Rewrite the function by completing the square. g
(
x
)
=
4
x
2
−
16
x
+
7
g(x)=4x
2
−16x+7g, left parenthesis, x, right parenthesis, equals, 4, x, squared, minus, 16, x, plus, 7
g
(
x
)
=
g(x)=g, left parenthesis, x, right parenthesis, equals

(
x
+
(x+left parenthesis, x, plus

)
2
+
)
2
+right parenthesis, squared, plus

Two line segments are shown in the figure below. suppose that the length of the line along the x-axis is 6, and the length of the hypotenuse of the triangle is 10. what is the equation of the hypotenuse line (shown in red, below)?

If abcde is reflected over the x-axis and then translated 3 units left, what are the new coordinates d?

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.