In general, what does a solution to an equation mean?
2 answers:
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For new line, slope m=2 and y-intercept c=(-10)
Step-by-step explanation:
<em>Note : Figure given is for reference to understand better.</em>
<em>Where redline is for given line and blueline for new line</em>
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The equation of given line 8x-4y=5 and it is dilated by a scale factor of 8 centered at the origin.
Step 1 : Find two points on given line.
When x=0, y=?
When y=0, x=?
We get points
Step 2: Find distance from centered and scale it.
Now, It is said that line 8x-4y=5 dilated by a scale factor of 8 centered at the origin and point A and point B is on same.
So that point A and point B will also get dilated by a scale factor of 8 centered at the origin or distance of points from origin will be scaled by 8.
For point A:
Distance of point from origin is
unit in x-direction and zero
unit in y-direction.
After scaled by factor of 8, the distance will multipy by 8 and new location is
For point B:
Distance of point from origin is
unit in x-direction and zero unit in y-direction.
After scaled by factor of 8, the distance will multipy by 8 and new location is
Step 3: Find Equation of new line.
Points and
make a new line
The equation of given as
Now, Comparing with the equation of the line : y=mx + c
Where m=slope and c is the y-intercept
We get, Slope m=2 and y-intercept c=(-10)
Allegation is a method to find the ratio in which two or more indignant are mixed to produce a mixture or solution.
The equation represents the total liters of acid that are needed is,
Thus the option 3 is the correct option.
<h3>What is allegation?</h3>Allegation is a method to find the ratio in which two or more indignant are mixed to produce a mixture or solution.
Given information-
A scientist needs 10 L of a solution that is 60% acid.
The percentage of two acid solution are 50% and 90%.
Variable<em> x</em><em> </em>represent the number of liters of the 50% solution.
Variable<em> y </em>represent the number of liters of the 90% solution.
Quantity of acid from 50% solution is liters, and quantity of acid from 90% solution is
liters.
As the scientist needs 10 L of a solution that is 60% acid. Therefore the quantity of acid in 60 percent acid solution is,
Thus 6 liters of acid required by the scientist. As to get the 6 liters of acid from 50% and 90 percent solution, we need to add the amount of acid in these solutions.Thus,
This is the required equation.
Hence the equation represents the total liters of acid that are needed is,
Thus the option 3 is the correct option.
Learn more about the mixture and allegation here;