If angle LNM =8x+12 and angle JNL =12x-32, find the measure of angle JNP.(JNP and LNM are congruent.

1 answer:

3 0

$Sum\ of\ congrugent\ angles\ is\ 180^{\circ}.\\\\
LNM+JNL=180^{\circ}\\\\
8x+12+12x-32=180\\\\
20x-20=180 \ \ \ |Add\ 20\\\\
20x=200\ \ \ |Divide\ by\ 20\\\\
x=10\\\\
JNL=12x-32=12*10-32=120-32=88^{\circ}$

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

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Answer:

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

Step-by-step explanation:

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

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