Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure A"B"C"D"E" using a series of two different transformations. They give two different answers.

Answer the questions to investigate ways to transform ABCDE.

1. Olivia finds a combination of two different transformations that moves ABCDE onto A"B"C"D"E". What is one way she might have done this?

2. Angelica reflects ABCDE over the y-axis and translates it up 8 units. Does her transformed figure match A"B"C"D"E"? If not, describe how her transformed figure compares to A"B"C"D"E".

3. Michael says he can move ABCDE onto A"B"C"D"E" with one transformation by translating ABCDE diagonally so that it moves 8 units up and 10 units right. Is he correct? Explain why or why not.

Problem 1

One method Olivia could have used is to reflect over the x axis and then translate 10 units to the right.

Let's apply these set of steps to point C.

C = (-2,-4)

C' = (-2,4) after reflecting over the x axis; y coordinate flips in sign

C'' = (8,4) after shifting to the right 10 units; add 10 to the x coordinate

Point C(-2,-4) moves to C''(8,4) which is shown in the diagram. I'll let you check the other four points.

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Another method Olivia could have used is to shift to the right 10 units first, then reflect over the x axis. In this case, the order doesn't matter. Though for some other combinations of transformations, order does matter.

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Problem 2

Reflecting over the y axis will have the point (x,y) turn into (-x,y). Only the x coordinate changes, and we flip the sign here. The y coordinate stays the same.

A point like C(-2,-4) becomes C'(2,-4) after the y axis reflection. Shifting up 8 units means we add 8 to the y coordinate to arrive at C''(2,4) but this does not match what the diagram shows. Therefore, Angelica's method is incorrect.

You should find other inconsistencies for the other four points as well.

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Problem 3

Michael's method isn't correct either. He does not apply an x axis reflection and instead relies entirely on translations to move ABCDE to A''B''C''D''E''

At a quick glance, it looks like Michael may be correct. But upon a much closer look, you'll see that things don't line up perfectly.

Instead of point C, we'll pick on point D this time.

D is located at (-6,-2). If we shift up 8 units, then we add 8 to the y coordinate to get to D'(-6,6). Then add 10 to the x coordinate to shift 10 units to the right. This leads us to D''(4,6).

However, the diagram shows D'' is actually at (4,2)

I'll let you check the other points. You should find that only points C and E go to the correct locations, but the other points do not. Again, this is because Michael did not apply an x axis reflection. His figure of A''B''C''D''E'' is upside down compared to what it should be.

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To summarize, the methods described in problem 1 are the correct way to get ABCDE to move to A''B''C''D''E''. If Olivia followed either of those two methods, then she is correct. Both Angelica and Michael have incorrect methods.

Tasha has foam blocks stored in a box that measures 314 ft long by 3 ft wide by 1 ft tall.

Each foam block is a cube with 14 -ft edge length.



How many blocks can fit into the box?




A. 156 blocks

B. 312 blocks

C. 624 blocks

D. 2496 blocks

PLEASE HELP WITH MATH ASAP!!!!! ITS DUE IN 10 MINS!!! ILL GIVE BRAINLIEST

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What does the length of the field measure in feet?

13,200 ft
15,840 ft
18,480 ft
21,120 ft

Please help me with number 2 I need to know the maximum length!

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help me please boyos

i'll give brainliest to first person to answer!!

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what is the volume?

3 cubic centimeters
24 cubic centimeters
124 cubic centimeters
48 cubic centimeters

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92 mg
920 mg
92,000 mg

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A)
yox
B)
y - 3x
y = 4x
D)
y - 12x

helpppppppppppppppppppppppppp

i just need helppppp

Extended Answer
IT IS ALGEBRA!!!! HELP ME PLZ

15. Evan is sewing trim on a pair of shorts. He needs four equal length pieces of trim to put two stripes down each side of the shorts. The teacher gives him a piece of black trim that is 185 cm long. He measures and cuts 4 equal lengths. He ends up with a small piece of leftover trim that is 13 cm long. How long is each piece of trim?

a) Write an equation to represent this situation.

Heather deposits $7000 into an account that pays simple interest at a rate of 2% per year. How much interest will she be paid in the first 3 years?

Help fast if you don’t know don’t answer

What is x
2(23x+34)=500

Show all your work!!!

B is already wrong (TRUST ME)

12 ft
B
B
2 If AABC – ADEF, what is
the value of x?
D
3 cm
E
7 cm
A 22 ft
26 ft
B
24 ft
D 28 ft

I will give brainliest to whoever helps me with this question. Also, if you could please explain to me how you solved it I would appreciate it!

someone actually help i dont get it

PLSSSS HELP IM SOOO BAD AT SIMPLIFYING FRACTIONS!!!!!!
a. 4/20=
b. 5/10=
c. 14/ 21=
d. 9 /15 =
e. 16/24=
f. 18/48=
g. 16/44=
h. 9/21=
i. 25/30=
j. 8/22=
k. 12/30=
l. 5/20=
q.There are 36 students in Frank's class. 27 of them are buying lunch today. Write and simplify the fraction of students that are buying lunch.

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Enter an equation below that describes the hanger.

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DUE TODAY!!!