To find the point of intersection, we want to set the two equations equal to each other to find where they meet. The problem is, we have two variables, which means we can't just set them equal to each other as is. We need to manipulate the equations so that we can remove one of the variables at a time to solve for the other one.
First, let's move y to one side so we can solve for x.
2x-3y=9
2x-9=3y
y=(2x-9)/3
5x+4y=11
4y=11-5x
y=(11-5x)/4
Now that they both equal the same thing (y), we can set them equal to each other and solve for x. This will give us the x value for the point of intersection of the lines.
(11-5x)/4=(2x-9)/3
3(11-5x)=4(2x-9)
33-15x=8x-36
33+36=8x+15x
69=23x
x=69/23
x=3
Now, we can do the opposite, and solve for x to find the y coordinate.
2x-3y=9
2x=3y+9
x=(3y+9)/2
5x+4y=11
5x=11-4y
x=(11-4y)/5
(3y+9)/2=(11-4y)/5
5(3y+9)=2(11-4y)
15y+45=22-8y
15y+8y=22-45
23y= -23
y= -1
The coordinates for the point of intersection of the two lines is (3, -1).
1800.00*3 which is 5400 then divide it by 100 so in 3 months she will earn 54%
Answer:
16.9 units
Step-by-step explanation:
Sometimes the easiest way to work these problems is to get a little help from technology. The GeoGebra program/app can tell you the length of a "polyline", but it takes an extra segment to complete the perimeter. It shows the perimeter to be ...
14.87 + 2 = 16.87 ≈ 16.9 . . . units
_____
The distance formula can be used to find the lengths of individual segments. It tells you ...
d = √((Δx)² +(Δy)²)
where Δx and Δy are the differences between x- and y-coordinates of the segment end points.
If the segments are labeled A, B, C, D, E in order, the distances are ...
AB = √(5²+1²) = √26 ≈ 5.099
BC = √(1²+3²) = √10 ≈ 3.162
CD = Δx = 3
DE = √(3²+2²) = √13 ≈ 3.606
EA = Δy = 2
Then the perimeter is ...
P = AB +BC +CD +DE +EA = 5.099 +3.162 +3 +3.606 +2 = 16.867
P ≈ 16.9
Answer: 0.72
Step-by-step explanation: 72/100 of the block are shaded. The decimal form of that fraction is 0.72
Answer:
47% of American adult population
Step-by-step explanation:
The reason why polls are carried out is to obtain information that can represent the opinions, status or habits of the population. The polls do not include the total population, then include a small number of participants, but the results are extrapolated to the general population. There are always small margins of error resulting from polls, that is why the confidence levels are usually +/- 3 or 4%.
