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kogti [31]
3 years ago
5

Suppose a linear transformation Upper T : Bold Upper R squared right arrow Bold Upper R squared is formed by taking a rotation c

ounterclockwise of 180​ degrees, followed by a reflection across the Bold x 2​-axis. Describe the points that will be moved back to their original position by this​ transformation?
Mathematics
1 answer:
kotykmax [81]3 years ago
8 0

Answer:

All points on line x+y = 0 or x-y=0 will satisfy the transformation.

Step-by-step explanation:

Let (x, y) be the general such point.

Hence rotating it by 180 deg. counterclockwise will give us (-y,-x).

Reflecting (-y,-x) on x axis gives us (-y,x).

Hence if (x,y) = (-y,x) then all ( x, y) where x = -y or x+y = 0 or x=y or x-y=0 will satisfy this condition.

All points on line x+y = 0 or x-y=0 will satisfy the transformation.

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First;
-8≤2x-4
-4≤2x
-2≤x

Then;
2x-4<4
2x<8
x<4

-2≤x<4
C is the correct answer.
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3 years ago
Identify the property demonstrated
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Answer:

  • D. Product of Powers Property

Step-by-step explanation:

  • 4^3 * 4^7 = 4^{3 + 7}

<u>The Product of Powers Property states: </u>

  • <em>when multiplying two exponents with the same base, you can add the exponents and keep the base</em>
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2 years ago
In comparing two distributions, which attribute would you not compare?
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A. Joint frequency, it’s right I checked it myself
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2 years ago
The illustration below shows the graphs of fourteen functions.
Travka [436]

Due to <em>length</em> restrictions, we kindly invite to check the explanation of this question to understand the derivation of the <em>polynomic</em> expressions.

<h3>How to determine a family of cubic functions</h3>

<em>Cubic</em> functions are polynomials of grade 3. In this case, we have pairs of <em>cubic</em> functions of the following form:

y = (x - h)³ + k       (1)

y = - (x - h)³ + k     (2)

a) Where (h, k) are the coordinates of the vertex of each <em>cubic</em> function. There is a translation of (x, y) = (3, 1) between each two <em>consecutive</em> pairs of <em>cubic</em> functions. Hence, we have the following fourteen cubic functions:

  1. y = (x + 9)³ - 3
  2. y = - (x + 9)³ - 3
  3. y = (x + 6)³ - 2
  4. y = - (x + 6)³ - 2
  5. y = (x + 3)³ - 1
  6. y = - (x + 3)³ - 1
  7. y = x³
  8. y = - x³
  9. y = (x - 3)³ + 1
  10. y = - (x - 3)³ + 1
  11. y = (x - 6)³ + 2
  12. y = - (x - 6)³ + 2
  13. y = (x - 9)³ + 3
  14. y = - (x - 9)³ + 3

b) Another family of functions with a similar pattern is shown below:

  1. y = (x + 9)² - 3
  2. y = - (x + 9)² - 3
  3. y = (x + 6)² - 2
  4. y = - (x + 6)² - 2
  5. y = (x + 3)² - 1
  6. y = - (x + 3)² - 1
  7. y = x²
  8. y = - x²
  9. y = (x - 3)² + 1
  10. y = - (x - 3)² + 1
  11. y = (x - 6)² + 2
  12. y = - (x - 6)² + 2
  13. y = (x - 9)² + 3
  14. y = - (x - 9)² + 3

To learn more on cubic functions: brainly.com/question/25732149

#SPJ1

8 0
2 years ago
How many constant terms are in this expression?<br><br> 11a + 9b + c + 2a
zzz [600]

Answer:

0

Step-by-step explanation:

11a + 9b + c + 2a

a constant is just a number...it has no variables (letters).

there are no constants in this expression

example :

3x + 2b + 7 + 4c + 2                                           x + 5 = 8

the constants in this are 7 and 2                 constants are 5 and 8

7 0
3 years ago
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