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liraira [26]
3 years ago
14

Which rigid transformation(s) can map AMNP onto ATSR?

Mathematics
1 answer:
ivanzaharov [21]3 years ago
6 0

Answer:

Option C

Step-by-step explanation:

Translation means moving the figure horizontally or vertically.

Reflection means flipping across a vertical or a horizontal line.

In the figure we see that we can vertically shift the point P to R down by some units.

Then we see that if we reflect that triangle NMP across the line which joins P & R we get the triangle STR.

So to have triangle MNP map onto to TSR we need to translate & then reflect.

Option C) is the right answer.

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A theater has a seating capacity of 750 and charges $3 for children, s5 for students, and $7 for adults. At a certain screening
-BARSIC- [3]

Answer:

Between 150 and 450

Step-by-step explanation:

We are going to find the number by resolving  a system of linear equations.

First we write the system equations :

C+S+A=750

Where C : children, S : students and A : adults

The equation represents the ''full attendance''

The second equation :

3C+5S+7A=3450

This equation represents the totaled receipts.

The system :

C+S+A=750\\3C+5S+7A=3450

has the following associated matrix :

\left[\begin{array}{cccc}1&1&1&750\\3&5&7&3450\end{array}\right]

By performing elementary matrix operations we find that the matrix is equivalent to

\left[\begin{array}{cccc}1&0&-1&150\\0&1&2&600\\\end{array}\right]

The new system :

C-A=150\\S+2A=600

Working with the equations :

C = 150 + A\\S = 600-2A

Our solution vector is :

\left[\begin{array}{c}C&S&A\end{array}\right] =\left[\begin{array}{c}150+A&600-2A&A\end{array}\right]

For example :

If 0 adults attended ⇒ A = 0

C = 150 + 0 \\C = 150\\S = 600 - 2A\\S = 600

This verify the totaled receipts equation :

150($3)+600($5) = $ 3450

A ≥ 0 ⇒ If A = 0 ⇒ C = 150

C = 150 is the minimum children attendance

From the equation :

S = 600 -2A

S ≥0

600 - 2A ≥ 0

600 ≥ 2A

300≥ A

A is restricted to the interval [ 0, 300]

When A = 0 ⇒ C = 150

When A = 300 ⇒C = 150 + A = 150 + 300 = 450

Children ∈ [ 150,450]

With C being an integer number (including 0)

Also S and A are integer numbers (including 0)

7 0
3 years ago
Need HELP!!!!
tino4ka555 [31]

Answer:

80.07

Step-by-step explanation:

3 0
2 years ago
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Please help me I can’t figure it out
sukhopar [10]

Y1 is 3x, y2 is x^3 and y3 is 3^x

8 0
3 years ago
How to change 3/4 to twelfths
ruslelena [56]
<span>Multiply both sides of the fraction by 3.

3/4 = 9/12 </span>
6 0
3 years ago
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Write the equation of a line with a slope of -7/2 passing through the point 2,-4
fiasKO [112]

Answer:

y = -7/2x+3

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = -7/2 x+b

Substitute the point into the equation

-4 = -7/2(2) +b

-4 = -7+b

Solving for b

-4+7 = -7+b+7

3 = b

The equation is y = -7/2x+3

5 0
2 years ago
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