parallelogram ABCD with vertices A(6,8) B(10,9) C(9,3) and D(5,2): 90 counterclockwise rotation about P(4,1)
A ( , )
B ( , )
C ( , )
D ( , )
Answers
Answer:
A(-3 , 3) B(-4 , 7) C(2 , 6) D(3 , 2)
Step-by-step explanation:
Rotation of the parallelogram about the point P(4, 1), is done by taking
point P as the origin, and using relative coordinates for the rotation.
[tex]\underline{A(-3, \, 3)}[/tex][tex]\underline{B(-4, \, 7)}[/tex][tex]\underline{C(2, \, 6)}[/tex][tex]\underline{D(3, \, 2)}[/tex]Reasons:
The given parameters are;
Vertices of the parallelogram ABCD are;
A(6, 8), B(10, 9), C(9, 3) and D(5, 2)
Point about the parallelogram is rotated = P(4, 1)
Angle of rotation = 90°
Direction of rotation = Counterclockwise
90° rotation counterclockwise of (x, y) about the origin gives → (-y, x)
Therefore, we have;
The given points relative to the point P are;
A'(6-4, 8 - 1) = A'(2, 7)
B'(10 - 4, 9 - 1) = B'(6, 8)
C'(9 - 4, 3 - 1) = C'(5, 2)
D'(5 - 4, 2 - 1) = D'(1, 1)
Therefore, we get;
A'(2, 7) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] A''(-7, 2)
B'(6, 8) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] B''(-8, 6)
C'(5, 2) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] C''(-2, 5)
D'(1, 1) [tex]\underrightarrow {R_{180^{\circ}}}[/tex] D''(-1, 1)
Which then gives;
The image location are;
A(-7 + 4, 2 + 1) = A(-3, 3)
B''(-8 + 4, 6 + 1) = B(-4, 7)
C''(-2 + 4, 5 + 1) = C(2, 6)
D''(-1 + 4, 1 + 1) = D(3, 2)
Therefore, we have;
A(-3, 3), B(-4, 7), C(2, 6), and D(3, 2)
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If you deposit $400 into an account that offers a 5% interest rate. How much interest will you earn after 1 year?
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Answer: The answer is $20
Multiply 400 by .05 or 5%.
If you wanna know 6 years it would be 536 usd
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This would be an compound interest. Meaning that your gain every year would increase exponentially.
The equation to calculate this would be: Kn = K0⋅
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jamie is 3 years less than three times Andys age. In five years the sum of their ages will be 59.How old are they now
Answers
Answer:
Andy : 13 years old and
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Step-by-step explanation:
Andy = x
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Answers
Answer:
13/18
Step-by-step explanation:
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Answer:
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this is your equation to your answer step by step
4.40+ 3.25=
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7.65+3.25=10.9
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Answer:
532,000
Step-by-step explanation:
10^5= 100,000
100,000 x 5.32
Move the decimal place 5 spaces to the right.
It gives you 532,000
Answer:
532000Step-by-step explanation:
5.32 × 10^5 =
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A rectangular farm is 600m long and 200m wide. If 1/3 of it is used for planting rice, what is the area of the remaining land in hectares? a) 4ha b) 8ha c) 12ha d) 80ha e) 120ha please respond its urgent.
Answers
Answer:
8ha
Step-by-step explanation:
600*200 = 120000
120000* 1/3 = 40000
120000 - 40000 = 80000
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What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
The total area of the rectangular farm is 600m × 200m = 120,000 square meters.
If 1/3 of it is used for planting rice, then the area used for planting rice is 1/3 × 120,000 = 40,000 square meters.
Therefore, the area of the remaining land is 120,000 - 40,000 = 80,000 square meters.
To convert this to hectares, divide by 10,000, so the area of the remaining land is 80,000 / 10,000 = 8 hectares. So the answer is 8 hectares.
Hence, the correct answer would be an option (B).
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Answer:
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
1 feet is 0.75 inches
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Answer:
9 inches
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answers
Answer:
Where is the Table?
Step-by-step explanation:
The number of students which prefer action-movies to scary movies are 25 students.
To predict how many more students prefer action movies to scary movies, we calculate difference based on proportion of students who prefer action movies from surveyed group and then apply that proportion to total number of students in school,
Number of students who prefer action movies = 14,
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Proportion of students who prefer action movies = (Number of students who prefer action movies) / (Total surveyed students),
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Predicted number of students who prefer action movies in school = Proportion of students who prefer action movies × Total school students
Predicted number of students who prefer action movies = 0.35×200 = 70,
Predicted number of students who prefer scary movies in the school = (Number of students who prefer scary movies) / (Total surveyed students) × Total school students,
Predicted number of students who prefer scary movies = (9/40)×200 = 45
Difference = (Predicted number of students who prefer action movies) - (Predicted number of students who prefer scary movies),
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Therefore, the correct prediction is that 25 more students prefer action movies to scary-movies.
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Abigail surveyed 40 students about their favorite kind of movie. The results are shown in the table. If there are 200 students in the school, predict how many more students prefer action movies to scary movies.
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Step-by-step explanation:
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Step-by-step explanation:
In pic
(Credits: Symbolab)
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Step-by-step explanation:
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Answers
Arithmetic Sequence
rows ---------32-n
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Sn = n/2( 2a+(n-1)d)
=32/2 (2*26+(31)4)
=16(52+124)
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If theater has 30 rows of seats, then the number of people that the theater will hold is 2400 people.
To find out how many people the theater will hold, we need to calculate the total number of seats across all 30 rows. Since the number of seats increases by 4 for each successive row, we can treat this as an arithmetic sequence.
The formula to find the sum of an arithmetic sequence is = (n/2) × (first term + last term),
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In this case : First term = 22,
Last term = 22 + (30 - 1) × 4 = 22 + 116 = 138,
Number of terms (rows) = 30,
Sum = (30/2) × (22 + 138) = 15 × 160 = 2400;
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For three consecutive homework assignments, each assignment had one more question than the previous assignment. The total number of questions on the three assignments is greater than 51 a.Write an inequality to represent this situation, where q is the number of questions on the first assignment
Answers
The inequality that represents the situation is:
[tex]3q + 3 > 51[/tex]
The first assignment had at least 17 questions.
On the first assignment, there were q questions.Each assignment had one more question than the previous one, so the second had q + 1 questions and the third had q + 2 questions.The total number of questions is:
[tex]T = q + q + 1 + q + 2 = 3q + 3[/tex]
Since the total is greater than 51, the inequality is:
[tex]3q + 3 > 51[/tex]
Solving the inequality, we have that:
[tex]3q > 48[/tex]
[tex]q > \frac{48}{3}[/tex]
[tex]q > 16[/tex]
Thus, it is found that the first assignment had at least 17 questions.
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Write an algebraic expression for three times the sum of the first two multiples of four.
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The table shows the probability distribution of Pamela seeing red cars and green cars on her way to office.
Pamela can expect to see ___ red cars and___ green cars on her way to office.
Answers
The expected value of a dataset is the mean of the dataset.
The complete text is: Pamela can expect to see 1 red car and 1 green car on her way to office.
Expected value is calculated as:
[tex]\mathbf{E(x) =\sum x \times P(x)}[/tex]
For the red cars, we have:
[tex]\mathbf{Red = 0 \times 0.43 + 1 \times 0.31 + 2 \times 0.14 + 3 \times 0.10 + 4 \times 0.02}[/tex]
[tex]\mathbf{Red = 0.97}[/tex]
Approximate
[tex]\mathbf{Red = 1}[/tex]
For the green cars, we have:
[tex]\mathbf{Green= 0 \times 0.45 + 1 \times 0.17 + 2 \times 0.22 + 3 \times 0.07 + 4 \times 0.09}[/tex]
[tex]\mathbf{Green= 1.18}[/tex]
Approximate
[tex]\mathbf{Green= 1}[/tex]
Hence, the expected values of red and green is 1.
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Sara says, "If you subtract 13 from my number and multiply the difference by -6, the result is
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Answers
24-13 is 11
And 11 x -6 is -66
Please mark brainliest.
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Answers
Answer:
28°
Step-by-step explanation:
1. We can see that ∠GFH has two smaller angles within it: ∠1 and ∠2. Given that m∠GFH is 53° (the whole thing), and m∠2 is 25° (a part of it), we just have to subtract 25 from 53 to get the measure of ∠1.
[tex]53 - 25[/tex] [tex]28[/tex]Therefore, m∠1 = 28°.