142 is the answer
The system of equations is graphed on the coordinate plane.
1 answer:
The solution is: (-1,-2)
Step-by-step explanation:
Given equations are:
In order to solve two equations with graphing method, the graphs of two equations are made which are straight lines the point of intersection is the solution of the equations.
Here,
The graph is given
To read the solution of the graph we see that on which x and y- coordinates the point of intersection is. then the answer is written as (x-coordinate , y-coordinate)
The solution point is highlighted with a circle. The x-coordinate is -1 and y-coordinate is -2
So,
The solution is: (-1,-2)
Keywords: Linear Equations, Graphing
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Answer:
The standard equation of the sphere is
Step-by-step explanation:
From the question, the end point are (3,-2,4) and (7,12,4)
Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.
The midpoint can be calculated thus
Midpoint =
Let the first endpoint be represented as and the second endpoint be
.
Hence,
Midpoint =
Midpoint =
Midpoint =
Midpoint =
This is the center of the sphere.
Now, we will determine the distance (diameter) of the sphere
The distance is given by
This is the diameter
To find the radius, r
From
∴
r =
Now, we can write the standard equation of the sphere since we know the center and the radius
Center of the sphere is
Radius of the sphere is
The equation of a sphere of radius r and center is given by
Hence, the equation of the sphere of radius and center
is
This is the standard equation of the sphere