Step-by-step explanation:
second one because
only x+2y=8 passes through the point (2,3)
the proof is 2+2*3=2+6=8
if we replace the given point to the other equations we will take wrong results for example
first equation
x+2y=4. 2+2*3=2+6=8 that is not equal to 4
The slopes of two lines are equal which means that the lines are parallel.
Further explanation:
The slopes of lines are used to find the relationship between two line.
- If two lines are parallel, then their slopes will be equal.
- If two lines are perpendicular, the product of slopes of both lines will be -1
The standard form of equation of line is:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
The coefficient of x is the slope here.
y=1/3x+4
Let m1 be the slope of first line:
![m_1=\frac{1}{3}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7B1%7D%7B3%7D)
![x-3y=-12\\-3y=-x-12\\-3y=-1(x+12)\\3y=x+12\\\frac{3y}{3}=\frac{x+12}{3}\\y=\frac{x+12}{3}\\y=\frac{x}{3}+\frac{12}{3}\\y=\frac{1}{3}x+4](https://tex.z-dn.net/?f=x-3y%3D-12%5C%5C-3y%3D-x-12%5C%5C-3y%3D-1%28x%2B12%29%5C%5C3y%3Dx%2B12%5C%5C%5Cfrac%7B3y%7D%7B3%7D%3D%5Cfrac%7Bx%2B12%7D%7B3%7D%5C%5Cy%3D%5Cfrac%7Bx%2B12%7D%7B3%7D%5C%5Cy%3D%5Cfrac%7Bx%7D%7B3%7D%2B%5Cfrac%7B12%7D%7B3%7D%5C%5Cy%3D%5Cfrac%7B1%7D%7B3%7Dx%2B4)
Let m2 be the slope of second line
![m_2=\frac{1}{3}](https://tex.z-dn.net/?f=m_2%3D%5Cfrac%7B1%7D%7B3%7D)
We can see that:
![m_1=m_2](https://tex.z-dn.net/?f=m_1%3Dm_2)
The slopes of two lines are equal which means that the lines are parallel.
Keywords: Parallel Lines, Perpendicular Lines
Learn more about lines at:
#LearnwithBrainly
If interpreted as shown, the order is shown in the lines following
1+sin(x)/1-sin(x)-1-sin(x)/1+sin(x)
=1 + ((sin(x))/1) - sin(x) -1 - (sin(x)/1) + sin(x)
which is completely meaningless for the purpose of this question.
The left-hand side is
![\frac{1+sin(x)}{1-sin(x)}-\frac{1-sin(x)}{1+sin(x)}](https://tex.z-dn.net/?f=%5Cfrac%7B%3Cspan%3E1%2Bsin%28x%29%7D%7B1-sin%28x%29%7D-%5Cfrac%7B1-sin%28x%29%7D%7B1%2Bsin%28x%29%7D)
common denominator is (1-sin(x))(1+sin(x)), so
![=\frac{(1+sin(x))(1+sin(x)-(1-sin(x))(1-sin(x))}{(1+sin(x)(1-sin(x)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%281%2Bsin%28x%29%29%281%2Bsin%28x%29-%281-sin%28x%29%29%281-sin%28x%29%29%7D%7B%281%2Bsin%28x%29%281-sin%28x%29%7D)
![=\frac{(1+sin(x))^2-(1-sin(x))^2}{(1+sin(x)(1-sin(x)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%281%2Bsin%28x%29%29%5E2-%281-sin%28x%29%29%5E2%7D%7B%281%2Bsin%28x%29%281-sin%28x%29%7D)
![=\frac{(1+1)(2sin(x))}{(1-sin^2(x)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%281%2B1%29%282sin%28x%29%29%7D%7B%281-sin%5E2%28x%29%7D)
using a^2-b^2=(a+b)(a-b)
![=\frac{4sin(x)}{cos^2(x)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4sin%28x%29%7D%7Bcos%5E2%28x%29%7D)
![=\frac{4tan(x)}{cos(x)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4tan%28x%29%7D%7Bcos%28x%29%7D)
![=4tan(x)sec(x)](https://tex.z-dn.net/?f=%3D4tan%28x%29sec%28x%29)
<span>
Therefore
</span>
Answer:
p equals two and four tenths
Step-by-step explanation:
First let's write our equation
five p plus three equals fifteen
<h3>Subtract three from both sides</h3><h3 />
five p equals twelve
divide both sides by 5
p equals two and four tenths
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Word Problem
You bought 5 pears that were worth x dollars, you have an extra 3 dollars, the total of the money you spent and you have is 15 dollars. How much does one pear cost?