**Answer:**

B

**Step-by-step explanation:**

-7 x 3^0.25x = -10

Which of the following is the solution of the equation?

Option A is correct!!!!!!!!

If x = 29°, find the measures of angles 1, 2, and 3.

**Answer:**

75.5

**Step-by-step explanation:**

Evaluate (if possible) the six trigonometric functions of the angle (0).

-5pi/6

**Answer:**

**Step-by-step explanation:**

You want the **6 trig functions** of the **angle -5π/6**.

The angle is in the 3rd quadrant, so all trig functions are negative except the tangent and cotangent. The reference angle is -5π/6 +π = π/6.

Trig functionsSince you have memorized the values of the trig functions for multiples of π/6, you know ...

** sin(-5π/6) = -1/2**

** cos(-5π/6) = -√3/2**

** tan(-5π/6) = sin/cos = √3/3**

** csc(-5π/6) = 1/sin = -2**

** sec(-5π/6) = 1/cos = -2√3/3**

** cot(-5π/6) = 1/tan = √3**

Answer/Step-by-step explanation:

Use a Unit Circle, you may have access to (hopefully) or have been asked to memorize.

To find -5pi/6 count clockwise the sixths to 5. Or add:

-5pi/6 + 2pi

= -5pi/6 + 12pi/6

= 7pi/6

-5pi/6 is the same as 7pi/6 on the Unit Circle.

Use the coordinates at that spot

(-root3/2 , -1/2)

to find the six trig ratios.

The Unit Circle is a big, giant, Answer Key. It has all the trig answers on it all in one place. It looks like a scary math pizza, but really its all the answers all in one place.

Once you find your angle, the sine is the y-coordinate.

sin theta = -1/2

The cosine is the x-coordinate.

cos theta = -root3/2

Tangent theta is the sine over the cosine, sin/cos,

= y/x

= (-1/2) / (-rt3/2)

Use Keep-Change-Flip to simplify this.

see image.

= root3/3

Sec is cos flipped over. Csc is sin flipped over. Cot is tan flipped over (the math word is reciprocal)

Yes, just flip over sin to get csc:

sintheta = -1/2

csctheta = - 2/1 = -2

Flip over cos to get sec:

costheta = -rt3/2

sectheta = 2/-rt3

Then rationalize, see image.

= -2rt3/3

Flip over tan to get cot.

tantheta = 1/rt3

Use a form that's easy to flip.

cottheta = rt3/1 = rt3

see image.

Write a fraction in simplified form that expresses the ratio of 0.27 to 0.06.

**Answer: 9/2**

**Step-by-step explanation:**

To express 0.27 and 0.06 as fractions, we first need to convert them to fractions with denominators that are powers of 10. We can do this by multiplying 0.27 by 100 to get 27/100, and multiplying 0.06 by 100 to get 6/100. The ratio of 0.27 to 0.06 is then equal to the ratio of 27/100 to 6/100, which simplifies to 27/6. To express this ratio in simplest form, we can divide both the numerator and denominator by the greatest common factor of 27 and 6, which is 3. This gives us a simplified fraction of 27/6 = 9/2.

PLEASE HELP ASAP

A line that passes through the points (-1, -4) and (4, 2) is shown.

Which equation is the equation of the line that is perpendicular to the given line and passes through the point (-3, 7) ?

The **equation** of the line that is **perpendicular** to the line that passes through the points (-1, -4) and (4, 2): D. 5x + 6y = 27.

**Perpendicular lines** have slopes with a product of -1, or are negative reciprocals.

First find the slope of the line that passes through (-1, -4) and (4, 2):

Slope (m) = change in y / change in x = (2 -(-4)) / (4 -(-1))

m = 6/5

The negative reciprocal of 6/5 is -5/6. This means that the **perpendicular line** is, m = -5/6.

To write the **equation** of the line that is **perpendicular** to the given line, substitute m = -5/6 and (a, b) = (-3, 7) into y - b = m(x - a):

y - 7 = -5/6(x - (-3))

y - 7 = -5/6(x + 3)

6(y - 7) = -5(x + 3)

6y - 42 = -5x - 15

6y = -5x - 15 + 42

6y = -5x + 27

5x + 6y = 27

The answer is: D. 5x + 6y = 27.

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Write an inequality for the graph

The **inequality **that represents the **line **in the **figure **will be y > - (2/3) x + 3.

**Inequality **is defined as an equation that does **not **contain an **equal **sign. Inequality is a term that describes a statement's **relative size **and can be used to compare these **two claims**.

From the figure, the **points **of the **line **are (0, 3) and (3, 1). And the **region **above the line is a **consideration**. Then the equation of the line is given as,

(y - 3) > [(3 - 1) / (0 - 3)](x - 0)

**Simplify **the equation, then we have

(y - 3) > [(3 - 1) / (0 - 3)](x - 0)

(y - 3) > - (2/3)x

y > - (2/3) x + 3

The disparity that **addresses **the line in the **figure **will be y > - (2/3) x + 3.

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Two members of the Math Competition Team solve 13 problems in 1 hour. Assume all team members solve problems at the same rate. How many team members are needed to solve in 1 hour 39 problems

**Two members of the maths competition team solve 13 problems in 1 hour.**

**Person=13**

**Time=1 hour**

**Then.**

**Rate=13/1 (person/time)**

**With the help of question,**

**Let us consider,**

**x team members are needed to solve in 1 hour 39 problems,**

**2M×1/13=1×xM/39**

**2M/13=x M/39**

**2M=x M/13**

**M=26**

**26 team members are needed to solve in 1 hour 39 problems,**

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The equation y−k = a(x−h) ^2 has graph a parabola with vertex (h, k).

Suppose a > 0. A horizontal line 1 unit above the vertex intersects the

graph at two points. Find the distance between these two points.

The **distance **between these** two points** is given as follows:

[tex]d = 2\sqrt{1 - a}[/tex]

How to obtain the distance between these two points?The equation of the **parabola **is given as follows:

y - k = a(x - h)².

Hence:

y = a(x - h)² + k.

The **horizontal line **one unit above the vertex has the equation given as follows:

y = k + 1.

(as k is the y-coordinate of the vertex).

Then the **intersection **of this line with the graph is obtained as follows:

k + 1 = a(x - h)² + k.

a(x - h)² = 1

(x - h)² = 1 - a

[tex]x - h = \pm \sqrt{1 - a}[/tex]

[tex]x = \pm \sqrt{1 - a} + h[/tex]

Then the **points **are given as follows:

The **distance **between these two points is of:

[tex]d = \sqrt{1 - a} + h - (-\sqrt{1 - a} + h)[/tex]

[tex]d = 2\sqrt{1 - a}[/tex]

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How many liters are in 4 quarts of milk? Round to the nearest tenth if needed. 1 quart = 0.95 liters.

**Answer:**

3.8

**Step-by-step explanation:**

4 x 0.95 = 3.8

Solve for x -13x<65 simplify

The value of x in the **inequality**, -13x < 65, is **simplified** as, x > 5.

Any **inequality **given can be **solved** by find the value of the variable in the **inequality**, which will make it a true statement. To do this, isolate the given variable to make it stand alone on one side.

Given the **inequality**, -13x < 65, **solve** as shown below:

-13x < 65 [given]

Divide both sides by -13:

-13x/-13 < 65/-13

x > -65/13 {the sign changes from < to > because we divided both sides by a negative quantity]

x > 5

The value of x is **simplified** as x > 5.

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find the interval of convergence of the power series. (be sure to include a check for convergence at the endpoints of the interval.) (7x)^n/(10n)!

The **interval** of **convergence** of the **power** **series** is (-10/7, 10/7).

**What does Interval of convergence tell you?**

A group of **x-values** on which a **power** **series** **converges** is known as the **interval** of **convergence**. In order to create a **convergent** series, you can plug in this interval of **x-values**.

The **interval** of **convergence** of a power series is the set of values of x for which the **series** **converges**. To find the **interval** of **convergence** of the given **power** **series**, we can use the **ratio** test.

The ratio **test** **states** that if the series [tex]∑ a_nx^n[/tex] has a **positive** radius of convergence R, then the **series** converges for |x| < R and diverges for |x| > R. The radius of **convergence** is given by the formula

[tex]R = 1/limsup|a_n+1/a_n|.[/tex]

In the given **power** **series**, the **coefficient** [tex]a_n[/tex] is given by [tex]a_n = (7x)^n/(10n)!.[/tex]

We can **rewrite** this as [tex]a_n = x^n(7/10)^n/n!.[/tex]

Taking the **limit** of the ratio [tex]a_n+1/a_n[/tex] as n goes to **infinity**, we get:

[tex]limsup|a_n+1/a_n| \\\\= limsup|x^(n+1)(7/10)^(n+1)/(n+1)!/(x^n(7/10)^n/n!)|\\\\= limsup|x(7/10)/(n+1)|\\\\= |x(7/10)|[/tex]

Therefore, the **radius** of **convergence** R is [tex]1/|x(7/10)|[/tex].

This means that the **interval** of **convergence** is [tex]|x| < 1/|7x/10| = 10/7.[/tex]

We can check the **endpoints** of the interval to see if the **series** **converges** at these points. At x = 10/7, the series becomes [tex](7(10/7))^n/(10n)! = 1^n/(10n)!.[/tex]

This series is a **geometric** **series** with first term 1 and **common** **ratio** 1/10, and it **converges** because [tex]|1/10| < 1.[/tex]

At x = -10/7, the **series** becomes[tex](7(-10/7))^n/(10n)! = (-1)^n/(10n)![/tex]. This series is an **alternating** series with first term 1 and **common** **ratio** (-1/10), and it also **converges** because [tex]|-1/10| < 1.[/tex]

Therefore, The **interval** of **convergence** of the **power** **series** is (-10/7, 10/7).

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Is (6, 8) a solution to this system of equations?

y =1/6x+5

y=5/6x+3

Yes

No

**Answer:No**

**Step-by-step explanation:**

**When we substitute x=6 into the first equation we get **

**y=1/6 *6+5=6 so we get (6, 6)**

**When we substitute x=6 into the second equation we get**

**y=5/6*6+3=8 so we get (6, 8) . it works for the second equation but not the first. It must be true for both equations**

Question 5 of 20:

Select the best answer for the question.

5. What's the sum of 667 and 23?

OA. 644

OB. 29

OC. 690

D. 15,341

Mark for review Will be highlighted on the review pagel

**Answer:**

C). 690

**Step-by-step explanation:**

When you see the word "sum" that means you add the numbers together

667 **+** 23 = **690**

**Answer:**

OC. 690

**Step-by-step explanation:**

To find the sum of 667 and 23, you need to add the two numbers together. When you do this, you get 690 as the result. Therefore, the sum of 667 and 23 is 690.

This can be written as an equation: 667 + 23 = 690. The symbol "+" is used to represent the operation of addition, and the equals sign "=" is used to show that the value on the right side of the equation is the result of the operation on the left side.

In general, when you add two or more numbers together, you find their sum by combining their values and counting the total. For example, to find the sum of the numbers 3 and 4, you would add them together to get 7. To find the sum of the numbers 5, 6, and 7, you would add them together to get 18.

I hope this helps to clarify the concept of addition and the meaning of the term "sum." Let me know if you have any further questions.

find the k-value so that the point is on the line

kx+3y=7; (1,-k)

**Answer:**

k = -7/2

**Step-by-step explanation:**

You want the **k-value** so that the **point (1, -k) **is on the **line kx+3y=7**.

The point will be on the line when its coordinates make the equation true. Using (x, y) = (1, -k), we have ...

k(1) +3(-k) = 7

-2k = 7 . . . . . . . . simplify

** k = -7/2** . . . . . . . divide by -2

The value of k = [tex]\frac{-7}{2}[/tex] so the point is on the** line** kx+3y=7

A line is an endlessly long object without breadth, depth, or curvature in **geometry**. Thus, despite the fact that they can exist in two, three, or higher dimensional environments, lines are **one-dimensional **things. The term "line" can also refer to a line segment that has two locations that serve as its ends in daily life.

given

the point of the line = ( 1 ,-k )

the line = kx + 3y = 7

the coordinates make the equation true when its points are on the line

so putting the values of x and y in equation of line

k( 1 ) + 3 ( -k ) = 7

k - 3k = 7

-2k = 7

k = [tex]\frac{-7}{2}[/tex]

The value of k = [tex]\frac{-7}{2}[/tex] so the point is on the line kx+3y=7

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A composite figure is represented in the image.

What is the total area of the figure?

A: 192 m2

B: 216 m2

C: 288 m2

D: 336 m2

The **total **area of the figure is **equal **to 192 square meters. The **correct **option is A.

The **space **occupied by any two-dimensional **figure **in a plane is called the area. The space **occupied **by the rectangle in a two-**dimensional **plane is called the area of the rectangle.

Calculate the **area **of the rectangle by the **formula **written below,

Area of the rectangle = L x W

Area of the rectangle = 8 x 18

Area of the rectangle = 144 square meters

The **area **of the triangle will be **calculated **by the formula **written **as,

Area of triangle = 1/2 x B x H

Area of triangle = 1/2 x ( 18 - 6 ) x 8

Area of triangle = 1 / 2 x 12 x 8

Area of triangle = 48 square meters

Total area = 144 + 48

Total area = 192 square meters

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There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean

B. Because the **standard deviation** is unaffected by a change in a single **data value, **it will remain unchanged.

A change in a single data value has no impact on the standard deviation, which measures the spread of a data collection. As a result, even if the single data value changes, the standard deviation won't.

The variability of a data set is measured by the standard deviation. It is calculated by taking the square root of the average of the sum of the squares of the differences between each value in a data set and the mean. When a **single value** in a data set is changed, the mean of the data set will change, but the standard deviation will not be affected. This is because the standard deviation is not calculated based on individual data points, but on the overall **variability of the data set. **Therefore, when a single data value is changed, the standard deviation of the data set will remain the same.

Let x be one of the students in the class

**Mean **= (76.9 + 82)/2 = 79.4

**Standard Deviation** = sqrt(((76.9 - 79.4)^2 + (82 - 79.4)^2)/2) = 3.2

The complete question is : There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean D. The standard deviation will increase because the change moved an exam score further from the mean

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Trey makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours.

**Answer:**

p=8h

**Step-by-step explanation:**

P is the total pay, so it will be on one side of the equation. 8 represents the fact that Trey receives 8 dollars per hour. It's multiplied by h to represent the number of hours he works.

division answer in feet and inches 8 divided by 34ft 8in

**Answer:**

since 12inches=1foot

x inches=34feet

34feet converted to inches =408inches

total inches=408+8

T=416inches

dividing 416 by 8 we have

52 inches left

converting back to feet we get

4ft 4in

Does meditation cure insomnia? Researchers randomly divided 400 people into two equal-sized groups. One group meditated daily for 30 minutes, the other group attended a 2-hour information session on insomnia.

At the beginning of the study, the average difference between the number of minutes slept between the two groups was about 0. After the study, the average difference was about 32 minutes, and the meditation group had a higher average number of minutes slept.

To test whether an average difference of 32 minutes could be attributed to chance, a statistics student decided to conduct a randomization test. She wrote the number of minutes slept by each subject in the study on an index card. She shuffled the cards together very well, and then dealt them into two equal-sized groups, representing those who meditated and those who attended the information session.

Which of the following best describes the outcome of the randomization test.

O The average difference between the two values on the two stacks of cards is expected to be about 0 minutes.

O If meditation is effective, the average difference between the values on the two stacks of cards is expected to be more than 32 minutes.

O The average difference between the two values on the two stacks of cards is expected to be about 32 minutes.

1. The **average** difference between the two values on the two stacks of cards is expected to be about 0 minutes best describes the outcome of the **randomization test**.

This randomization test was conducted to test whether the average **difference** of 32 minutes between the two groups could be attributed to chance. The test essentially involved shuffling the index cards containing the minutes slept by each subject and then dealing them into two equal-sized groups.

This process allows for a fair **comparison** between the two groups and ensures that any differences in the average minutes slept are due to chance. Since the cards are shuffled randomly, the average difference between the two stacks of cards is expected to be about 0 **minutes**.

If meditation is effective, then the difference between the **values** on the two stacks of cards would be expected to be more than 32 minutes.

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NO LINKS!!

The inverse function of the exponential function f(x) = a^x is the (a. transcendental, b. logarithmic, c. rational, d. polynomial, e. algebraic) function with base a.

**Answer:**

The inverse function of the exponential function f(x) = a^x is the logarithmic function with base a.

The inverse function of a function f is a function that "undoes" the original function, meaning that it reverses the transformation applied by the original function. In the case of the exponential function, the inverse function is the logarithmic function, which "undoes" the transformation applied by the exponential function.

For example, suppose we have the exponential function f(x) = 2^x. The inverse function of this function is the logarithmic function with base 2, which is written as y = log_2 x. If we apply the inverse function to 2^x, we get:

y = log_2 (2^x)

Solving for x gives:

x = 2^y

This means that the inverse function of the exponential function f(x) = a^x is the logarithmic function with base a, which is written as y = log_a x.

The other options (a. transcendental, c. rational, d. polynomial, e. algebraic) are not correct, since they do not describe the inverse function of the exponential function.

**Answer:**

b. logarithmic

**Step-by-step explanation:**

Given exponential function:

[tex]f(x)=a^x[/tex]

The **inverse **of the given function is the **logarithmic function** with base a.

To find the **inverse **of a function, replace f(x) with y:

[tex]\implies y=a^x[/tex]

Swap the x and y:

[tex]\implies x=a^y[/tex]

Take **logs **with **base a** of both sides of the equation:

[tex]\implies \log_ax=\log_aa^y[/tex]

Apply the **log power law**: logₐ xⁿ = n logₐ x

[tex]\implies \log_ax=y\log_aa[/tex]

Apply the **log law**: logₐ a = 1

[tex]\implies \log_ax=y[/tex]

[tex]\implies y=\log_ax[/tex]

**Replace **y with f⁻¹(x):

[tex]\implies f^{-1}(x)=\log_ax[/tex]

Thus proving that the **inverse **of the exponential function f(x) = aˣ is the **logarithmic function **with** base a**.

James was also measured at 23 inches long. How many centimeters long was he at birth

The **length **of the **birth **in centimeters will be 58.42 **centimeters**.

Algebra is the **study **of abstract symbols, while **logic **is the manipulation of all those **ideas**.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This **approach **is used to answer the problem **correctly **and **completely**.

James was also measured 23 **inches **long.

We know that, in **one **inch, there are 2.54 **centimeters**.

The **length **of the **birth **in centimeters is calculated as,

⇒ 23 inches

⇒ 23 x 2.54 centimeters

⇒ 58.42 centimeters

The number of **birth **in centimeters will be 58.42 **centimeters**.

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The question is in the picture

**Answer:**

-6/6 or -1

**Step-by-step explanation:**

To find the equation of the line (or the slope, assuming that's what equation means, ) we need to write the formula Y1-Y2/X1-X2

So, we need to fill in the numbers, which gives us the fraction -6-0/-2-(-8)

When we solve for the numerator (-6-0), we get -6.

When we solve for the denominator (-2 - {-8}), we get 6.

So, we have -6/6, which, when simplified, is -1.

(If the problem is not asking for slope when it says equation, then sorry!)

Please answer my quistion in math the quistions are in the picture

**Step-by-step explanation:**

i hope this helps u get an idea how to solve the problems, sorry for the bad handwriting though

Good luck!!

The map of a walking trail is drawn on a coordinate grid with three points of interest. The trail starts at R(−1, 4) and goes to S(5, 4) and continues to T(5, −2). What is the total walking trail of units?

**Answer:**

Exact answer 12 + 6[tex]\sqrt{2}[/tex]

Answer rounded to the nearest whole number 20

**Step-by-step explanation:**

Ravi sells real estate. Based on previous data, he knows that 5% of home tours result in a sale. Assume that the results of these tours are independent from each other. Which of the following choices are binomial random variables? Choose all answers that apply: A. Take a random sample of 30 tours and let L = the number of tours that result in a sale. B. Take a random sample of 3 tours and let K = the number of tours that result in a sale. C. Take a random sample of 3 tours and let M = the amount of sales (in dollars) generated by the tours

The following choices are **binomial **random variables: **A**. Take a random sample of 30 tours and let L = the number of tours that result in a sale. **B**. Take a **random sample **of 3 tours and let K = the number of tours that result in a **sale**.

**Choice A** is a binomial random variable because it represents the number of tours that result in a sale in a random sample of 30 tours. The trials are independent, as the results of one tour do not affect the results of other tours, and the **probability **of success (a sale) is constant at 5%.

**Choice B** is also a binomial random variable because it represents the number of tours that result in a **sale **in a random sample of 3 tours. The trials are independent and the probability of success is **constant **at 5%.

Choice C is not a binomial random variable because it represents the **number **of **sales **generated by a random sample of 3 tours, which is a continuous variable. Binomial random variables are always discrete, as they represent the number of **successes **in a sequence of trials.

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Question

Solve the equation.

−2w=−9

w=

**w=9/2 =4,5**

**Step-by-step:**

**:)**

Cooper has 35 video games in his collection, and Maria has 15 in hers. Cooper decides to add 10 video games to his collection each month. Maria decides to add 8 video games to her collection each month. Part A Drag the values to the positions in the table to show how many video games each of them will have at the ends of months 1, 2, 3, and 4. 314533436529 Month Cooper Maria Start 35 15 1 23 2 55 3 39 Part B Which of the following is a true statement about the relationship between the number of video games collected by Cooper and Maria after each month? A. Cooper will always have 20 more video games than Maria. B. Maria will always have 20 more video games than Cooper. C. Cooper will always have 28 more video games than Maria. D. There is no constant relationship between the number of video games collected by Cooper and Maria.

From the values that we have here, the **statement **that can be said to be true here would be that: There is no **constant relationship **between the number of video games collected by Cooper and Maria. Last option

A** relationship** with a fixed ratio between two quantities is referred to as **proportionate.** The graph will therefore be linear, or straight.

When two** variables** are directly or indirectly** proportional** to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

The values between these two does not show any constant relationship hence the last option

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Answer: part a

cooper- 35 45 55 65

maria 15 23 31 39

part B

there is no constant relationship between the number of video games collected by coopeer and maria

Step-by-step explanation:

Mathematical models are used as tools to describe reality. These models are supposed to characterize the important features of the analyzed phenomena and provide insight. The normal distribution is an example of a random variable that is widely used by researchers to model real data.

Researchers often model real observations using the normal distribution, but sometimes the real distribution is a bit different from the perfect, normal distribution. List some reasons why researchers might make approximations like this and describe at least one situation when researchers should not use this approximation.

When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable can serve as a model.

There are several reasons why **researchers** might not use the normal distribution to model real data which are due to assumptions of** normal distribution**.

First, the normal distribution assumes that the data is **symmetric** and is distributed around the mean. However, in some cases, the data may be skewed, making the normal distribution an inappropriate model.

Second, the normal distribution assumes that the data is **homoscedastic**, meaning that the variance is constant across the sample. However, in some cases, the variance may be heteroscedastic, meaning that the **variance** changes across the sample. This makes the normal distribution an inappropriate model for this type of data.

One situation in which researchers should not use the normal distribution approximation is when **modeling** financial data. Financial data often follows a power-law distribution, which is not normal. Therefore, researchers should use a power-law distribution to model this type of data.

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Use the model to help you find 1/(8/12)

1/(8/12)=___

**Answer:**

3/2 or 1.5 or 1 1/2 in mix number

9. If point Q is reflected across x = 1, what are the coordinates of its reflection image?

The **coordinates** of** reflection image** are (**-1, -2)**.

**What is point reflection?**

A particular kind of Euclidean space isometry is known as a **point reflection** in geometry. A thing is said to have **point** **symmetry** if it is **invariant** under a **point** **reflection**; if it is invariant under a **point** **reflection** through its center, it is said to have central symmetry or to be centrally symmetric.

Given:

point Q is reflected across x = 1.

From graph the point Q is (3, -2).

We have to find the coordinates of its reflection image.

x = 1 is a vertical line passing through all points with an x- coordinate of 1.

(3, - 2) is 2 units to the right of x = 1 ( 3 - 1 ), thus

The reflection is 2 units to the left of x = 1 ( 1 - 2 = - 1 )

Q(3, - 2 ) → Q'(- 1, - 2 )

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Hence, the **coordinates** of** reflection image** are (**-1, -2)**.

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