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3 years ago

Always, sometimes, or never true.

Mathematics

1 answer:

labwork [276]3 years ago

7 0

Step-by-step explanation:

sometimes ....................

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3 years ago

Morris has 2 3/4 gallons of ice tea. He gives 3/7 of it to her friend. How many gallons of ice tea does Morris have left?

lara31 [8.8K]

Answer:

$2 \frac{9}{28}$ gallons of ice tea is left with Morris

Step-by-step explanation:

Morris has 2 3/4 gallons of ice tea. He gives 3/7 of it to her friend.

Morris has 2 3/4 gallons of ice tea

$2\frac{3}{4}= \frac{2*4+3}{4}=\frac{11}{4}$

He gives 3/7 of it to her friend.

To find how many gallons of ice tea does Morris have left , we subtract 3/7 from 11/4

$\frac{11}{4}- \frac{3}{7}$

Make the denominators same

$\frac{11*7}{4*7}- \frac{3*4}{7*4}$

$\frac{77}{28}- \frac{12}{28}$

$\frac{65}{28}$

$\frac{65}{28} = 2 \frac{9}{28}$

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3 years ago

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