What is the solution of the system of inequalities?
y is more than or equal to x^2+6x+10
y<-x^2-8x-14
(1 point)
Responses
graph a- A quadratic function is graphed with a solid line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The interior of the graph of the quadratic function is shaded.
A second quadratic function is graphed with a dashed line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The interior of the graph of the quadratic function is shaded.
The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. The region is bounded above by the second quadratic function and bounded below by the first quadratic function. The points where these two boundaries meet are left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis.
graph b- A quadratic function is graphed with a dashed line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The interior of the graph of the quadratic function is shaded.
A second quadratic function is graphed with a solid line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The interior of the graph of the quadratic function is shaded.
The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. The region is bounded above by the second quadratic function and bounded below by the first quadratic function. The points where these two boundaries meet are left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis.
graph c- A quadratic function is graphed with a dashed line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The exterior of the graph of the quadratic function is shaded.
A second quadratic function is graphed with a solid line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The exterior of the graph of the quadratic function is shaded.
The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. This region is outside the graphs of both quadratic functions.
graph d- A quadratic function is graphed with a solid line. It has a minimum at left-parenthesis negative 3 comma 1 right-parenthesis and passes through the points left-parenthesis negative 4 comma 2 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The exterior of the graph of the quadratic function is shaded.
A second quadratic function is graphed with a dashed line. It has a maximum at left-parenthesis negative 4 comma 2 right-parenthesis and passes through the points left-parenthesis negative 5 comma 1 right-parenthesis and left-parenthesis negative 3 comma 1 right-parenthesis. The exterior of the graph of the quadratic function is shaded.
The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. This region is outside the graphs of both quadratic functions.
The correct solution is graph b: A quadratic function is graphed with a dashed line and a second quadratic function is graphed with a solid line. The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. This region is bounded above by the second quadratic function and bounded below by the first quadratic function. The points where these two boundaries meet are (-4, 2) and (-3, 1).
The correct option is graph b.
In graph b, a quadratic function is graphed with a dashed line. It has a minimum at (-3, 1) and passes through the points (-4, 2) and (-2, 2). The interior of the graph is shaded.
A second quadratic function is graphed with a solid line. It has a maximum at (-4, 2) and passes through the points (-5, 1) and (-3, 1). The interior of the graph of the quadratic function is shaded.
The region of the coordinate plane where the two shaded areas overlap is shown in a dark color. The region is bounded above by the second quadratic function and bounded below by the first quadratic function. The points where these two boundaries meet are (-4, 2) and (-3, 1).
To solve the system of inequalities, we need to find the region on the coordinate plane where both inequalities are satisfied. This can be done graphically by graphing the two quadratic functions and shading the regions that satisfy each inequality. Then, we identify the overlapping region, which represents the solution to the system of inequalities.
Based on the descriptions provided, it seems that graph b is the correct representation of the solution. In graph b, a quadratic function with a dashed line is graphed. It has a minimum at (-3, 1) and passes through the points (-4, 2) and (-2, 2). The interior of the graph is shaded.
A second quadratic function is also graphed with a solid line. It has a maximum at (-4, 2) and passes through the points (-5, 1) and (-3, 1). The interior of this graph is also shaded.
The overlapping region, represented by the dark shaded area, is bounded above by the second quadratic function and bounded below by the first quadratic function. The points where these two boundaries meet are (-4, 2) and (-3, 1).
Therefore, the solution to the system of inequalities is the region on the coordinate plane that is inside both quadratic functions, as shown in graph b.
Simplify the number using the imaginary unit i.
Root negative 25 EndRoot
The square root of -25 can be simplified using the imaginary unit i. We know that the square root of -1 is defined as i.
The square root of -25 can be written as the square root of -1 times the square root of 25.
√(-25) = √(-1) * √(25) = i * 5 = 5i