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2 years ago

12 9 6 3 60 45 30 15 what is the constant of proportionality

Mathematics

1 answer:

Mice21 [21]2 years ago

6 0

Answer:

Step-by-step explanation:

A constant of proportionality is the ratio that forms between each x y pair as the fraction y/x. In a proportional relationship it is constant or the same every time.

60/12 = 5

45/9 = 5

30/6 = 5

15/3 = 5

The constant of proportionality is 5.

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F(x)=2x-4. F(x)=2x-4 f-1x=_x+_. Complete the inverse function

natita [175]

Answer:

$f^{-1}(x) = \frac{1}{2}(x +4)$

Step-by-step explanation:

Given

$f(x) = 2x - 4$

Required

Determine the inverse function

Start by replacing f(x) with y

$y = 2x - 4$

Swap the positions of y and x

$x = 2y - 4$

Make y the subject: Add 4 to both sides

$x+4 = 2y - 4+4$

$x+4 = 2y$

Make y the subject: Divide through by 2

$\frac{1}{2}(x + 4) = y$

$y = \frac{1}{2}(x + 4)$

Replace y with f-1(x)

$f^{-1}(x) = \frac{1}{2}(x +4)$

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2 years ago

Cynthia invests some money in a bank which pays 5% compound interest per year. She wants it to be worth over £8000 at the end of

Agata [3.3K]

$\bf \qquad \textit{Compound Interest Earned Amount}\\\\A=P\left(1+\frac{r}{n}\right)^{nt}\quad \begin{cases}A=\textit{accumulated amount}\to &8000\\P=\textit{original amount deposited}\\r=rate\to 5\%\to \frac{5}{100}\to &0.05\\n=\begin{array}{llll}\textit{times it compounds per year}\\\textit{is only once, so}\end{array}\to &1\\t=years\to &3\end{cases}$

$\bf 8000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 8000=P(1.05)^3\implies \cfrac{8000}{1.05^3}=P\\\\\\6910.70\approx P\implies \stackrel{\textit{rounded up}}{6911 = P}\qquad therefore\qquad 6911~~\leqslant ~~P$

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2 years ago

A linear function has an x-intercept of 12 and a slope of StartFraction 3 Over 8 EndFraction. How does this function compare to

ehidna [41]

Answer:

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Step-by-step explanation:

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2 years ago

Kelly has 50% more money than Luis. Luis has $40. If Luis gets $8 more, will Kelly still have more money than Luis? What percent

OverLord2011 [107]

Answer:

Kelly will still have more money than Luis

Kelly will have 25% more

Step-by-step explanation:

Let x represent the amount of money Kelly has and y, Luis

Luis has $40

and Kelly has 50% more money than Luis

Therefore, Kelly has;

50% of $40 + $40

= 0.5*40 + 40

= $60

If Luis gets $8 more, Luis will have;

$8 + $40 = $48

since Luis' $48 is less than Kelly's $60, Kelly will still have more money than Luis

Difference in their money = $60 - $48 = $12

Therefore, Kelly will have;

12/48 * 100 more than Luis

= 25% more

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2 years ago

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