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____ [38]
1 year ago
12

Which of the following represents the translation of R (-3, 4) along the vector

Mathematics
1 answer:
Semenov [28]1 year ago
6 0

By applying concepts of linear algebra, the point P'(x, y) = (-3, 4) represents the translation of P(x, y) = (-3, 4) along the vectors <7, -6> and <-1, 3>.

<h3>How to determine the resulting point by applying translations</h3>

Translations are a kind of <em>rigid</em> transformation. A transformation is <em>rigid</em> if and only if <em>Euclidean</em> distances are conserved. By linear algebra, an image as a consequence of <em>consecutive</em> translations is described by the following formula:

P' (x,y) = P(x,y) + \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)     (1)

Where:

  • P(x, y) - Original point
  • P'(x, y) - Image
  • \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right) - Net translation vector

Now we proceed to determine the image of the given point:

P'(x, y) = (-3, 4) + (7, -6) + (-1, 3)

P'(x, y) = (-3 + 7 - 1, 4 - 6 + 3)

P'(x, y) = (3, 1)

By applying concepts of linear algebra, the point P'(x, y) = (-3, 4) represents the translation of P(x, y) = (-3, 4) along the vectors <7, -6> and <-1, 3>.

To learn more on rigid transformations: brainly.com/question/1761538

#SPJ1

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(-2,12) (1,1) what would the anwser be ?​
Fed [463]

Answer:

-11/2

Step-by-step explanation:

To solve this, use slope intercept formula

y2 - y1

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x2-x1

1-12

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1-(-2)

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2

-11/2

6 0
2 years ago
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There wegens ales and red apples instag Fyou pick one apple without looking the probability that the apple is greencaragaatiyars
Verdich [7]

Let:

A = Pick a green apple

B = Pick a red apple

m = Number of favourable outcomes

n = Total number of outcomes

The probability that the apple is green is:

P(A)=\frac{m}{n}=\frac{4}{4+6}=\frac{4}{10}=\frac{2}{5}

Answer:

2/5

The probability that the apple is red is:

P(B)=\frac{6}{4+6}=\frac{6}{10}=\frac{3}{5}

Answer:

3/5

4 0
10 months ago
Which of the following is the graph of the quadratic function y = x2 - 4x +4?​
Airida [17]

Answer:

B. Graph D

Step-by-step explanation:

Start with the vertex formula for each, <em>y</em><em> </em><em>=</em><em> </em><em>a</em><em>(</em><em>x</em><em> </em><em>-</em><em> </em><em>h</em><em>)</em><em>²</em><em> </em><em>+</em><em> </em><em>k</em><em>,</em><em> </em>where (<em>h</em><em>,</em><em> </em><em>k</em>) → (<em>2</em>, <em>0</em>) is the vertex, plus, -h gives you the OPPOSITE terms of what they really are, and k gives you the EXACT terms of what they really are. So, insert the vertex into the Vertex Equation FIRST, y = (x - 2)². We reason why there is no <em>k</em><em> </em>is because it is represented by 0. So, squaring this monomial will give us <em>x</em><em>²</em><em> </em><em>-</em><em> </em><em>4x</em><em> </em><em>+</em><em> </em><em>4</em><em>.</em><em> </em>Ta Da!

I am joyous to assist you anytime.

7 0
3 years ago
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Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution? y = x+1 1 X+ 3 2.
Troyanec [42]

Answer:

D. (4, 5)

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Algebra I</u>

  • Solving systems of equations using substitution/elimination
  • Solving systems of equations by graphing

Step-by-step explanation:

<u>Step 1: Define systems</u>

y = x + 1

y = 1/2x + 3

<u>Step 2: Solve for</u><u><em> x</em></u>

  1. Substitute in <em>y</em>:                              x + 1 = 1/2x + 3
  2. Subtract 1/2x on both sides:        1/2x + 1 = 3
  3. Subtract 1 on both sides:              1/2x = 2
  4. Divide both sides by 1/2:              x = 4

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Define original equation:                   y = x + 1
  2. Substitute in <em>x</em>:                                    y = 4 + 1
  3. Add:                                                     y = 5

<u>Step 4: Graph</u>

<em>We can confirm our answer.</em>

8 0
3 years ago
HELPP PLEASEEE
MrRa [10]

Answer: The answer to your question is 6\sqrt{3}

Step-by-step explanation:

To solve this problem we will use proportions. We will compare the largest right triangle and the medium size triangle.

                          Medium triangle                     Large triangle

hypotenuse                 y                                            9 + 3

adjacent size               9                                               y

- Write the proportions

                                  y/9 = (9 + 3)/y

-Solve for y

                                  y² = 9(12)

                                  y² = 108

                                  y =   \sqrt{180}

-Find the prime factors of 108

                                  108  2

54 2

                                     27 3

                                      9  3

                                      3   3

                                       1

then,       108 = 2² 3³

-Expressthe root as fractional exponents

                                  2²/² 3²/² 3¹/²

-Simplification

                                   2(3)(3)¹/²

-Result

                                      6\sqrt{3}

8 0
3 years ago
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