Graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7). Use the Polygon tool to graph the quadrilateral by connecting all its vertices.

Answers

Answer 1

Answer:

Here's what I get.

Step-by-step explanation:

Assume the figure is like Image 1  below.

We must dilate each point by a scale factor of 3 centred at (2, −7).

1. Determine the transformation rules

Each point moves to three times its original distance from the centre.

Let P = a point on the figure and

let O = the centre of dilation

and L = the distance from the point to the centre. Then

L = P - O

Three times that distance is  

3L = 3P - 3O

We want to find the point P' that is 3L from O, so we add this distance to the coordinates of O.

P' = 3L + O = 3P - 3O + O = 3P + 2O

If P is at (x,y) and O is at (h,k), the transformation rule is

(x,y) ⟶ (3x - 2h, 3y - 2k)

2. Make a table of the new coordinates

[tex]\begin{array}{cclc}\textbf{Point} & \mathbf{(x,y)} &\textbf{Image Coordinates } \mathbf{(3x - 2h, 3y - 2k)}&\mathbf{(x',y')} \\A & (-2,-7) & (-6,-21) -2(2,-7) = (-6 - 4, -21 + 14) & (-10,-7) \\B & (0,-4) & (0,-12) -2(2,-7) = (0 - 4, -12 + 14)& (-4,2) \\C & (3,-3) & (9,-9) -2(2,-7) = (9 - 4, -9 + 14) & (5,5) \\D & (4,-5) & (12,-15) -2(2,-7) = (12 - 4, -15 +14) & (8,-1) \\\end{array}[/tex]

3. Graph the new shape

You should get a graph like Fig. 2.

The rays from Point O pass through corresponding points in the two shapes, so this is a dilation about O.

Point B is two units left of O and three units up.

Also, B' is six units left and nine units up, so the scale factor is three.

 

Graph The Image Of The Figure After A Dilation With A Scale Factor Of 3 Centered At (2,7). Use The Polygon
Graph The Image Of The Figure After A Dilation With A Scale Factor Of 3 Centered At (2,7). Use The Polygon

Related Questions

i need 29 part b and c please help!

Answers

Answer:

$1.50

Step-by-step explanation:

29 part c

3÷2= 1.50

3 is the cost

and 2 is the cups

for 3 drinks it would cost $1.50

For the graph, what is a reasonable constraint so that the function is at least 300?
(Graph Below)

A) x ≥ 0

B) −5 ≤ x ≤ 30

C) 0 ≤ x ≤ 25

D) All real numbers

Answers

Answer:

C) 0 ≤ x ≤ 25

Step-by-step explanation:

We are supposed to find a reasonable constraint so that the function is at least 300 i.e. the value of x at which f(x) is greater or equal to 300

A)x ≥ 0

Refer the graph

At x = 0

f(x)=300

On increasing the value of x , f(x) increases but at x = 12 it starts decreasing

So, x ≥ 0 can also have f(x)<300

So, Option A is wrong

B)−5 ≤ x ≤ 30

At x = -5

f(x) = 100

So, Option B is wrong since we require f(x) is greater or equal to 300

c)0 ≤ x ≤ 25

At x = 0

f(x)=300

At x = 12 , it starts decreasing

At x = 25

f(x)=300

So, The value of f(x) is at least 300 when 0 ≤ x ≤ 25

D)All real numbers

At x = 30

f(x)=0

But we require f(x) greater or equal to 300

Hence Option C is true

Answer:

C) 0 ≤ x ≤ 25

Its correct! Hope this helps :)

What is the acceleration of a toy rocket that accelerates from 10.0 m/s to 30.0
m/s in 15.0 m?

Answers

Answer:

26.67m/s²

Step-by-step explanation:

From the question we are given

Final velocity = 30m/s = v

Initial velocity = 10m/s = u

We were not given time but we were given distance = 15m

Therefore we would be using the formula:

Acceleration = v² - u²/ 2s

Where S = distance

v = final velocity

u = initial velocity

Acceleration (a) = 30² - 10²/ 2 × 15

a = 900 - 100/ 30

a = 200/30

a = 26.666666667m/s²

a = 26.67m/s²


6) A passenger train has tickets available for 12 window seats and 8 aisle seats. The next person to buy a ticket will be randomly assigned to one of those seats. What is the probability that the next person will be assigned to an aisle seat?

11) At a store, customers are randomly selected to participate in a survey. On Friday, there were 500 customers at the store. Of those, 90 were selected to participate in the survey. On Saturday, the store manager expects 700 customers in the store. If the probability of being selected to participate in the survey on Saturday is the same as it was on Friday, how many customers will be selected to participate in the survey on Saturday?
13) An owner of a small store knows that in the last week 54 customers paid with cash, 42 paid with a debit card, and 153 paid with a credit card. Based on the number of customers from last week, explain in words why 15 is closest to the probability that the next customer will pay cash.
14) A store owner made a list of the number of greeting cards sold last month. The store sold 167 thank-you cards, 285 birthday cards, and 56 blank cards. Based on these data, write a decimal, rounded to the tenths place to show the probability that the next customer will buy a blank card.

Answers

The answer to number 6 is 2/5

square root of x²-6x+9 if x is greater than or equal 3​

Answers

Answer:

x-3

Step-by-step explanation:

x²-6x+9 is equal to (x-3)²

The square root of any term that is positive is equal to the absolute value of the term. If x is greater or equal to 3, it makes the term positive.

So the root of x²-6x+9 is x-3  

A pair of shoes usually sells for $65. If the shoes are 30% off, and sales tax is 6%, what is the total price of the shoes, including tax?
A. $44.79
B.
$49.40
C
$51.68
D
$48.23

Answers

Answer:

Step-by-step explanation:

Since 20% is taken off, 100%-20% or 80% remains.

80% of $65 is 0.80�$65 or $52.  That's the price without tax.  

The tax on $52 is 0.06�$52 or $3.12,

$52 + $3.12 = $55.12

Answer:

d

Step-by-step explanation:

Alex measured the rainfall on his property to be 10.5 cm in June which he calculated to be a 35% increase compared to the previous month. how much had it rained in may explain the steps you took to turn in the solution

Answers

Answer: 3.675 cm

Step-by-step explanation:

June was 35% more compared to May

35% of 10.5 cm = 3.675 cm in May

Maria has a jewelry box and wants to increase its size. She decides she will double the length, width and height. How many times
bigger will the volume of the new box be?
2
3
5
8

Answers

Answer:

64 times bigger

Step-by-step explanation:

I will use random values for this explanation to make it more understandable.

Lets say the length of the box is 1 inch, width is 1 inch, and height is 1 inch.

The volume would be l*w*h = 1*1*1 = 1 cubic inch

If the dimensions were 4 times bigger, the length, width and height would all be 4 inches.

4*4*4 = 64 cubic inches, which is 64 times bigger than the smaller box with a volume of 1 cubic inch.

Hope this answer helped! :)

Step-by-step explanation:

Classify the triangle by its angles and by its sides


Right isosceles
Acute scalene
Acute isosceles
Obtuse isosceles

Answers

Answer:

Acute isoceles

Step-by-step explanation:

Two base angles of the triangle are equal making it isosceles

The top angle is less than 90° making it an acute angle

A) work out (8 x 10^-3) x (2 x 10^-4). Give your answer in standard form.
B) work out (6 x 10^2) ÷ (3 x 10^-5). Give your answer in standard form.​

Answers

Step-by-step explanation:

[tex]A) \\ (8 \times {10}^{ - 3} ) \times (2 \times {10}^{ - 4} ) \\ = 8 \times 2 \times {10}^{ - 3} \times {10}^{ - 4} \\ = 16 \times {10}^{ - 3 - 4} \\ = 16 \times {10}^{ - 7} \\ = 1.6 \times {10}^{ - 6} \\ \\ B) \\ (6 \times {10}^{ 2} ) \div (3\times {10}^{ - 5} ) \\ \\ = \frac{6 \times {10}^{ 2}}{3\times {10}^{ - 5}} \\ \\ = \frac{2\times {10}^{ 2}}{ {10}^{ - 5}} \\ \\ = 2 \times {10}^{ 2 + 5} \\ \\ = 2 \times {10}^{7} \\ [/tex]

The shadow cast by a television tower is 171 ft 10 in. A pole that is stuck in the ground nearby has 2 ft sticking above the ground and casts a shadow that is 6 ft 3 in. in length. Based on this information, how high is the television tower?

Answers

Answer:

the height is 54.99 ft or 659.84 in

Step-by-step explanation:

We know that the sides of similar triangles are proportional, so we can write:

2 ft / 6 ft 3 in = x / 171 ft 10 in

Now what we must do first and pass everything to the same unit of measurement:

Knowing that 1 foot equals 12 inches:

6 ft 3 in = 6 ft * 12 in / ft + 3 in = 72 + 3 = 75 in

171 ft 10 in = 171 ft * 12 in / ft + 10 in = 2052 + 10 = 2062 in

2 ft = 2 ft * 12 in / ft = 24 in

replacing:

24 in / 75 in = x / 2062 in

x = 24 * 2062/75

x = 659.84 in

Or they would also be 659.84 in * 1 ft / 12 in = 54.99 ft

That is, the height is 54.99 ft or 659.84 in

a toy car can go 3 mph. How long would it take to go 4 mph

Answers

Answer:

1 hour

Step-by-step explanation:

mph means miles per hour so in 1 mile it would be 1 hour

Sara is moving into a new apartment. The Resort complex charges a $600 security
deposit and costs $950 a month for rent. The Uptown Suites Duplex charges a $300
security deposit and costs $1100 a month for rent. After how many months would the
apartments cost the same amount? Which apartment would you recommend Sara move
to if she plans on staying for 6 months? Please show work!

Answers

Answer:

1) 2 months

Step-by-step explanation:

y = 950x + 600

y = 1100x + 300

950x + 600 = 1100x + 300

-950x -950x

____________________ subtract slope from both sides

600 = 150x + 300 ( doesn't matter which one)

-300 - 300

____________________ subtract

300 = 150x

_________ Divide each # with the slope

150 = 150

2 = x

____________Answer 2_____________

Answer:

The Resort Complex would save you 300.

step-by-step solution:

you have to do is plug in the number of months.

then multiply

then subtract both Complexes

and compare

The Resort Complex. : y = 950(6) + 600 - 6300

The uptown suite duplex : y = 1100(6) + 300 - 6900

HOPE THIS HELPS!

what is the quotient of 3 and y? Is it 3 over y or y over 3?

Answers

Answer:

it is 3/y.

Step-by-step explanation:

the answer is 3/y because 3 comes before y in the question.

Can someone please help with this math problem I'd really appreciate it.

Answers

Answer:

[tex]\mathrm{F}[/tex]

Step-by-step explanation:

[tex]y+8=4(x-5)[/tex]

[tex]x=5\\y=-8[/tex]

[tex](-8)+8=4((5)-5)[/tex]

[tex](-8)+8=4(0)[/tex]

[tex]0=0[/tex]

Integers and polynomials are both _[blank 1]_ under addition, subtraction, and multiplication; however, operations on polynomials _[blank 2]_ while operations on integers _[blank 3]_.

Answers

Answer:

Integers and polynomials are both closed under addition, subtraction, and multiplication; however, operations on polynomials can sometimes be open while operations on integers produce irrational results .

Step-by-step explanation:

Closed means that addition, subtraction, and multiplication of integers gives as result a new integer; and addition, subtraction, and multiplication of polynomials gives as result a new polynomial.

Operations on polynomials can sometimes be open, like in division.

Operations on integers can produce irrational results , for example, dividing 11 by 9.

Jesse had $421.56 dollars in his checking account
when he deposited g twenty-dollar bills and k quarters
Write an expression that represents the amount of
money in his account after his deposit.

Answers

Answer:

An expression that represents the amount of  money in his account after his deposit is [tex]421.56+20g+0.25k[/tex]

Step-by-step explanation:

Jesse had $421.56 dollars in his checking account

Now he deposited g twenty-dollar bills

Now new amount =$421.56+20g

Now he deposited k quarters

1 quarter = 0.25

k quarters = 0.25k

So, Amount in the account = 421.56+20g+0.25k

Hence an expression that represents the amount of  money in his account after his deposit is [tex]421.56+20g+0.25k[/tex]

1 | 4
2| 8
3| 12
4| 16
Write a function rule for the table.
A. S=40
B. c=4s
C. s=c+ 4
D. C= 4+ S​

Answers

b. c=4s

you multiply x times 4 to get y


Solve this equation: 3x –1/5- 2/9x= 124/5
Step 1: Simplify by combining like terms. Which terms can
be combined?​

Answers

Answer:

x = 9

Step-by-step explanation:

Given

3x - [tex]\frac{1}{5}[/tex] - [tex]\frac{2}{9}[/tex] x = [tex]\frac{124}{5}[/tex] ( add [tex]\frac{1}{5}[/tex] to both sides

3x - [tex]\frac{2}{9}[/tex] x = [tex]\frac{124}{5}[/tex] + [tex]\frac{1}{5}[/tex] = [tex]\frac{125}{5}[/tex] = 25 ← combine x- terms on left side

[tex]\frac{25}{9}[/tex] x = 25 ( multiply both sides by 9 )

25x = 225 ( divide both sides by 25 )

x = 9

Show and explain why 6 is not a solution to the inequality below.
2x - 9 ≥ 5

Answers

Answer:

x ≥ 7

Step-by-step explanation:

2x -9 ≥  5

          +9

      x ≥  14

           14/2

             =7

        x ≥ 7

PLEASE HELP A boat is carrying containers that weigh 1000 pounds each. Use this information to fill in the table. Then plot the ordered pairs given by the table.

Answers

Answer:

For the table, the answers are 2000, 4000, 7000. for the graph the plots will be at (2,2000) (4,4000) (7,7000)

Step-by-step explanation:

A boat is carrying containers that weigh 1000 pounds each.

For the table

2 x 1000 = 2000

4 x 1000 = 4000

7 x 1000 = 7000

For the graph

2, 4, and 7 are given as your X  axis points. You will then raise those answers to your corresponding answers for the table. so your Y axis points will be 2000, 4000, and 7000.

Mind helping me out a bit? (Which of the rectangular boxes shown has the greater volume?) (Will give Brainliest if you are the first person, and IF YOUR CORRECT) ^.^

Answers

Answer:

Both are equal in volume

Select the correct solution in each column of the table.
Solve the following equation.
18
12 + 6s
Examine the given table, and select the accurate number of each type of solution, as well as any real solutions that exist.
Number of
Real Solutions
Number of
Extraneous
Solutions
Real Solutions
0
0
x = 0
1
1
x= 3
2
x = 0, x= 3
N

Answers

Answer:

Number of  Real Solutions = 1

Number of  Extraneous Solutions = 1

Real Solutions = (x = 3)

Which of the following is equivalent to 0.0009?
A 0.0009%
B 0.009%
C 0.09%
D 0.9%

Answers

Answer:

C

Step-by-step explanation:

If you multiply by 100 u get C

Answer:

C

Step-by-step explanation:

To turn a number into a percentage, you must multiple it by 100.

Describe the solutions of 6+y<10 in words.
The value of y is a number less than 4.
The value of y is a number equal to 3.
The value of y is a number less than or equal to 3.
The value of y is a number greater than 4.​

Answers

The value of y is a number equal to 3

Chris deposited $445 in an account that earns 3.4% compounded annually. Find the balance in his account after 6 years.

Answers

Answer:

$535.78

Step-by-step explanation:

First find out the annual earnings. So multiply 3.4% by 445

0.034 x 445 = 15.13

That's what the account earns every year. Now multiply it by 6 to know what it'll get in 6 years.

15.13 x 6 = 90.78

Now add that to the initial value.

90.78 + 445 = 535.78

That's the balance in the account after 6 years...

$535.78

The sum of three numbers is 10. The first number minus the second plus the third is 6. The first minus the third is 2 more than the second. Find the numbers.

Answers

Answer:

The answers are :

The first number : 6

The second number : 2

The third number : 2

Step-by-step explanation:

The value of the variable x, y, and z will be 6, 2, and 2.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Let the numbers be x, y, and z.

The sum of three numbers is 10.

x + y + z = 10   …1

The first number minus the second plus the third is 6.

x – y + z = 6   …2

The first minus the third is 2 more than the second.

x – y = z + 2   …3

Add equation 1 and 3, we have

x + x + z = 10 + z + 2

         2x = 12

           x = 6

Subtract equation 2 from 1, we have

2y = 4

  y = 2

Then the value of z will be

6 + 2 + z = 10

            z = 2

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ2

plz do both ill mark u brainliest

Answers

Answer:

1. C

2. A

Step-by-step explanation:

Hope these are right!

Answer:

Question 16's answer is choice B. divide both sides by 6

Step-by-step explanation:

6a=27

You need to get the variable by it's self so you need to divide both sides by 6 because the 'a' is being multiplied by 6 on the left side.

Answer:

Question 25's answer choice is B. 5

Step-by-step explanation:

1 3/4 + 5/6 =

7/4 + 5/6 =

21/12 + 10/12 = 31/12 = 2 7/12 = round to nearest whole number 3 so about three pizzas were eaten! so subtract 3 from 8 to get 5 pizzas left! :)

Good luck! Have a great day! Hope this helps!

(SHORT ANSWER IS BOTH QUESTIONS ARE B) LOL! ;)

A survey of 50 people found that 14 people like building a snowman. If 600 people had responded, how many would have been expected to list building a snowman as their favorite winter activity?

theoretical or experimental probability, and why

Answers

Answer:

168, a little of both

Step-by-step explanation:

Make 14 out of 50, 14/50 simplified its 7/25, multiply it by 600 and you get 168 its a little of both because half the info we were given its experimental since it is not theorized, what we're being given (the question) and what we gave is theorized since we didn't actually perform an experiment to get a real answer

A survey of 50people

Which graph represents the function f(x) = log10(x) − 2? (1 point) logarithmic function passing through point 3, 0. logarithmic function passing through point negative 1, 0. logarithmic function passing through point 1, 2. logarithmic function passing through point 1, negative 2.

Answers

Answer:

logarithmic function passing through point 1, -2.

Step-by-step explanation:

f(x) = log10(x) - 2

Option: logarithmic function passing through point 3, 0 is incorrect because:

f(3) = log10(3) - 2 ≈ -1.5

Option: logarithmic function passing through point -1, 0 is incorrect because log10 is not defined for x < 0

Option: logarithmic function passing through point 1, 2 is incorrect because:

f(1) = log10(1) - 2 = -2

which means that option: logarithmic function passing through point 1, -2 is correct.

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