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Kisachek [45]
3 years ago
5

A parallelogram has coordinates A(1, 1), B(5, 4), C(7, 1), and D(3, -2). What are the coordinates of parallelogram A′B′C′D′ afte

r a 180° rotation about the origin and a translation 5 units to the right and 1 unit down? I need Help
Mathematics
1 answer:
saul85 [17]3 years ago
5 0

Hey there! I'm happy to help!

First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).

Let's convert this below

A: (1,1)⇒(-1,-1)

B: (5,4)⇒(-5,-4)

C: (7,1)⇒(-7,-1)

D: (3,-2)⇒(-3,2)

Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.

A: (-1,-1)⇒(4,-2)

B: (-5,-4)⇒(0,-5)

C: (-7,-1)⇒(-2,-2)

D: (-3,2)⇒(2,1)

Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)

Now you know how to find the coordinates of translated figures! Have a wonderful day! :D

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On Saturday, the Anderson
Bond [772]

Answer:

\left\{\begin{matrix}2p + 4c = 31.50\\3p + 2c = 33.25\end{matrix}\right.

Step-by-step explanation:

Let's call (as suggested)

p = the cost of one pizza

c = the cost of one cheeseburger

The Anderson Family ordered 2 pizzas and 4 cheeseburgers and paid $31.50, thus:

2p + 4c = 31.50             [1]

Next weekend, they ate at the same restaurant and ordered 3 pizzas and 2 cheeseburgers for $33.25, thus:

3p + 2c = 33.25           [2]

To know the cost of one pizza and one cheeseburger, we need to solve the system of equations defined by [1] and [2]

\left\{\begin{matrix}2p + 4c = 31.50\\3p + 2c = 33.25\end{matrix}\right.

4 0
3 years ago
The rectangle is 20 by 16 and the scale factor is 0.25. What are the dimensions of the reduced rectangle?
antoniya [11.8K]

Answer:

1,280

The dimensions are 5 by 4

Step-by-step explanation:

You multiply 20 and 16 then, divide 0.25 then you get 1,280

4 0
3 years ago
The price of a mountain bike increased by 20% in the past year the value is $150 what was the value of the mountain bike last ye
n200080 [17]

I hope I am reading the problem right: The price of a mountain bike increased by 20% in the past year. The value is $150. What was the value of the mountain bike last year?

Let's simplify this. One year, there was this radical mountain bike that used to have an unsaid price, <em>x. </em>That year, that price of x increased by 20% more than it was before, or <em>120% times the original value</em>. Because of that, it's now $150.

We can equation this.

1.20x = 150

x = 150/1.2

x = 125

The bike, I believe, cost $125 last year. Hope this helps!


8 0
3 years ago
A Family purchased tickets to the movies in spent a total of $40.75. The family purchase five tickets there was a $.90 processi
muminat

Answer:

$7.25

Step-by-step explanation:

Total amount spent on the ticket   = $40.75

Number of ticket purchased  = 5

Processing fee per ticket  = $0.90

Unknown:

Cost of each ticket = ?

Solution:

To solve this problem, we need to find the processing fee for the 5 tickets purchase;

      Processing fee = number ticket x processing fee per ticket

      Processing fee  = 5 x 0.9  = $4.5

Now, the real cost a ticket = $40.75  - $4.5  = $36.25

So, cost per ticket is;

        Cost  = \frac{36.25}{5}   = $7.25

7 0
3 years ago
Convert 0.0045 from standard form to scientific notation.
djyliett [7]
I did not catch well, but i think you already got your answers. Let me explain. For the first part you got your notation right: for 0.0045 the correct scientific notation is 4.5 x 10^-3. Now the second part, the answer would be the first one, the notation that you are giving is the one who corresponds to <span>4.5 x 10^-2, the first option you have. Hope it helps</span>
3 0
4 years ago
Read 2 more answers
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