What are the solutions to the system shown?  A coordinate plane shows a red circle centered at the origin with a radius of about 7 units. The circle reaches approximately (0, 7), (7, 0), (0, −7), and (−7, 0). A dark gray line with negative slope crosses the graph, running from the upper left quadrant to the lower right quadrant. The line appears to pass through points near (−5, 0) and (0, −5). It intersects the circle at two points—one in the upper left portion of the circle and one in the lower right portion. The axes are labeled from about −10 to 10 on both x and y.

Find the standard equation of the ellipse .

A parabolic headlamp has a bulb placed at the focus. A cross-section of the parabola is 6 cm deep and 12 cm wide. How far from the vertex should the bulb be placed?  

Find the solutions to the system. Select all that apply.  Be sure to check for extraneous solutions.

How does the graph of  change from the parent graph  ?

Write as a single logarithm  .

The just-world hypothesis would best explain which of the following phenomena?

Find the vertex and axis of symmetry:  . Vertex: ([answer0], [answer1]) Axis of symmetry:  [answer2]

Which is the equation for the graph shown?   A coordinate plane displays a single straight orange line with negative slope. The line slopes downward from left to right, passing through the upper left quadrant and continuing into the lower right quadrant. It crosses the y-axis slightly below −2 and crosses the x-axis slightly to the left of 0. The grid is marked in one-unit increments, with labeled ticks at −5 and 5 on both axes. The line appears linear and continuous across the visible window.

Ultrasound waves are used in Indoor Positioning Systems in hospitals to detect the location of equipment. If the system must be centrally located in a hospital that measures 860 meters in the east-west direction by 950 meters in the north-west direction, which would be an equation that models the range of the IPS for this hospital?