7. Given the vertices of ∆ABC are A (2,-5), B (-4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices: a. Rx = 3 b. T<3,-6> c. r(90◦, o)

Answers

Answer 1

Q1)
Rx = 3
in this reflection, the image has been reflected along the x = 3 line. then all the points on the image are reflected along this vertical line. the distance between each point and the vertical line is noted and by that same distance its moved to the opposite side of the vertical line, while the y coordinates stay the same.
A(2,-5)- x coordinate is 2, its 1 unit away from x=3, it should move by 1 unit to the other side of x = 3, then x = 4. y stays as it is.
A' - (4,-5)

B(-4,6) - distance from x = 3, is (-4-+3) is seven units, moves by 7 units to the other side
B' (10,6)

C(3,1) = distance from 3 = 0, therefore the point stays at is,
C' (3,1)

Q2)
next is a translation, in translation the size nor shape changes, each point in the original image moves the same distance in the same direction.
T (3,-6) (x,y) = this means that the x coordinates move by +3 points to the right and y coordinates move downwards by 6 units
A (2,-5) ---> (2+3,-5-6)
A' (5,-11)
B (-4,6) ---> (-4+3,6-6)
B' (-1,0)
C (3,1) ---> (3 + 3, 1-6)
C' (6,-5)

Q3)
r(90°,0)
this is a rotation done in the clockwise direction. then the image takes a rotation to the right direction around the origin.
then the x, y coordinates of the preimage become ;
(x,y) = (y,-x)
A(2,-5) --> A' = (-5,-2)
B(-4,6) ---> B' = (6,4)
C(3,1) ---> C' = (1,-3)

Related Questions

What is the graph of the function f(x) = the quantity of x plus 4, all over x plus 6?

Answers

I've downloaded a graph for you. It is one of the first things you should always think about with a question like this one. You should notice the following about it:
1. The denominator gives a discontinuity point at (x = - 6). You can tell that is happening just by looking at the graph at x = - 6. The range at that point is - infinity to plus infinity. Other critical points are much better behaved. The y intercept is when x = 0 or 4/6 = 2/3. So the point is (0,2/3)

There is one x intercept at y = 0. When that happens
x + 4 = 0
x = - 4
Point (-4,0)

Notice the whole denominator gets multiplied out. 0 * (x + 6) = 0

Which solid has six faces, four lateral faces, two bases, eight vertices, and 12 edges? square pyramid triangular prism rectangular prism triangular pyramid

Answers

Rectangular Prism
*********************************************

Answer:

Rectangular Prism

Step-by-step explanation:

what is the inverse and then graph the function and its inverse f(×)=-5n-14

Answers

You could write the original equation as y = - 5x - 14. That's what f(x) looks to mean. In inverse interchanges x and y

The inverse is x = -5y - 14 Now solve for y
x + 14 = - 5y
y = (x + 14)/-5 I have included a graph to show these two relationships.

Red Line: y = -5x - 14
Blue Line: y = (x + 14)/-5

Great Dish believes that it will need new equipment in 8 years. The equipment will cost $26,000. What lump sum should be invested today at 12%, compounded semiannually, to yield $26,000? a. $20,186.02 c. $16,388.00 b. $16,145.82 d. $10,234.80

Answers

Answer:

d. $10,234.80

Step-by-step explanation:

we are given

The equipment will cost $26,000

so, Amount is $26000

A=26000

should be invested today at 12%

r=12%=0.12

It is compounded semiannually

so, n=2

t=8

now, we can use formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

now, we can plug values

[tex]26000=P(1+\frac{0.12}{2})^{2\times 8}[/tex]

now, we can solve for P

[tex]P=10234.80338[/tex]

help!!!!!!! please !!!!!!!

Answers

c is the answer hope it helps

The corners are right angles, but the sides are different lengths. The figure is a rectangle.

A system of inequalities is graphed below. The variable x represents the number of cans someone is buying, and y represents the number of bottles. Conditions on the maximum amount of total weight and volume lead to two of the inequalities.
Which descriptions correspond to solutions of this system?
7 cans and 140 bottles
12 cans and 40 bottles
8 cans and 120 bottles
9 cans and 70 bottles

Answers

we have that
We will analyze each case to verify the answer
see the attached figure

Point A) 7 cans and 140 bottles------------> (x,y)=(7,140)----> is not solution
Point B) 12 cans and 40 bottles------------> (x,y)=(12,40)----> is not solution
Point C) 8 cans and 120 bottles------------> (x,y)=(8,120)----> is a solution
Point D) 9 cans and 70 bottles------------> (x,y)=(9,70)-------> is a solution

the answer is
the solutions are
8 cans and 120 bottles
9 cans and 70 bottles

solving the whole thing

Answers

Let
x---------------> distance from people living to the city center

we Know that
Zone 1 covers people living within three miles of the city center
Zone 1 ------------> [x < 3 miles]

Zone 2 covers those between three and seven miles from the center
Zone 2 ------------> [ 3 <= x < = 7 miles]

Zone 3 covers those over seven miles from the center
Zone 3 ------------> [ x > 7 miles]

calculate the distance between two points to find the value of x

case A) point (0,0) point (3,4)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(4-0)² +(3-0)²]------> √[16+9]
x=√25-------------> x=5 miles

the answer Part A)
people living in (3,4)
x=5 miles -------------> covers Zone 2 [ 3 < =x <= 7 miles]

case B) point (0,0) point (6,5)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(5-0)² +(6-0)²]------> √[25+36]
x=√61-------------> x=7.81 miles

the answer Part B)
people living in (6,5)
x=7.81 miles -------------> covers Zone 3 [ x > 7 miles]

case C) point (0,0) point (1,2)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(2-0)² +(1-0)²]------> √[4+1]
x=√5-------------> x=2.23 miles

the answer Part C)
people living in (1,2)
x=2.23 miles -------------> covers Zone 1 [ x < 3 miles]

case D) point (0,0) point (0,3)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(3-0)² +(0-0)²]------> √[9]
x=√9-------------> x=3 miles

the answer Part D)
people living in (0,3)
x=3 miles -------------> covers Zone 2 [ 3 < =x <= 7 miles]

case E) point (0,0) point (1,6)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(6-0)² +(1-0)²]------> √[36+1]
x=√37-------------> x=6.08 miles

the answer Part E)
people living in (1,6)
x=6.08 miles -------------> covers Zone 2 [ 3 < = x <= 7 miles]

Select the ratios whose simplest form is 8/7

Answers

48:42
16:14
56:49
I hope this helps.

Answer:

48:42

16:14

56:49

Step-by-step explanation:

I hope I made your day

the distance between between two distinct points on number line is always greater than zero?

true or flase,

Answers

The answer here is true. It is logically impossible to create a negative distance between two lines on a number line. Even using negative numbers, there would still be a distance between the two. This also applies to a microscopic difference. At the end of the day, there is still a difference.

A 3 lb bag of one brand of cat food costs $3.52. A 6 lb bag of another brand costs $6.80. Which brand is cheaper per pound?

Answers

A 6 lb bag of another brand

For this case what we should do is find the price per pound of each of the brands of cat food.
We have then:
Mark 1:
3 lb costs $ 3.52
P = (3.52) / (3) = 1.17 $ / lb
Mark 2:
6 lb costs $ 6.80
P = (6.80) / (6) = 1.13 $ / lb
Answer:
Mark 2 is cheaper per pound:
1.13 $ / lb

A scientist has 350 mg of a radioactive material. The material will cut in half every month. After how many months will there be .68mg left?

Answers

The answer would be about 9 months.

What is the inverse of f(x) = 8x - 7

Answers

y=(x+7)/8

Work:
Y=8x-7 —> x=8y-7
Solve for y
x+7=8y
y=(x+7)/8

Final answer:

The inverse of the function f(x) = 8x - 7 can be found by switching the x and y, then solving for y. This gives the inverse function as f^-1(x) = (x + 7) / 8.

Explanation:

The inverse of a function is calculated by switching the input and output variables. Given your question, we are to find the inverse of the function f(x) = 8x - 7. To do this, we first rename f(x) as y, giving us y = 8x - 7.

Next, we switch the positions of x and y, leading to x = 8y - 7. Then, to isolate y which represents the inverse function, we should solve the equation for y: x + 7 = 8y and y = (x + 7) / 8. So, the inverse of the function f(x) = 8x - 7 is f^-1(x) = (x + 7) / 8.

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Tropical forests are being lost at the rate of 5 million hectares per year. how many hectares per day is that? how many hectares per minute?

Answers

5,000,000/365= 13,698.630137 hectatres per day /1440 = 9.5129375951388..... hectares per minute

365 days in a year
1440 minutes in a day (24hrs)

1. _____is when an asset increases in value.
~depreciation
~appreciation
~inflation
~purchasing power

2. when money loses some of its value over time, it is caused by_____
-inflation
-FICA
-purchasing power
-recalculating worth
ive tried i need help @bibby @phi someone :( @SolomonZelman,

Answers

1) Appreciation is when an asset increases in value. The increase can happen for several reasons whether it is a decreased supply or an increased demand for example. 2) When money loses some of its value over time, it is caused by inflation

1) Appreciation is when an asset increases in value.

2) When money loses some of its value over time, it is caused by inflation

The appreciating assets is any asset which value is increasing it is a an increased demand.

Therefore,

When value of assets increases in value?

Appreciation

1) Appreciation is when an asset increases in value.

Next,

The impact inflation has on the time value of money is that decrease the value of dollar over time.

Therefore,

2) When money loses some of its value over time, it is caused by inflation

Therefore,

1) Appreciation is when an asset increases in value.

2) When money loses some of its value over time, it is caused by inflation

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Will give Metal! From 1948 to 1994, South Africa existed under a system of apartheid. Under this system, white South Africans- about 18% of the population- controlled all of the instruments of government: the Parliament, the Executive Branch, and the courts. Black and non-white South Africans had few legal rights and could not vote in elections. Voting was limited to white South African citizens. . This passage is describing what type of government? A) autocratic B) democratic C) dictatorship D) oligarchic,

Answers

Oligarchic An oligarchy is a small group of people having control of a country, organization, or institution. White South Africans were a very small percentage of the population, but had control over the entire government.

Your sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks. you reach into the drawer in the dark and randomly pick out 2 pairs for your business trip. what is the probability your pick out in this order. 2 black pairs?

Answers

All socks together: 13
Black socks: 3

Probability to pick out black socks: 3/13

After one pick out (You picked out a pair of black socks):

Probability to pick out black socks: 2/12

Multiply them:

2/12 * 3/13 = 1/26 ≈ 0,038

The probability your pick out in this order 2 black pairs 1/26.

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Mathematics to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory.

According to the question,

The sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks.

All socks together = 3+4+5 = 13

Black socks = 3

Probability to pick out black socks: 3/13

After one pick out (You picked out a pair of black socks),

Probability to pick out black socks: 2/12

Then, the probability = 2/12 × 3/13 = 1/26.

Hence the required probability = 2/12 × 3/13 = 1/26.

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mafaaaaaaaaaaaaaaaaaaaaa

Answers

Hey there!

Add [tex]2[/tex] each of your sides

Like:

[tex]-5 + 2 \leq n - 2 + 2 \leq 2 +2 \\ \\ -3 \leq n \leq 4 \\ \\ Answer: C. \\ \\ \\ Good \\luck \\ on \\ your \\ assignment \\ and \\ enjoy \\ your \\ day\\ \\ \\ \\ LoveYourselfFirst:)[/tex]

-5 ≤ n - 2 ≤ 2

-5 ≤ n - 2 AND n - 2 ≤ 2

-5 + 2 ≤ n
-3 ≤ n
n ≥ -3

n - 2 ≤ 2
n ≤ 2 + 2
n ≤ 4

So -3 ≤ n ≤ 4 (Third one)

Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest hundredth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank) (4 points)

Answers

do the volume of a circle then multiply by the length of the cylinder
area of a circle =
diameter/2 = radius
so 4^2 = 16 16*3.14 = 50.24
50.24*(4*3) = 50.24*12 = 602.88

A credit card advertises an annual interest rate of 23%.

What is the equivalent monthly interest rate?

i=__^_t

Answers

the monthly rate is:

[1 + 23%]^(1/12) =1.23^(1/12) =1.0174 - 1 x 100 =1.74%

Which statement below completes Anastasia's proof?

Answers

What are the Statements?

In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are congruent)

In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are parallel)

In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent)

In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are parallel)

are the statments

Help please, explain each step or no points.

Answers

The proportion pop/total = 5/7 is presumed to hold for the next 500 songs.

pop/500 = 5/7
pop = 500*5/7 ≈ 357

357 of the next 500 songs downloaded are expected to be pop songs.

what is 62% of 25 ?
im horrible at this plz help

Answers

To do this, multiply 62% by 25 !

Convert 62% into a decimal: 0.62. Then multiply them: 0.62 · 25, which equals 15.5 !

62% of 25

'of' means multiplication.

[tex]\sf 62\%\times 25[/tex]

Convert 62% to a decimal, divide it by 100(since percentages are parts of 100):

62/100 = 0.62

[tex]\sf 0.62\times 25[/tex]

Multiply:

[tex]\sf\boxed{\sf 15.5}[/tex]

Which of the following will typically offer the lowest interest rate?

A. Basic savings
B. Certificate of deposit
C. Savings bond
D. Money market savings
@countonme123 @sara17,

Answers

The lowest interest rate out of those options would be (A) Basic Savings Account. This is usually a liquid asset at banks that will not offer high interest. Next would be (D) Money Market, which is also offered mainly by banks. (B) and (C) are both safe investment options that will offer higher rates than normal bank accounts.

If mike drank more than half the juice inhis glass.what fraction of the juice could mike have drunk.

Answers

1/2 would be the answer for that question. Although- it might be wrong though. So if is, I apologize.

1. Let f(x)=8/1+3e^−0.7x. What is the value of f (−3)?
2. Let f(x)=20/1+9e^3x. What is the y-intercept of the graph of f(x)?
3. Let f(x)=24/1+3e^−1.3x. What are the asymptotes of the graph of f(x)?
4. Let f(x)=15/1+4e^−0.2x. What is the point of maximum growth rate for the logistic function f(x)?
5. Let f(x)=24/1+3e^−1.3x. Over what interval is the growth rate of the function decreasing?

Answers

Final answer:

This detailed answer covers evaluating functions at specified values, identifying the y-intercept of a function's graph, determining asymptotes, identifying points of maximum growth rate in logistic functions, and intervals where the function's growth rate is decreasing, all critical concepts in understanding mathematical functions in high school.

Explanation:

The questions provided are focused on evaluating specific values of functions, understanding the y-intercept of a graph, determining asymptotes, identifying points of maximum growth rate, and assessing intervals of decreasing growth rate for various exponential and logistic functions. Each of these concepts plays a crucial role in understanding the behaviors and characteristics of different types of mathematical functions, which are fundamental in high school mathematics.

To find f(-3) for the function f(x)=8/(1+3e^{-0.7x}), substitute x=-3 and evaluate.The y-intercept of a graph is found by evaluating the function at x=0.Asymptotes can be determined by evaluating the limits of the function as x approaches infinity or negative infinity.The point of maximum growth rate for a logistic function occurs at the point where the function's second derivative changes sign.The growth rate is decreasing over intervals where the second derivative of the function is negative.

HELP WITH THESE SERIES OF QUESTIONS!!
1. Factor the polynomial. 3x^3 − 27x^2 + 19

2. Factor the polynomial. 15z^3 + 25z^2

3. Factor the polynomial. 9x^7 + 33x^3

Answers

1. Simplified already
2. 5x^2 x (3x+5)
3. 3x^3 x (3x^4 +11)

Glamour runs 2/3 mile each day she wants to know how many days she has to run before she has run a whole number of miles

Answers

Hello!

2/3 × 1 = 2/3

2/3 × 2 = 4/3 (or 1 1/3)

2/3 × 3 = 2

You can also convert 2/3 to a decimal by dividing the numerator by the denominator and then multiply that to get a whole number.

ANSWER:

Glamour will have to run for 3 days to run a whole number of miles. The whole number is 2.

Answer ASAP

Find the area

Answers

In this problem, you are asked to find the area of the trapezoid. The formula in finding the area of the trapezoid is:

A = [(a + b)/2] x h

Where a = base 1

b = base 2

h = height

Substituting the given measurements to the formula:

A = [(1.7 m + 6.7 m) / 2] x 5 m

A = (8.4 m / 2) x 5 m

A = 4.2 m x 5 m

A = 21 m^2

Therefore, the area of the trapezoid is 21 square meters.

solve for X
This is 10th grade Geometery (USA)

Answers

You can set up proportions:
[tex] \frac{55}{35} = \frac{x}{42} [/tex]

Now you can cross multiply:
[tex]55(42) = 35x[/tex]

Solve for x:
[tex]x = \frac{55(42)}{35} = 66 [/tex]

So, x = 66.

An explosion causes debris to rise vertically with an initial velocity of 160 feet per second. What is the speed of debris when the height is 300 feet?

I am using the formula: -16t^2 + vot + h0 because the question is referring to feet.

Answers

The question is asking what v_final is, given that v_initial is at 300 feet. and v_initial is at 0 feet.
We know there will be a constant downward acceleration of 32.15 ft/s^2.
Use the following equation:
v_final^2 = v_initial^2 + 2ah
v_final^2 = (160 ft/s)^2 + 2(-32.15 ft/s^2)(300 ft) = 6310 ft^2/s^2
v_final = (6310 ft^2/s^2)^1/2 = 79.4 ft/s.

The speed of the debris is 79.4 ft/s

Calculation of the speed:

Since there is an initial velocity of 160 feet per second, height is 300feet

So, we applied the below formula

[tex]v_({final})^2 = v_({initial})^2 + 2ah\\\\ v_({fina})l^2 = (160 ft/s)^2 + 2(-32.15 ft/s^2)(300 ft)\\\\ = 6310 ft^2/s^2\\\\ = (6310 ft^2/s^2)^{1/2}\\\\ = 79.4 ft/s.[/tex]

Therefore, The speed of the debris is 79.4 ft/s

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