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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A theater has 30 rows of seats. There are 22 seats in the first row, 26 in the second row, 30 in the third row, etc. How many people will the theater hold ?
Answers
Arithmetic Sequence
rows ---------32-n
first term ------------26-----------a
d---------------------------4
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Answer:
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Answer:
Step-by-step explanation:
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Answer:
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Answer:20 mins
Step-by-step explanation:
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Answer:
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Answer:
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1 feet is 0.75 inches
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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:
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Answer:
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Step-by-step explanation:
In pic
(Credits: Symbolab)
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Answer:
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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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The given question is incomplete, the complete question is
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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Answers
Answer:
the slope is 2 and a=8 b=6
Step-by-step explanation:
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
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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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Point S lies on AB. If AB = 34 units, AS = 5 + 2x units, and SB = x + 2 units, what is the length of AS in units?
Enter the correct answer in the box.
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Answer:
AS=9
Step-by-step explanation:
Write an algebraic expression for three times the sum of the first two multiples of four.
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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 =
532/100 × 100000 =
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532000
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
10000m = 1ha
80000m = 8ha
The area of the remaining land is 8 hectares. The correct answer would be an option (B).
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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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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