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Snezhnost [94]
3 years ago
5

Based on the graph, what is the cyclist's speed in miles per

Mathematics
1 answer:
Aleksandr [31]3 years ago
8 0
The answer is a) 16mph
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Which sequence of transformations confirms congruence by mapping shape I onto shape II?
Lubov Fominskaja [6]

Answer:

  • Neither of the choices is correct.

Explanation:

<u>1. Coordinates of the vertices of the figure I (preimage):</u>

  • (10, - 5)
  • (15, -5)
  • (10, - 10)
  • (15, -10)

<u />

<u>2. Coordinates of the vertices of the figure II (image):</u>

  • (0,10)
  • (0,15)
  • (-5,10)
  • (-5, 15)

Since many different rigid transformations can map the figure I into the figue II, you will need to use trial and error.

The most important is to do it in an educated way.

I will start by eliminating some options.

The first option, a reflection across the x-axis and 15 units left, does not work, because the reflection across the x-axis would shift the figure to a lower position than what you need.

The third option, a 90º counterclokwise rotation about the origin then a translation 10 units up, would move the figure to the second quadrant, and we need it in the third quadrant.

I will try now with the second choice, a 90º clockwise rotation and then 25 units up:

First, a 90º clockwise rotation, which is the same that a 270º counterclockwise rotation, follows the rule (x, y) → (y, -x)

Then, that results in:

  • (10, - 5) → (-5, -10)
  • (15, -5) → (-5, -15)
  • (10, - 10) → (-10, -10)
  • (15, -10) → (-10, -15)

Now, you can see that shifting 25 units up will not work, because you need that two x-coordinates become 0 (zero). So, this is not the correct set of transformations either.

A 180º rotation about the origin and a translation 10 units right follow this chain of rules:

  • (x, y) → (-x, -y) → (-x + 10, -y)

That means:

  • (10, - 5) → (-10,5) → (-10 + 10, 5) = (0, 5)
  • (15, -5) → (-15, 5) → (-15 + 10, 5) = (-5, 5)
  • (10, - 10) → (-10, 10) → (-10 + 10, 10) = (0, 10)
  • (15, -10) → (-15, 10) → (-15 + 10, 10) = (-5, 10)

        These last points do not coincide either with the vertices of the figure II.

In conclusion, neither of the choices gives the correct answer to the question.

8 0
3 years ago
Read 2 more answers
At a particular music store, CDs are on sale at $11.00 for the first one purchased and $9.00 for each additional disc purchased.
Mrac [35]
The answer is 7, 7 cds were purchased, hope this helps have a great day!
6 0
3 years ago
How can you do a picture using 2.8÷7
Margarita [4]
The answer to this question is 0.4

7 0
3 years ago
Which expression shows: add 99 and 15, then multiply by 11?
Jobisdone [24]
The answer is(99+15)11 

i hope this help

4 0
3 years ago
Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons. Now, it costs her $42.56 to fill the t
harina [27]

Answer:

Proportion states that the two fractions or ratios are equal

As per the statement: Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons. Now, it costs her $42.56 to fill the tank. Once the new tank is in, it will cost her $72.96

Let the tank size now be x

Since, the gas tank expanded by 10 gallons = x + 10

by definition of proportion ;

\frac{x}{42.56}=\frac{x+10}{72.96}

by cross multiply we get;

72.96x = 42.56(x+10)

using distributive property;a\cdot (b+c) =a\cdot b + a\cdot c

72.96x = 42.56x+425.6

Subtract 42.56x from both sides we get;

30.4x =425.6

Divide both sides by 30.4 we get;

x = 14

Therefore, the tank is her now is, 14 gallons


5 0
3 years ago
Read 2 more answers
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