Parallelogram BCDE with vertices B(2, -3), C(6,-4), D(7.-6), and E(3.-5):
a) 270° counterclockwise rotation about the point (1,-2)
b) translation along the vector (0,8)

Parallelogram BCDE With Vertices B(2, -3), C(6,-4), D(7.-6), And E(3.-5):a) 270 Counterclockwise Rotation

Answers

Answer 1
Rotation 270 counterclockwise about origin is easy, swap the x and y then reverse the sign of the y
so (x, y) rotates to (y, -x)
Sadly to change the centre we need to translate the centre to the origin, rotate and the translate back.
In this case that means adding -1, 2 to x,y respectively, rotating, adding 1, -2 to x,y respectively

B(2, 3) translates to (1, 5) which rotates to (5, -1) and translates back to B’(6, -3)
C(6, -4) translates to (5, -2) which rotates to (-2, -5) and translates back to C’(-1, -7)
D(7, -6) translates to (6, -4) which rotates to (-4, -6) and translates back to (-3, -8)
E(3, -5) translates to (2, -3) which rotates to (-3, -2) and translates back to (-2, -4)

The translation is much easier simply moving each point 8 to the right
B’(2, 11), C’(6, 4), D’(7, 2) and E’(3, 3)

Using the grid will everything clear!
Answer 2

a) After 270° counterclockwise rotation about the point (1,-2) the coordinates are B'(-1, -1), C'(-2, -5), D'(-4, -6) and E'(-3, -2).

b) After translation along the vector (0,8) are B''(2, 5), C''(6, 4), D''(7, 2) and  E''(3, 3).

Given that, parallelogram BCDE with vertices B(2, -3), C(6, -4), D(7, -6), and E(3, -5).

When rotating a point 270 degrees counterclockwise about the origin our point A(x, y) becomes A'(y,-x). This means, we switch x and y and make x negative.

a) 270° counterclockwise rotation about the point (1,-2)

So, the new coordinates are

B(2, -3)→(1, -1)

C(6, -4)→(5, -2)

D(7, -6)→(6, -4)

E(3, -5)→(2, -3)

After 270° counterclockwise rotation, we get coordinates as

B(1, -1)→B'(-1, -1)

C(5, -2)→C'(-2, -5)

D(6, -4)→D'(-4, -6)

E(2, -3)→E'(-3, -2)

b) Translation along the vector (0,8)

B(2, -3)→B''(2, 5)

C(6, -4)→C''(6, 4)

D(7, -6)→D''(7, 2)

E(3, -5)→E''(3, 3)

Therefore,

a) After 270° counterclockwise rotation about the point (1,-2) the coordinates are B'(-1, -1), C'(-2, -5), D'(-4, -6) and E'(-3, -2).

b) After translation along the vector (0,8) are B''(2, 5), C''(6, 4), D''(7, 2) and  E''(3, 3).

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Related Questions

You have at most $20 to spend at an arcade. Arcade games cost $0.75 each, and snacks cost $2.25 each. Write an inequality that represents the numbers of games (x )you can play and snacks( y) you can buy.
The inequality is ??

Answers

Answer:

y ≤ -1/3x+80/9

Step-by-step explanation:

(1). 0.75(x)+2.25(y) ≤ 20

0.75 - Number of arcade games (X).

2.25 - Number of snacks (Y).

20 - The total.

(2). 0.75x+2.25y≤20

(After multiplying the x's and y's together, with the numbers).  

(3). 0.75x (-0.75x) + 2.25y ≤ 20 (-0.75x)

(Subtract -0.75x to each side, which allows the equation to get closer to the answer).

(4). 2.25y       -0.75x + 20

   ————   =   ————

    2.25            2.25

(Divide by 2.25 to each side).

(5). y ≤ -1/3x + 80/9

(The result and the inequality).

HELPPPPP I NEEED TO GET A GOOD GRADE OR I'M BUSTEDDDDDDDD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

(MATH)

I WILL GIVE BRAINILEST! PIC DOWN BELOW!!

Answers

Answer:

D) -31

Step-by-step explanation:

use PEMDAS

3^2-(5 x 2^3)

3^2-(5 x 8)

3^2-40

9-40

-31


Brandon is offered two jobs. One has a starting salary of $32,000 plus a raise of $1,000 every year. The other offers a starting salary of $28,000 plus a raise of $1,800
when the two jobs will have the same salary?

Answers

The difference in starting pay:

32,000 - 28,000 = 4,000

The difference in raises:

1,800 -1,000 = 800

Number of years to be the same:

4,000 / 800 = 5

Answer 5 years

Two or more expressions with an Equal sign is called as Equation. After 5 years the two jobs will have the same salary

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that,

Brandon is offered two jobs. One has a starting salary of $32,000 plus a raise of $1,000 every year.

The other offers a starting salary of $28,000 plus a raise of $1,800.

The difference in starting pay:

Thirty two thousand minus twenty eight thousand equal to four thousand.

32,000 - 28,000 = 4,000

The difference in raises:

Eighteen thousand minus thousand equal to eight hundred.

1,800 -1,000 = 800

Number of years to be the same:

4,000 / 800 = 5

Hence after 5 years the two jobs will have the same salary.

To learn more on Equations:

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Please help me solve questions 10 & 11 (WILL MARK BRAINLY)!!!!!!

Answers

Answer:

10 c 100 b 1000 D 8888 A 2337

Also if I can I give brainiest answer to first person


10. A stockbroker charges his customers $30 to open an account and
$15 per month to manage the account. Write an equation to represent the
number of months, n, an account has been open if the total cost is $360.





Answers

Answer:

the answer is 22

the equation is 30 + 15n

Step-by-step explanation:

15n as it increases each month and 30 as it never changes and will always be a value of 30

Answer:

15n+30=360

Step-by-step explanation:

$15 per month is being charged

The flat fee is $30

The Total cost is 360

15n+30=360

Given matrices A and B shown below, find (3)A+(8)B.

Answers

Answer:

[tex]\left[\begin{array}{ccc}32&-55\\3&39\end{array}\right][/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}0&-15\\3&15\end{array}\right] +\left[\begin{array}{ccc}32&-40\\0&24\end{array}\right] =\left[\begin{array}{ccc}0+32&-15+(-40)\\3+0&15+24\end{array}\right] = \left[\begin{array}{ccc}32&-55\\3&39\end{array}\right][/tex]

o
Addison is considering two sales jobs. She
estimates her total monthly sales will average $18,000. Which job should Addison take if she wants to earn more money each month? How much more will she earn?

A commission of 24% of her total
monthly sales.

Salary of $4,000 with a commission of 12.25% on her total monthly sales
over $14,500.


Answers

Answer: job 2     $ 108.75

Step-by-step explanation:

The total income after adding commission will be $5776.25.

What is an expression?

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that salary of $4,000 with a commission of 12.25% on her total monthly sales of over $14,500.

Total income will be calculated as:-

Total income = 4000 + 12.25% of 14500

Total income = 4000 + 1776.25

Total income = $5776.25

Therefore, the total income after adding the commission will be $5776.25.

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Solve for the values of x for each of the following exponential equations and inequalities.
1. 82− = 2
3. 5 = 25−2
4. 3+2 ≥ 27
5. 43 = 8−1

Answers

Answer:

8

2−x

=2

8^{2-x}=8^{1/3}8

2−x

=8

1/3

2-x=\dfrac{1}{3}2−x=

3

1

x=\dfrac{5}{3}x=

3

5

2.

(\dfrac{1}{2})^{x}<\dfrac{1}{8}(

2

1

)

x

<

8

1

(\dfrac{1}{2})^{x}<(\dfrac{1}{2})^{3}(

2

1

)

x

<(

2

1

)

3

x>3x>3

3.

5^x=25^{x-2}5

x

=25

x−2

25^{x/2}=25^{x-2}25

x/2

=25

x−2

\dfrac{x}{2}=x-2

2

x

=x−2

\dfrac{x}{2}=2

2

x

=2

x=4x=4

4.

3^{x+2}\geq273

x+2

≥27

3^{x+2}\geq3^33

x+2

≥3

3

x+2\geq3x+2≥3

x\geq1x≥1

5.

4^{3x}=8^{x-1}4

3x

=8

x−1

2^{6x}=2^{3x-3}2

6x

=2

3x−3

6x=3x-36x=3x−3

3x=-33x=−3

x=-1x=−1

Step-by-step explanation:

If 400 kids went to the amusement park and only 120 came back how many got lost?

Answers

Answer:

280

Step-by-step explanation:

400 - 120=280

280= number of children lost

Please help!!!
I need help finding the answer.

Answers

Answer:

2nd option

Step-by-step explanation:

The shaded area = outside area - inner area

                           = x² - (x - 6)² ← expand using FOIL

                         = x² - (x² - 12x + 36) ← distribute parenthesis by - 1

                        = x² - x² + 12x - 36 ← collect like terms

                        = 12x - 36

In Canada, 92% of the households have televisions.
72% of households have televisions and internet access.
5% have neither. Use appropriate probability notation to answer the following:

A) create a relative frequency table of this situation.

Answers

Answer: Let "T" denote households with television

"I" denote households with internet

and "N" denote households with neither of these.

Since P(N) = 0.05 then it means P(TuI) = 0.95. We know from set theory that P(TuI) = P(T) + P(I) - P(TnI). Thus,

0.95 = 0.92 + 0.72 - P(TnI) ==> P(TnI) = 0.69. This means P(T/I) = P(T) - P(TnI) = 0.92 - 0.69 = 0.23, and P(I/T) = P(I) - P(TnI) = 0.72 - 0.69 = 0.03. So,

a)

House                 Probability

Nothing                0.05

Only television      0.23

Only internet         0.03

Both                   0.69

b) P(internet but no television) = P(only internet) = 0.03

c) P(internet | there is television) = (By Bayes' Rule) P(TnI) / P(T) = 0.69 / 0.95 = 0.726 (rounded to 3 decimal points)

d) P(internet | there is no television) = (By Bayes' Rule) P(I/T) / P(T') = 0.03 / 0.08 = 0.375

e) From (c) and (d) ==> In Canada, it is (0.726/0.375 ≈ 2 ) twice more likely that if there's television in the household, then there is internet.

Step-by-step explanation:

If a bag contains 16 red, 4 yellow, 20 blue, and eight white balloons, what is the part to whole ratio of red balloons to all balloons?

Answers

Answer:  1:3

Step-by-step explanation:

(add) 16 + 4 + 20, + 8 = 48.

Then simplify 16:48 = 2:6 = 1:3

Hope this helped, have a great day/night!

~IFoundJiminsLostJams~

(Pre calc) I only need to do part A i would love to have some help I will make it 120 Points

Answers

Answer:

The domain should be X

Step-by-step explanation:

I'm a bit unsure but I think it's correct

Cho các tập hợp
A =( x∈R|x²-5x+4≤0)
B= (x∈R|x-1|≤1)
C=(x∈R|x²-7x+6≤0)
xác định: (A∪B)∩C
(A∩B)∪C

Answers

ANSWER:

B.

CAN YOU BRAINLEST ME THANK YOU

HOPE IT HELPS YOU

_
Write 0.34 as a fraction using the steps below.

Answers

Answer:

31/90

Step-by-step explanation:

3.1 x 10 = 31 which is the numerator

9x10 = 90 which would be the denominator

Answer:

It would be 17/50 hope that helps

In a circle L, M, N are the points on the circle forming a triangle with LM = LN and mZMLN is 35' then what is m(arc LN)?​

Answers

Answer:

145°

Step-by-step explanation:

ΔLMN is isosceles with angle L being 35°.

Angle  measure of M and N is same:

m∠M = m∠N = 1/2(180 - 35) = 72.5

Arc measure is twice the intercepting angle, since the angle is not central:

mLN = 2*72.5 = 145

ANSWER PLEASE !!!!!!

Answers

Answer:

B= 40 degress

Step-by-step explanation:

1x+ 5xc /3xc = 40

Class 6 MATHS is this correct? ​

Answers

Answer:

yes it is correct great job

Find the distance from point A(15,−21) to the line 5x+2y = 4 . Round your answer to the nearest tenth.

Answers

Answer:

5.4 units

Step-by-step explanation:

5x + 2y - 4 = 0 and (15, - 21)

d = |(A*Px)+(B*Py)+C| / (sqrt A^ + B^2)

A=5, B=2, C= - 4 and Px=15, Py= -21

d =|(5*15)+(2*-21)+ -4| / (5^2 + 2^2)

= |75-42-4| / sqrt 29

= 29/sqrt 29 = 5.4

pls help i’m so confused

Answers

Answer:

I think your answer is i

Step-by-step explanation:

The rotational symmetry would be letters i

The letter with rotational symmetry is i

Jane paid $110 for an item at 40% off. What was the original price?

Answers

Answer:

$183.33

Step-by-step explanation:

The cost of making a cake is $9. The Baker wants to make a profit of $ 9 per cake and the cake is to be cut into 36 pieces, what is the selling price of each piece?

Answers

$9+$9=$18
36/18= 0.5
Each piece= $0.50

Answer:

$0.50

Step-by-step explanation:

Given

Cost price = $9

Selling price of the cake is:

$9 + $9 = $18

Selling price of each piece:

$18/36 = $0.50

Solve for c.

-2.2 - 0.1c = -1.9

Answer: c = _____

Answers

Answer:

c = -3

Step-by-step explanation:

-2.2 - 0.1c = -1.9

-0.1c = 0.3

c = -3

Hopefully this helps!

Brainliest please?

For this function: f(x)=I-3x-1I
find each of the following:
a. f(-1)
b. f(0)
c. f(3)

Answers

Step-by-step explanation:

a. f(-1)=(3-1)

=2

b.f(0)=(0-1)

=-1

c.f(3)=(-9-1)

=-10

What will NEVER change?
In a sequence of translations, reflections, and rotations,
what will NEVER change from the pre-image to the
image?
(Select all that apply)
The lengths of the line segments.
T
The position of the object.
The measures of the angles.
The orientation of the object.

Answers

Answer:

Step-by-step explanation:

the lengths of the line segments

Select the correct answer.
An archway is modeled by the equation y = -2x2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?

A.
8 units

B.
6 units

C.
5 units

D.
3 units

Answers

Answer:

D. 3 units

Step-by-step explanation:

after you add you get a another number you make a another unit and get your answer or you can get the answer of the another number and add it to together.

that what I think it is

PLEASE HELP ME ITS ALGEBRA THANK YOUUUU

Answers

Answer: 2,208$

Step-by-step explanation:

To solve this problem, simply determine how much each attendee costs by doing 960$/30attendees = 32$/attendee.  Then, simply multiply this number by 69 to get: 2,208$

Hope it helps :) and let me know if you want me to elaborate further.

What is one of the distinctions between a population parameter and a sample statis- tic? A. A sample statistic changes each time you try to measure it, but a population parameter remains xed. B. A population parameter changes each time you try to measure it, but a sample statistic remains xed across samples. C. The true value of a sample statistic can never be known but the true value of a population parameter can be known. D. A population parameter is only based on conceptual measurements, but a sam- ple statistic is based on a combination of real and conceptual measurements.

Answers

Answer:

jaiana jsijejeren8sninsun9nsuns

Calculate the area of the shape below. Give your answer in cm².​

Answers

Answer:

area of the shape below is

53cm^2

.......

Write the equation of the line , in slope - intercept form , with following information : rate of change: -1 point : (3, - 3)

Answers

Answer:

y = -x

Step-by-step explanation:

Slope-intercept form looks like this: y = mx + b, with m being the slope or rate of change and b being the y-intercept. We already know the rate of change, so we can put -1 as m: y = -1x + b. To find our y-intercept, we can plug the point (3, -3) into the equation and solve for b:

-3 = -1(3) + b

-3 = -3 + b

b = 0

So we have y = -1x + 0. This can be simplified to y = -x.

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