Answer:
(x – 1)² + (y +2)² = 5
Step-by-step explanation:
recall that the general form of the equation for the circle is as follows:
(x – h)² + (y – k)² = r²
where, (h,k) are the coordinates for the center of the circle and r is the radius of the circle.
We are given that the center of the circle is at (1,-2). Comparing this with the description of h & k above, we can immediately conclude that h = 1 and k = -2.
Hence the only thing we are missing now is radius r.
It is given that the circle passes through the origin, hence if we draw a line between the origin (0,0) and the center (1,-2), this distance is the radius.
to find the distance between 2 points, we use the attached formula
Distance = radius, r = √ [ (1-0)² + (-2-0)²]
r = √ [ (1² + (-2)²]
r = √ [1 + 4] = √ 5
hence we can assemble the equation
(x – 1)² + (y – (-2))² = (√5)²
(x – 1)² + (y +2)² = 5
When we are given a system of 3 linear equations, with 3 variables, we proceed as follows:
We consider 2 pairs or equations, for example (1, 2) and (2, 3), and eliminate one of the variables in each pair, creating a system of 2 linear equations with 2 unknowns.
Note that the third equation contains -2y which can be used to eliminate easily -6y in the second equation, and -4y in the fourth.
i) consider equations 1 and 3:
-3x-4y-3z=-7
5x-2y+5z=9
multiply the second equation by -2:
-3x-4y-3z=-7
-10x+4y-10z=-18
adding the 2 equations we have -13x-13z=-25
ii) consider equations 2 and 3. Multiply the third equation by -3:
2x-6y+2z=3
-15x+6y-15z=-27
adding the 2 equations we have -13x-13z=-24
So we got -13x-13z is -25, but also -24. this means the system is inconsistent, so it has no solution.
Answer: the system has no solutions
Answer:
Step-by-step explanation:
Ms Fowler's ratio would be 8:7 and Ms Rivera's would be 16:15, they are not equivalent because the numbers didn't come out to the same ratio when i divided them and 16 and 1 aren't divisible by the same numbers.
here are the steps i took:
1. wrote down the original ratios (16:15 and 64:60)
2. I divided all the numbers by 2 and got them reduced to 8:7 and 30:32
3. I saw that the 8:7 couldn't be divided anymore, so I left it and divided 30 by 2 and 32 by 2 and got 16:15
4. I saw that I couldn't divide those anymore so I compared the ratios and saw that they were not the same so they weren't equal.
hope this helped!
Answer:
y=3x+4
Step-by-step explanation:
Slope-intercept form is written as y=mx+b
m = the slope
slope is rise over run or (y2-y1)/(x2-x1). We need to choose which y value is y2 and the corresponding x value is the x2. If -2 is y2, then:
x2 = -2
y1 = 1
x1 = -1
then plug in the values.
(-2-1)/(-2-(-1))
-3/-1 = 3
m =3
then plug in values for the first equation. you can use any point on the line.
y = 3x+b
4 = 3*0 +b
4=0+b
b = 4
then write it with out x or y
y = 3x+4
Answer:
3rd one is correct......:)
