both m and n are integers. 5m 3n is divisible by 11.what is the remainder when 9m n is divided by 11?

1 answer:

4 0

Hello,

9m+n is divisible by 11 (remainder =0)

Since
$5m+3n=11*k\\

m= \dfrac{11*k-3n}{5}\\

9m=9*\dfrac{11*k-3n}{5}\\

9m+n=9*\dfrac{11*k-3n}{5}+ \dfrac{5n}{5} \\

9m+n= \dfrac{99k-27n+5n}{5}\\

9m+n=11* \dfrac{9k-2n}{5}\\

$

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What is the height of the tree in the image below? 10 points Wall 4 6 ft 24 O I foot O 36 foot None of the above

Zinaida [17]

16 ft

Explanation

Step 1

because the ligth comes in the same angle, we have 2 similar triangles .

so,as the triangles are similar,the ratio of the shorter leg to the bigger leg must be equal.

$\begin{gathered} ratio=\frac{shorter\text{ leg}}{\text{bigger leg}} \\ ratio1=ratio2 \\ \frac{h}{24}=\frac{4}{6} \end{gathered}$

Step 2

solve for h

$\begin{gathered} \frac{h}{24}=\frac{4}{6} \\ \text{cross multiply} \\ 6\cdot h=4\cdot24 \\ 6h=96 \\ \text{divide boths} \\ \frac{6h}{6}=\frac{96}{6} \\ h=16 \end{gathered}$

therefore, the heigth of the tree is 16 ft