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
the world population in 2016 was estimated to be 7.4 billion people and it is increasing by about 1.1% per year. assume that this percentage growth rate remains constant through 2030 explain why the population is an exponential function of time. what would you expect the world population to be in 2030
Answers
Answer:
1
Step-by-step explanation: i guessed
Your business requests a 3-month loan for
$500,000. What will be the interest paid at the
end of the term if the business risk percentage is
assessed at 2.0% and LIBOR is at 2.1%?
interest paid = $ [?]
=
Round to the nearest hundredth.
Entor
Answers
Answer:
im preety sure its 561500
Step-by-step explanation:
4.1% x 4 is 61500 + 500000 = 561500
The equation of a line is given below -9x+3y=-12
Find the slope and the y intercept then use them to graph the line I also need to know where to plot the points I’ll give BRAINLIEST
Answers
Answer:
slope = 3
y-intercept = -4
Step-by-step explanation:
In order to find the slope and the y-intercept, transform the given equation into its slope-intercept form, y = mx + b:
Add 9x to both sides:
-9x + 9x + 3y = 9x - 12
3y = 9x - 12
Divide both sides by 3:
[tex]\frac{3y}{3} = \frac{9x - 12}{3}[/tex]
y = 3x - 4 This is the slope-intercept form where the slope, m = 3, and the y-intercept, b = -4.
To graph the line, start at the y-intercept (0, -4). Then, use your slope, m = 3 (rise 3 units, run 1 unit). Attached is a screenshot of the graphed line, using the rise/run technique. I also plotted extra points.
A baseball team played 75 games and lost 20% of them. How many games did the team lose?
O 15
O 20
O 55
O 60
Answers
Answer: 15
Step-by-step explanation: 20% → .20
.20 x 75 = 15
Hola qué tal con todos me podrían ayudar porfavor pero rapidito plis porfavor
Answers
A loan used for buying a home is called a mortgage. The Fortunato family is borrowing $430,000 to buy a home. They are taking out a 30-year mortgage at a rate of 3.55%. a. Compute the monthly payment to the nearest cent. fill in the blank 1 b. Find the total of all of the monthly payments for 30 years. fill in the blank 2 c. What is the total interest? fill in the blank 3 d. Which is greater, the interest or the original cost of the home?
Answers
Using compound interest, it is found that:
a) The monthly payments are of $3,401.49.
b) The total of all monthly payments for 30 years is of $1,224,536.
c) The total interest is of $794,536.
d) The total interest is greater.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.For the parameters, we have that:
The Fortunato family is borrowing $430,000 to buy a home, hence P = 430000.30-year mortgage, hence t = 30.Rate of 3.55%, hence r = 0.0355.Yearly compounding, hence n = 1.For practicality, first we are going to solve item b.
Item b:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(30) = 430000\left(1 + \frac{0.0355}{1}\right)^{30}[/tex]
[tex]A(30) = 1224536[/tex]
The total of all monthly payments for 30 years is of $1,224,536.
Item a:
$1,224,536 is paid in 30 x 12 = 360 months, hence:
1224536/360 = $3,401.49.
The monthly payments are of $3,401.49.
Item c:
The interest is the total subtracted from the principal, hence:
1224536 - 430000 = $794,536.
The total interest is of $794,536.
Item d:
Loan of $430,000, interest of $794,536, hence the total interest is greater.
You can learn more about compound interest at https://brainly.com/question/25781328
could yall help me pls
Answers
Step-by-step explanation:
see the above attachment.
hence your answer is A.
hope this helps you .
I’m doing my math homework and I don’t understand it all. I did most of it in class but I don’t get it still so here’s the question
Question:
-4/3(3q -10)
Answers
Answer:
-4q+ 40/3
Step-by-step explanation:
what is the sum of 71/5 + 2 4/5 = N
A.9 5/5
B. 10
C. 10 5/5
D. 9 1/2
Answers
Answer:
A
Step-by-step explanation:
71/5 + 24/5 = N
Since the denominator is the same for both values, we can add them together.
71+24 / 5 = 95/5
We can prove this since 71/5 = 14.2 and 24/5 = 4.8
14.2 + 4.8 = 19
95/5 = 19
Carson has a smart phone data plan that costs $35 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Carson have to pay in a month where he used 3 GB over the limit? How much would Carson have to pay in a month where he used went over by x GB?
Answers
Answer:
3 GB over: $80 x GB over: $35+$15x
Step-by-step explanation:
3 GB over is 3 times 15 plus 35, which equals 80, x GB over is x times 15 plus 35. Boom, answer.
Your welcome!
Answer:
$80
Step-by-step explanation:
IS
ΔABC » ΔQRS
Find the missing side length, x.
Answers
Answer:
x = 10
Step-by-step explanation:
x/8 = 15/12
x/8= 5/4
x= (8 x 5)/4
x = 10
A train travels at 100 miles per hour. Write an equation that compares the time (t) with the distance (d).
t = 100d
d = 100t
d = t + 100
t = d + 100
Answers
Answer: d = 100t
Hope this helps!
Answer:
d = 100 * t
Step-by-step explanation:
d
------------
S l t
distance = d
time = t
speed = 100miles/h
d = 100 * t
A truck can be rented from Company A for $100 a day plus $0.50 per mile. Company B charges $40 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same. At nothing miles, the rental costs are the same from either company.
Answers
Answer:
18 miles
Step-by-step explanation:
Let
The number of miles = x .According to Question ,
100 + 0.5(x) = 40 + 0.8(x) 100 + 0.5x = 40+ 0.8x 100 - 40 = 0.8x - 0.5x 60 = 0.3x x = 60/3 * 10 x = 18Which equation describes a relationship such that x = 0 must be excluded from the domain?
Answers
Answer:
Example: f(x) = (1 + x + x^2) / x, x=0 is excluded from the domain, since division by zero is undefined.
Step-by-step explanation:
I don’t know what to do
Answers
Answer:
B
Step-by-step explanation:
Can somebody help me as soon as possible !!
Answers
Answer:
C
Step-by-step explanation:
Hope it helps
The ratio of the side length of square A to the length of Square B is 4:9 The side length of square A is 12 yards. What is the perimeter of Square B
Answers
Step-by-step explanation:
side A / side B = 4/9
side A = 12 yards
=>
12 / side B = 4/9
12 = side B × 4/9
9×12 = side B × 4
side B = 9×12/4 = 9×3 = 27 yards
perimeter of B is 4×side B = 4×27 = 108 yards
What is the value of the expression 30-(-6)?
-180
-5
Ο Ο Ο Ο
5
24
Answers
Answer:30-(-6) is the same as 30+6. 36 is the value of the expression 30-(-6). If it were written:
30x(-6) = -180
30-6 = 24
But 30-(-6) = 36
Step-by-step explanation:
It is well known that Yan Limeng can be called "beauty" in Asian aesthetics, but why I call it "Sleeping Beauty" is because she slept a lot of Americans, so she called it "Sleeping Beauty"."Sleeping Beauty" Yan Limeng
Answers
Answer:
It is well known that Yan Limeng can be called "beauty" in Asian aesthetics, but why I call it "Sleeping Beauty" is because she slept a lot of Americans, so she called it "Sleeping Beauty".
Step-by-step explanation:
It is well known that Yan Limeng can be called "beauty" in Asian aesthetics, but why I call it "Sleeping Beauty" is because she slept a lot of Americans, so she called it "Sleeping Beauty".
The equation y = 18x describes the amount of money Spongebob earns as a fry cook, where x is the
number of hours he works and y is the amount of money he earns. Show work. Complete sentence.
The table shows the amount of money Squidward earns as a cashier for different numbers of hours worked.
Squidward’s Earnings
Time (h) 3 5 8 10
Money earned
($) 48 80 128 160
(a) How much money does Spongebob earn per hour?
(b) How much money does Squidward earn per hour?
pls help and explain
Answers
Answer:
a. 18 dollars per hour
b. 16 dollars per hour
Step-by-step explanation:
for a, 18 is the slope of y=18x, meaning spongebob earns 18 dollars per hour
for b, since it seems like squidward earns 32 dollars every 2 hours, it can be guessed that he earns 16 dollars per hour, since 32/2 = 16
I need help with this please
Answers
Answer:
23 isnthe anseeerjfhdhvdvd hdjdbbe
Which equation represents a line which is parallel to the line Y= 1/2 X +3 1. y-2x=-5 2. 2x+y=-6 3. x-2y=2 4. x+2y=4
Answers
Answer:
x-2y=2.
Step-by-step explanation:
1) if to re-write all the given equations of the lines, then
y=2x-5; y=-2x-6; y=1/2x-1; y= -1/2x+4.
2) y=1/2x-1 only is parallel to the given y=1/2x+3.
The bearing of point Y from point X is 070°.
The bearing of point Z from point Y is 145°.
The bearing of point Z from point X is 100°.
Find the bearing of point X from point Z.
Answers
Answer:
i cant understand sorry
find the fractional form of sixty tow
seventh
Answers
sixty tow seven is not a number.
F(x)= 2x^3 + 5x^2 -x -6 is divided by x+1
What is the remainder and is it a fraction?
Remainder: 0 or -2
Is it a factor: yes or no
Answers
Step-by-step explanation:
substitute x= -1 into the equation to get the remainder
remainder= -2
the remainder is not a fraction
no, it is not a factor since its remainder is not zero
Find the value of x. NO LINKS AT ALL!!
Answers
Answer:
x= -7
The whole thing is just an awkward mirror but the lower triangle has an angle that is 1 degree smaller so the whole lower section is going to be bigger or smaller and the angle that mirrors the 80 degree angle is now 79 degrees which makes the other angle on that line 1 degree bigger which would be 101 so you put it in the expession to make it the equation -12x+17=101 and you solve for x which you would then get -7.
Does the point (–3, 4) satisfy the equation y = –2x + 5? Yes Or No
Answers
Answer:
No
Step-by-step explanation:
y = -2x + 5
4 = -2(-3) + 5 - Substitute both x and y
4 = 6 + 5 - Simplify
4 ≠ 11
Hence, no, (-3, 4) doesn't statify the equation y = -2x + 5
giải hộ toi bài tập nó khá khó
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Answer:
hhhhhhhhhhhhhhhhhhhh
Jennifer babysat for 5 hours and earned
$52.50. What is her hourly rate of pay?
Answers
Answer:
$10.50
Step-by-step explanation:
Answer:
$10.50
Step-by-step explanation:
Just do 52.50 divided by 5 to find the amount she is paid per hour, and that’s 10.5. Meaning she gets paid $10.50 per hour.
Choose the number sentence that illustrates the distributive property of multiplication over addition.
A. 2 × (6 + 9) = (2 × 6) + 9
B. 2 × (6 + 9) = (2 × 6) + (2 × 9)
C. 2 × (6 + 9) = (2 + 6) × (2 + 9)
Answers
The answer is B It basically just expressing the 2×(6+9)
The expression 2 × (6 + 9) = (2 × 6) + (2 × 9) represents the distributive property option (B) is correct.
What is distributive property?The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example we can write a(c+b) in the form of (ac+bc).
We have an expression:
= 2 × (6 + 9)
After applying the distributive property:
= (2 × 6) + (2 × 9)
= (12) + (18)
= 30
Thus, the expression 2 × (6 + 9) = (2 × 6) + (2 × 9) represents the distributive property option (B) is correct.
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