Answer:
Step-by-step explanation:
Let the two numbers be 2x and 3x.
According to the question,
2x+3x=45
5x=45
x=45/5
x=9
so th required numbers are 18 and 27 as
2x=2*9=18
3x=3*9=27
With that table of values, you can come up with a slope intersect form of a line
7 = -8m + b
1 = -5m + b
-5 = -2m + b
7-1 = -3m
6 = -3m
m = -2
1 = -5 * -2 + b
b = 1 - 10
b = -9
so it is y = -2x - 9
Now we can find where those intersect
-2x - 9 =2 (x+4)^2 - 5
-2x - 9 = 2(x^2 + 8x + 16) - 5
-2x - 9 = 2x^2 +16x + 32 -5
2x^2 + 18x +36 = 0
x^2 + 9x + 18 = 0
D = 81 - 72 = 9 = 3^2
x1 = (-9 - 3) / 2 = -6; y1 = 3
x2 = (-9 + 3) / 2 = -3; y2 = -3
so the solutions are (-6; 3) and (-3; -3)
Answer:
3x - 14 = y
Step-by-step explanation:
The equation of the line parallel to a given line ax + by + c₁ = 0 is ax + by + c₂ = 0.
In other words, equation of parallel lines differ only in their constants.
Now the given line is: 3x + 4 = y.
This can be written as: 3x - y + 4 = 0. Therefore, the line parallel to this would be: 3x - y + c = 0.
Since the point passing through the line is given, that point should satisfy this equation. So, it can used to find the values of c.
Substituting (4,-2) in the equation we get: 3(4) - (-2) + c = 0
⇒ c = -14
Substituting this we get: 3x - y -14 = 0.
or, 3x -14 = y
He starts out with 150.
150+ 50+200
200-20=180
180+75= 255
255-100= 155
After all the transactions, he had $155.