Is it possible that image of a point after a reflection could be the same as the preimage?

Answer:

C.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Standard Form: ax² + bx + c = 0
• Quadratic Formula:

Algebra II

• Imaginary Roots: √-1 = i

Step-by-step explanation:

Step 1: Define

x² - 5x + 7 = 0

Step 2: Identify Variables

a = 1

b = -5

c = 7

Step 3: Find solutions

1. Substitute [Quad Formula]:                    
2. Evaluate Exponents:                              
3. Evaluate Multiplication:                          
4. Evaluate Subtraction:                            
5. Factor:                                                    
6. Simplify:                                                  

The solutions to the equation x² - 5x + 7 = 0  are:

x = (5 + i√3) / 2 or x = (5 - i√3) / 2

Option C is the correct answer.

We have,

To find the solutions of the quadraticequation x² - 5x + 7 = 0, we can use the quadraticformula:

x = (-b ± √(b² - 4ac)) / (2a)

For the given equation, the coefficients are:

a = 1

b = -5

c = 7

Substituting these values into the quadraticformula,

x = (-(-5) ± √((-5)² - 4(1)(7))) / (2(1))

Simplifying further:

x = (5 ± √(25 - 28)) / 2

x = (5 ± √(-3)) / 2

Since the discriminant (the value inside the square root) is negative, √(-3) is imaginary, meaning there are norealsolutions to this quadratic equation.

The solutions exist in the complex number system.

So,

√-1 = i

x = (5 ± i√3) / 2

This can be written as,

x = (5 + i√3) / 2

and

x = (5 - i√3) / 2

Thus,

The solutions to the equation x² - 5x + 7 = 0  are:

x = (5 + i√3) / 2 or x = (5 - i√3) / 2

Learn more about solutionsofequations here:

brainly.com/question/545403

#SPJ6

The figure which is rotated and translated correctly about the x-axis is figure a.

What is graph?

The graph of a function f is that the set of ordered pairs, where\f(x)=y. within the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

How to form graph of function?

We have been given four graphs of a function and first function has coordinates (-5,7) (-2,6) (-7,4) (-4,1) and that we must identify correct reflected graph.

The coordinates of a pure reflected graph are going to be (4,7) (2,4) (5,1) (7,6) which are the coordinates of figure a which is in first quadrant.

Hence the proper reflected graph of function having coordinates (-5,7) (-2,6) (-7,4) (-4,1) is that the graph of coordinates (4,7) (2,4) (5,1) (7,6).

Learn more about function at brainly.com/question/10439235

#SPJ2

Answers:

Figure a has been translated only (translated 9 units to the right)

Figure b has been reflected over the x axis

Figure c has been rotated and translated

=======================================

Explanation:

Pick on a point like (-7,4) and note how it moves 9 units to the right to get to (2,4). All points on the upper left figure follow this same translation rule. This rules in figure a.

Figure b is a result of reflecting over the x axis. The rule used is . The x coordinate stays the same while the y coordinate flips from positive to negative. So for example, (-7,4) flips to (-7,-4)

Figure c is a combination of rotating and translating the original figure. It looks like a 90 counterclockwise rotation has been applied followed by a translation. The actual translation and rotation rules used will depend on how you define the center of rotation.