3 years ago

How many solutions exist for the system of equations in the graph?

Mathematics

1 answer:

shutvik [7]3 years ago

8 0

Answer:

Two solutions

Step-by-step explanation:

The number of points of intersections represents the number of solutions to the system of equations. Since the parabola intersects the circle at two points, there are two solutions to the circle.

Furthermore, these two points of intersection are exactly the solutions to the system of equations. Finding the coordinates of the points of intersection will give you the solutions to the system of equations.

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What is the midpoint of the line segment with endpoints (–5.5, –6.1) and (–0.5, 9.1)?

astraxan [27]

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
(\stackrel{x_1}{-5.5}~,~\stackrel{y_1}{-6.1})\qquad 
(\stackrel{x_2}{-0.5}~,~\stackrel{y_2}{9.1})
\qquad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{-0.5-5.5}{2}~~,~~\cfrac{9.1-6.1}{2} \right)\implies \left( \cfrac{-6}{2}~~,~~\cfrac{3}{2} \right)\implies \left(-3~,~1\frac{1}{2} \right)$