Answer:
4x + 3y + 9 = 0
Step-by-step explanation:
When a slope of a line and a point passing through it is given then we use slope - one point form to determine the equation of the line.
It is given by:
where is the slope of the line and
is the point passing through it.
Here, and
.
Substituting in the formula
Answer:
(g, f) = (-1, 2)
Step-by-step explanation:
The equation can be put into standard form:
(x^2 +2gx) +(y^2 +2fy) = 15
(x^2 +2gx +g^2) +(y^2 +2fy +f^2) = 15 +g^2 +f^2
(x +g)^2 +(y +f)^2 = 15 +g^2 +f^2 . . . . equation in standard form
The point (3, 2) is on the circle, so one of the equations we have is ...
(3+g)^2 +(2 +f)^2 = 15 +g^2 +f^2
9 +6g +g^2 +4 +4f +f^2 = 15 +g^2 +f^2
6g +4f = 2 . . . . . . . subtract g^2 +f^2 +13
3g +2f = 1 . . . . . . . divide by 2
__
A line through the center of the circle is perpendicular to the tangent at the point of tangency. That line will have a slope that is the negative reciprocal of the tangent's slope: m = -1/(-1/2) = 2. Then in point-slope form the equation of the line through the center is ...
y -2 = 2(x -3)
2x -y = 4 . . . . rearrange to standard form
The point at the center of the circle, (-g, -f), satisfies this equation, so we have another relation for f and g:
2(-g) -(-f) = 4
2g -f = -4 . . . . . . multiply by -1
Adding twice this equation to the one above, we have ...
2(2g -f) +(3g +2f) = 2(-4) +(1)
7g = -7 . . . . . . . . . simplify
g = -1 . . . . . . . . . . divide by 7
f = 2g +4 = 2(-1) +4 = 2 . . . find the corresponding value of f
The values of f and g are: f = 2 and g = -1.
Answer:
The equation which gives the total cost y of x pounds of dried cherries is
Step-by-step explanation:
Given:
Cost of 3 pounds of dried cherries = $15.90
Cost of 5 pounds of dried cherries = $26.50
Cost of 9 pounds of dried cherries = $47.70
Let Number of of pounds of dried cherries be 'x'
Let Total Cost be denoted by 'y'
We need to find the equation for total cost y for x pounds of dried cherries.
First we will find the cost of each pound of dried cherries.
Now we know that;
3 pounds of dried cherries = $15.90
1 pound of dried cherries = Cost of 1 pounds of dried cherries
Hence By using Unitary method we get;
Cost of 1 pounds of dried cherries =
Total Cost of dried cherries is equal to Number of of pounds of dried cherries multiplied by Cost of 1 pounds of dried cherries.
framing in equation form we get;
Hence The equation which gives the total cost y of x pounds of dried cherries is