Eloise started to solve a radical equation in this way: square root of negative 2x plus 1 − 3 = x
square root of negative 2x plus 1 − 3 + 3 = x + 3
square root of negative 2x plus 1 = x + 3
square root of negative 2x plus 1 − 1 = x + 3 − 1
square root of negative 2 x = x + 2
(square root of negative 2 x)2 = (x − 4)2
−2x = x2 − 8x + 16
−2x + 2x = x2 + 8x + 16 + 2x
0 = x2 + 10x + 16
0 = (x + 2)(x + 8)

x + 2 = 0 x + 8 = 0
x + 2 − 2 = 0 − 2 x + 8 − 8 = 0 − 8
x = −2 x = −8

Both solutions are extraneous because they don't satisfy the original equation.

What error did Eloise make?

A) She added 2x after squaring both sides.
B) She subtracted 1 before squaring both sides.
C) She factored x2 + 10x + 16 incorrectly.
D) She did not check for extraneous solutions.

Saline iv fluid bags cost $64.20 for 24, 1000 ml bags from one supplier. a new supplier sells 500 ml bags for $2 each. the hospital uses about 10,000, 1000 ml bags each month. nurses report that about half of the bags are more than half full when they are discarded. if you are going to use only one supplier, which size bag provides the best deal, and how much will you save each month? compare the cost of the new supplier to the current one.

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.

In a two-digit number the units' digit is 7 more than the tens' digit. the number with digits reversed is three times as large as the sum of the original number and the two digits. find the number.