Write a rule in function notation to describe the transformation that is a reflection across the x-axis.

Answers

Answer 1

Answer:

R(x, y) = (x, -y)

Step-by-step explanation:

When we have a reflection across some line, the distance between the original point and the reflected point to the line is invariant.

For a reflection around the x-axis, the x-value is invariant, then the only value that can change is the y-value.

So if we have a point like (4, 7)

Which is at a distance of 7 units to the x-axis, the only other point that is also at a distance of 7 units to the x-axis that has the same x-value is (4, -7)

Here we already can see the rule.

If we have a point (x, y), the reflection across the x-axis gives us the point (x. -y)

Then we can write this reflection as a function in the next way:

R(x, y) = (x, -y)

This means that if the input is the point (x, y), the output is the point (x, -y)


Related Questions

Triangle ABC with vertices A(-3, 4), B(0, 2),
and C(-2, 1) is translated 4 units right and 5
units down. Which quadrant is the image?

Answers

A(-3, -1)

B(0, -7)

C(-2, -4)

Therefore, the image is in the III quadrant (bottom left).

calculate the volume of the prism by first finding the total number of half unit cubes that will fill it.There are 8 half unit cubes in every unit cube pls help guys this is my exam

Answers

Answer:

I think its C

Step-by-step explanation:

Can someone pls help me find the correct answers pls and thank you!

Answers

Answer:

IJ

Step-by-step explanation:

BH and AG = 1/2 diameter of the circle therefore are radii

IJ is not 1/2 the diameter of the circle so it's not a radius.

HELP ME PLEASE ILL BRAINLIEST YOU IF YOU GET IT RIGHT
which lines, if any, are parallel in the diagram below?

Answers

The correct answer would be C
The correct answer is c

Find the value of unknown anlges from the figure.​

Answers

X would equal 30 because if you plug 30 into the equation you would get 180. X=30

CAN SOMEONE PLEASE HELP ME!!!

!!!

Answers

I’m not sure but I think the answer is (a)
Bc in -50, the x value is 0

Your classmate showed their thought process to the problem below. However, They made a mistake. What mistake did they make? Describe it below

Answers

Answer:

It's not 5x + 100 = 180,

it's 5x = 180 because they are vertical angles.

x = 36

What is the gravitational potential energy of a 2.5 kg object that is 300 m above the surface of the earth

Answers

Answer:

7350 J

Step-by-step explanation:

The gravitational potential energy of a body can be found by using the formula

GPE = mgh

where

m is the mass

h is the height

g is the acceleration due to gravity which is 9.8 m/s²

We have

GPE = 2.5 × 9.8 × 300

We have the final answer as

7350 J

Hope this helps you

Answer these questions but show your work for them!
1. 5+4(3)
2. 2-(3+ -4)
3. 24/6 -2^3 +2(-3)
4. 3+2(5^2-5 x 4)
5. 3+2(5^2 - 5 x 4)

Answers

173-10105105

mark as brainliest

simplify 3/x-1 + 1/x-2

Answers

Answer:

4-3x over x or 4-3x/x

I'm not sure. but I hope it can help you:))

Al cine paraíso fueron el sábado 1.350 espectadores y el domingo 1.120 cuánto se recaudo si cada entrada costaba 540?

Answers

Answer:

1,333,800

Step-by-step explanation:

Spectators on Saturday = 1,350

Spectators on Sunday = 1,120

Total spectators = 1,350 + 1,120 = 2,470

Price per ticket = 540

So, we can calculate the total amount collected by using following formula,

Total amount collected = Total spectators × Price per ticket

By putting value, we get

= 2,470 × 540

= 1,333,800

To determine a student’s overall test score for the semester, Ms. Lopez throws out the lowest test score and takes the average of the remaining test scores. Victor earned the following test scores in Ms. Lopez’s class this semester: 62, 78, 83, 84, and 93. What overall test score did Victor earn in Ms. Lopez’s class this semester?

67.6
67.6

80.0
80.0

83.0
83.0

83.5
83.5

84.5

Answers

Answer:

80%

Step-by-step explanation:

I'm assuming you want the average of the class.

62 + 78 + 83 + 84 + 93

= 400

400/5

= 80

Therefore Victor's overall test score is 80%

what is the average value of 3+9=12​

Answers

Answer:

the mean (average) is 6 bc you divide the answer by the amount of numbers

Step-by-step explanation:

Please help solve ASAP!! <3

Answers

Answer: The answer is 280 ft.

Step-by-step explanation:

divide the green area into a triangle and a rectangle so it's easier to calculate. Then find the area of the rectangle by multiplying 14 times 16. That should get you 224. Then, find the area of the tringle by multiplying 14 times 18, times 1/2. That will get you 56. If you add 56 to 224, that gets you 280.


If ax – b = 0 and a #0, then x =

Answers

Answer:

x = [tex]\frac{b}{a}[/tex]

Step-by-step explanation:

Given

ax - b = 0 ( add b to both sides )

ax = b ( divide both sides by a )

x = [tex]\frac{b}{a}[/tex]

Figure ABCD is a kite. Find the value of x.

BC = 2x - 5
DC = x+3

Answers

Here's the solution,

the given figure is a kite,

So, BC = DC

=》

[tex]2x - 5 = x + 3[/tex]

=》

[tex]2x - x = 3 + 5[/tex]

=》

[tex]x = 8[/tex]

value of x = 8

I have to factor polynomials by grouping
The question is: 6f^3 - 8f^2 + 20 - 15f
The answer is supposed to be; (2f^2 - 5)(3f - 4)
Pls show your work

Answers

Answer:

Step-by-step explanation:

Factor 6f3−8f2+20−15f

6f^3−8f^3−15f

=(3f−4)(2f2−5)

Answer:

(3f−4)(2f^2−5)

Find the group you want to factor, such as in the first parenthesis, you remove 3f from the whole equation, and end up with 3f-4. You take the end value, and group it with -5. You will then end up with 2f^2 -5.

Hope this Helps!

Arjun's family is traveling in a car at a constant speed of `65` miles per hour. How far do they travel in `25` minutes?

Answers

Answer:

can you say me which chapter question is this

Answer:

Step-by-step explanation:

1. it takes 3.1 hours

2.27.08 miles is how far they travel in 25 minutes

please give me a brainliest, i worked pretty hard to find these out, if you need a explanation, i will add it

What is the equation of the trend line in the scatter plot?
Use the two yellow points to write the equation in slope-intercept form. Write any coefficients as integers, proper fractions, or improper fractions in simplest form.

Answers

Answer:

y = 7/5x - 21/5

Step-by-step explanation:

points to use to find slope:  (3,0) and (8,7)

slope = 7-0 / 8-3

slope = 7/5

find y-intercept (or 'b')

0 = 3(7/5) + b

0 = 21/5 + b

-21/5 = b

b = -4 1/5

2.
2.
Which of the following functions would give the population Plt) as a function
of t, in years, given that the initial population is 2,500 and that the population
is growing at an annual rate of 4%?
(1) P(t)=2500(0.96)
(3) P(t)=2,500(1.04)
(2) P(t)=(1.04) +2,500
(4) P(t)= 1.04t +2,500

Answers

Answer:

[tex]P(t)=2500(1.04)^t[/tex]

Step-by-step explanation:

None of your proposed answers has an exponent t.

Here's the logic behind the answer:

Year 0: pop. = 2500

Year 1:  pop. = 2500(1.04)  That is 104% of the previous year's pop.

Year 2: pop. = 2500(1.04)(1.04) = 2500(1.04)^2

Year 3: pop. = 2500(1.04)^2 x (1.04) = 2500(1.04)^3

See the pattern?  The exponent matches the year number.

Marcus is rolling a number cube with sides labelled 1 to 6 .find the probability it will show 10​

Answers

Answer:

Probability of getting number 10  = 0

Step-by-step explanation:

Given;

Total sides of cube die = 6

Find:

Probability of getting number 10

Computation:

Total number of cube = 1, 2, 3, 4, 5, 6

Favorable outcome for 10 = 0

Probability of an event = Favorable outcome / Number of outcomes

Probability of getting number 10 = 0 / 6

Probability of getting number 10  = 0

Find the median of this data set: 4, 9, 1, 3, 7, 1

Answers

The median is 3.5

Hope this helped

(*^▽^*)

1 + 3 = 4 divided by 2 equals 2. hope this helped!

9/2 - 23/9=? plss help ​

Answers

Answer:

35/ 18

(Decimal: 1.944444)

Step-by-step explanation:

Answer

Step-by-step explanation:35/18

Find the measure of arc DB in OP.
mDB=

Answers

Answer:

90

Step-by-step explanation:

First of all you have to know that when 2 lines are perpendicular to each other,they produce a 90° angle, therefore DP||TD. Then you should remember that the measure of an arc is the same as the measure of the angle. So angle DB is 90°.

In a random sample of 800 seniors at Mill Creek High School, 100 students are asked if they prefer graduation at the High School or at the Gwinnett Infinite Energy Arena, Eighty-four students preferred to have graduation in the Mill Creek stadium. How many seniors prefer to have the Graduation Ceremony at Mill Creek?
504
608
672
706

Answers

Answer:

Step-by-step explanation:

84%

800*.84 = 672 students prefer the stadium

Jordan sold his used lawn tractor and accessories for $980. If he received nine times as much money for the lawn tractor as he did for the accessories, find how much money he received for the lawn tractor

Answers

Answer: [tex]\$882[/tex]

Step-by-step explanation:

Given

Jordan sold lawn tractor and accessories for [tex]\$980[/tex]

he receives 9 times more money for a tractor than for accessories

Suppose, he receives x amount for accessories

So, for tractor it is [tex]9x[/tex]

total amount is

[tex]\Rightarrow 9x+x=980\\\Rightarrow 10x=980\\\Rightarrow x=\$98[/tex]

He receives [tex]9x=\$882[/tex] for tractor

what is equivalent (2 - 6) cubed

Answers

Answer:

solution given:

equivalent (2 - 6) cubed=(-4)³=-64

The population density of a city is 1,148 persons per square mile.
If 40,173 people live in the city, what is the approximate land area of the city?
А.
6 square miles
B.
35 square miles
C.
70 square miles
D.
1,225 square miles

Answers

Answer:

B. 35 Square Miles

Step-by-step explanation:

The answer is b :))))))))

Which statement identifies how to show that j(x) = 11.6ex and k(x) = In (StartFraction x Over 11.6 EndFraction) are inverse functions?

Answers

Answer:

The answer is "It must be shown that both [tex]j(k(x))\ and \ k(j(x))=x[/tex]"

Step-by-step explanation:

Given:

[tex]j(x) = 11.6 e^{x} \\\\k(x) =\ln\frac{x}{11.6}[/tex]

To show that both are equal functions, and  show that both[tex]j(k(x))\ and\ k(j(x)) =x,[/tex]

For [tex]j(k(x));[/tex]  

[tex]j(k(x)) = j[(\ln \frac{x}{11.6})]\\\\j[(\ln (\frac{x}{11.6})] = 11.6e^{\ln (\frac{x}{11.6})}\\\\j[(\ln \frac{x}{11.6})] = 11.6(\frac{x}{11.6})\\\\[/tex](The natural logarithm is canceled by exponential function)  

[tex]j[(\ln \frac{x}{11.6})] = 11.6 \times\frac{x}{11.6}\\\\j[(\ln \frac{x}{11.6})] = x\\\\j[k(x)] = x\\\\for\ \ k[j(x)]:\\\\k[j(x)] = k[11.6e^x]\\\\k[11.6e^x] = \ln (\frac{11.6e^x}{11.6})\\\\k[11.6e^x] = \ln(e^x)[/tex]

Its natural logarithm leaving x will nullify expanding universe.

[tex]k[11.6e^x] = x\\\\k[j(x)] = x[/tex]

In the question, it is seen that[tex]j[k(x)] = k[j(x)] = x[/tex], shows that the functions [tex]j(x) = 11.6 e^{x} \ and \ k(x) = \ln \frac{x}{11.6}[/tex] is inverse functions.

Answer:

C

Step-by-step explanation:

Ed2021

the answer is 5286 i think hope this helps

Answers

Answer:

We can’t see the question

Step-by-step explanation:

we need a question to solve for the question

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