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)
Answers
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!
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
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:
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
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
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
CAN YOU BRAINLEST ME THANK YOU
HOPE IT HELPS YOU
Calculate the area of the shape below. Give your answer in cm².
Answers
Answer:
area of the shape below is
53cm^2
.......
ANSWER PLEASE !!!!!!
Answers
Answer:
B= 40 degress
Step-by-step explanation:
1x+ 5xc /3xc = 40
(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
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
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?
Class 6 MATHS is this correct?
Answers
Answer:
yes it is correct great job
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.
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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]
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).
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
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
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:
Jane paid $110 for an item at 40% off. What was the original price?
Answers
Answer:
$183.33
Step-by-step explanation:
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
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
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.
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
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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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
_
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
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
36/18= 0.5
Each piece= $0.50
Answer:
$0.50Step-by-step explanation:
Given
Cost price = $9Selling price of the cake is:
$9 + $9 = $18Selling price of each piece:
$18/36 = $0.50If 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 me solve questions 10 & 11 (WILL MARK BRAINLY)!!!!!!
Answers
Answer:
10 c 100 b 1000 D 8888 A 2337
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) = 72.5Arc measure is twice the intercepting angle, since the angle is not central:
mLN = 2*72.5 = 145If 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!
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