Provide an appropriate response.
-You are graphing $2 x ^ { 2 } + 3 y ^ { 2 } 5$. You have drawn the graph of $2 x ^ { 2 } + 3 y ^ { 2 } = 5$. What single point will allow you to determine the correct region?
A) $( 2,5 )$
B) $( 2,3 )$
C) The origin
D) $( 3,5 )$

Question

Provide an appropriate response.
-You are graphing $2 x ^ { 2 } + 3 y ^ { 2 } > 5$. You have drawn the graph of $2 x ^ { 2 } + 3 y ^ { 2 } = 5$. What single point will allow you to determine the correct region?
A) $( 2,5 )$
B) $( 2,3 )$
C) The origin
D) $( 3,5 )$

Quizplus · Accepted Answer

The origin (0,0) is the most effective point to test because it is easy to substitute into the inequality. If the origin satisfies the inequality, the region containing the origin is the solution. If not, the opposite region is the solution. For $2x^2 + 3y^2 > 5$, substituting (0,0) gives $2(0)^2 + 3(0)^2 > 5$, which simplifies to $0 > 5$, which is false. Therefore, the region that does not contain the origin is the correct region.

Provide an Appropriate Response 2x2+3y2>52 x ^ { 2 } + 3 y ^ { 2 } > 52x2+3y2>5

Provide an Appropriate Response $2 x ^ { 2 } + 3 y ^ { 2 } > 5$