1}{5}Crochet(Day)\\Crochet(Day)=5*1=5\end{gathered}

1=

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1

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Crochet(Day)=5∗1=5

So, she can crochet 1 blanket every 5 days.

- Finding the number of days needed to crochet three (3) blankets:

If she needs 5 days to crochet 1 blanket, to crochet 3 blankets she will need 15 days because:

\begin{gathered}DaysNeeded=\frac{NumberOfBlankets}{Rate}\\\\DaysNeeded=\frac{3}{\frac{1}{5}}=3*5=15\end{gathered}

DaysNeeded=

Rate

NumberOfBlankets

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5

1

3

=3∗5=15

- Writing the inequality

If she has 60 days to crochet a minimum of 3 blankets but she can complete it in 15 days, she can skip crocheting 45 days because:

AvailableDays=60-RequiredDaysAvailableDays=60−RequiredDays

AvailableDays=60-15=45DaysAvailableDays=60−15=45Days

So, the inequality will be:

s\leq 45s≤45

The inequality means that she can skip crocheting a maximum of 45 days since she needs 15 days to crochet a minimum of 3 blankets.

Have a nice day!

3 0
3 years ago
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Answer:

(x-1)^2 + (y+4)^2 = 100\\\\

=====================================================

Work Shown:

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You could expand terms out and simplify, but I think it's more handy to leave it in this form so you can easily spot the center and radius from a glance.

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Vilka [71]

Answer:

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Step-by-step explanation:

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