Express 80 as a product of its prime factors, write the prime numbers in accending order

Mathematics

1 answer:

Alex73 [517]2 years ago

4 0

Answer:

80 as a product of prime numbers can be expressed as 2×2×2×2×5

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Find a fraction equivalent to 5/7 whose squared terms add up to 1184.

bogdanovich [222]

The system of equations of two unknowns is formulated and solved.

$\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y } \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28 } \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{ x=\dfrac{5}{7}(\pm 28)=\pm 20 } \end{gathered}$}$

The fraction that satisfies the request is $\bf{\dfrac{20}{28}}$ , since in $\bf{\dfrac{-20}{-28}}$ the negative signs are canceled and the first fraction is obtained.

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2 years ago

Jacqueline reach the end of the trail in two hours and 15 minutes. Write the amount of hours he spent on the trail as a mixed nu

LenaWriter [7]

You would keep the 2 hour for the whole number of the mixed number and then, make the minutes (15) as a fraction with 60, and divide them both by 20. that is just for the mixed number.

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4 years ago

Can someone help me answer

siniylev [52]

Answer: 9 kilos total thats it

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3 years ago

S - 1/3 equals 4/9 so S equals what?

bekas [8.4K]

$s - \frac{1}{3} = \frac{4}{9} \\ \\ s = \frac{4}{9} + \frac{1}{3} \\ \\ s = \frac{7}{9} \\ \\ Answer: \fbox {s = 7/9} \ or \ \fbox {s = 0.7778}$

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3 years ago

Find all sets of four consecutive integers whose sum is between 95 and 105

Nat2105 [25]

Hello,

Let n-2,n-1,n,n+1 the foru numbers
s=n-2+n-1+n+n+1=4n-2

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3 years ago