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Mathematics

2 answers:

Alex777 [14]3 years ago

7 0

Its the 2 one do you want me to give you a reasoning more or..

VARVARA [1.3K]3 years ago

4 0

It’s the second one.

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. A square picture frame occupies an area of 112 ft2 . What is the length of each side of the picture in simplified radical form

saw5 [17]

Recall that a square is just a rectangle with all sides equal.

and the area of a rectangle is just length * width.

$\bf \textit{area of a rectangle}\\\\
A=length\cdot width\quad 
\begin{cases}
length=x\\
width=x\\
A=112
\end{cases}\implies 112=x\cdot x\implies 112=x^2
\\\\\\
\sqrt{112}=x\implies \sqrt{16\cdot 7}=x\implies \sqrt{4^2\cdot 7}=x\implies 4\sqrt{7}=x$

3 0

3 years ago

A positive integer is twice another.the sum of the reciprocal of the two positive integer is 3/14. Find the integers

icang [17]

Answer:

$\huge\boxed{14\ \text{and}\ 7}$

Step-by-step explanation:

$n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right$

$\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}$