The equation of a line that is parallel to 3x=4y and has the same y-intercept as 2x-3y=6 is:
y = (3/4)*x - 2
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How to get the equation of the line?</h3>
A general linear equation is written as:
y = a*x + b
Where b is the y-intercept and a is the slope.
Such that two lines are parallel if the lines have the same slope but different y-intercepts.
So, if we want to have a line parallel to:
3x = 4y
y = (3/4)*x
Then the slope must be 3/4.
And the line must have the same y-intercept than:
2x - 3y = 6.
We can rewrite that to get:
-3y = 6 - 2x
y = (6/-3) + (2/3)*x
y = (2/3)*x - 2
So this linear equation has a y-intercept equal to -2, then our linear equation is:
y = (3/4)*x - 2
If you want to learn more about linear equations:
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Consider an angle M with measure m≠90°, in a right triangle.
Let
OPP denote the length of the side opposite to M,
ADJ denote the length of the side adjacent to M, and
HYP denote the hypotenuse.
then:
Sin(M) = OPP/HYP
Cos(M)= ADJ/HYPP
Tan(M)=OPP/ADJ
Back to our problem,
using the Pythagorean we can find the length of AB:
Answer: 1, 3, 4
If you assign variables to the problem, it can make things a lot simpler. Lets say chairs are x and tables are y. Therefore you have:
2x+6y=40
5x+3y=25
Now you can isolate the variable of one equation and put it into another (it doesn't matter which. I'm going to manipulate the top equation to plug into the bottom one).
2x=40-6y
x=20-3y
Now I plug into bottom equatioin:
5(20-3y) + 3y=25
100-15y+3y=25
100-12y=25
-12y=-75
y=$6.25
Now you can plug in y in either equation to get x.
2x+6(6.25)=40
37.5+2x=40
2x=2.5
x=1.25
So it costs $6.25 for each table and $1.25 for each chair. If you think about it, it would make sense for the table to cost more for the chair.
Answer:
It will take the apprentice 24 days working alone
Step-by-step explanation:
Let the number of days it takes the apprentice be x
It will take the landscaper x/3 ( since he is three times faster)
The rate for both will be 60/6 = 10 sq m per day
Rate for apprentice is 60/x
rate for the boss is 60/x/3 = 180/x
Adding the rates together;
60/x + 180/x = 10
240/x = 10
240 = 10x
x = 240/10
x = 24 days
Answer:
4 gallons
Step-by-step explanation:
as martizas used up 3/4 gallons, we can calculate the fraction of gas left using: 1−3/4=1/4.
so now we use the fraction we calculated to times with the total volume of gas : 1/4×16=4 gallons
