Answer:
x=5
Step-by-step explanation:
Lets first solve for y on both sides:
![2x-4=3y\\\frac{2x-4}{3}=y\\ y=\frac{2x-4}{3}](https://tex.z-dn.net/?f=2x-4%3D3y%5C%5C%5Cfrac%7B2x-4%7D%7B3%7D%3Dy%5C%5C%20y%3D%5Cfrac%7B2x-4%7D%7B3%7D)
![5y-x=5\\5y=5+x\\y=\frac{5+x}{5}](https://tex.z-dn.net/?f=5y-x%3D5%5C%5C5y%3D5%2Bx%5C%5Cy%3D%5Cfrac%7B5%2Bx%7D%7B5%7D)
Set the two equations equal to each other and solve for x:
![\frac{2x-4}{3}=\frac{5+x}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2x-4%7D%7B3%7D%3D%5Cfrac%7B5%2Bx%7D%7B5%7D)
Multiple both sides by 3:
![2x-4=\frac{3(5+x)}{5}](https://tex.z-dn.net/?f=2x-4%3D%5Cfrac%7B3%285%2Bx%29%7D%7B5%7D)
Multiply both sides by 5:
![5(2x-4)=3(5+x)](https://tex.z-dn.net/?f=5%282x-4%29%3D3%285%2Bx%29)
Apply distributive property to both sides:
![10x-20=15+3x](https://tex.z-dn.net/?f=10x-20%3D15%2B3x)
Add 20 to both sides:
![10x=35+3x](https://tex.z-dn.net/?f=10x%3D35%2B3x)
Subtract 3x from both sides:
![7x=35](https://tex.z-dn.net/?f=7x%3D35)
Divide both sides by 7:
![x=5](https://tex.z-dn.net/?f=x%3D5)
Answer: 8 students have brown eyes
Step-by-step explanation:
Unit rate: 5 % = 1 student.
5 x 10 = 50%. 10 students have blue eyes.
5 x 8 = 40%. 8 students have brown eyes.
In conclusion, 8 students have brown eyes.
Hope this helps!
Answer:
<h3>
Therefore the angles of the triangle are 52.5°, 105°,49.5°.</h3>
Step-by-step explanation:
Triangle:
- The sum of the angle of triangle = 180°
- Heron's formula the area of triangle =
s= semi-perimeter ![=\frac{a+b+c}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D)
Given that , first angle is twice the second angle, and the second angle is 30° larger than the third angle.
Consider the second angle of the triangle be x.
Then first angle = twice the second angle
=2× second angle
=2x
The third angle+30° = second angle
⇒third angle= second angle -30°
= x- 30°
We know that,
First angle + second angle+ Third angle = 180°
⇒2x+x+x-30°= 180°
⇒4x = 180° +30°
⇒4x=210°
![\Rightarrow x= \frac{210^\circ}{4}](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D%20%5Cfrac%7B210%5E%5Ccirc%7D%7B4%7D)
⇒x=52.5°
Therefore the angles of the triangle are 52.5°, (2×52.5°),(52.5°-30°)
=52.5°, 105°,49.5°
In geometry, the segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.