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Alona [7]
3 years ago
12

A figure lies on a coordinate plane with point B located at (2,-5). The figure is rotated 90 degrees counter-clockwise around a

point R located at (3,4). What will be the coordinates of B'?

Mathematics
1 answer:
Rufina [12.5K]3 years ago
7 0
<h3>Answer:  (12,3)</h3>

======================================================

Explanation:

R is located at (3,4). Move it 3 units to the left and 4 units down to have it move to (0,0). Call this point A. Apply the same translation rule to point B so that (2,-5) moves to (-1,-9). Let's call this point C

Now you'll use the rule (x,y) \to (-y,x) which rotates any point around the origin 90 degrees counterclockwise. So we're rotating C around A.

Point C has the coordinates (-1,-9). When you use the rotation rule (x,y) \to (-y,x) we get (-1,-9) \to (-(-9), -1) = (9, -1). We'll call this point D

Finally, undo the translation rule done at the start of the problem. So we'll go 3 units to the right and 4 units up to have point D move to point E = (12,3) which is exactly where point B' is located.

Check out the diagram below.

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Find the circumference and area of a circle with diameter 12 ft. Express your answer in terms of pie
xz_007 [3.2K]

Answer:

Circumference: 12π

Area: 36π

Step-by-step explanation:

The equation for the circumference of a circle is:

C = πd

Where C is the circumference and d is the diameter. Knowing this, we will be able to find the circumference by pugging in 12 for d.

C = 12π

And now we have found the circumference of the circle.

The equation for the area of a circle is:

A = πr²

Where A is the area and r is the radius. Remember that the diameter is double the radius, so we can find the radius:

12 = 2r

r = 6

Now that we know r, we can find the area of the circle:

A = π(6)²

A = 36π

Now we have found the area.

So the circumference is 12π and the area is 36π.

I hope you find my answer and explanation to be helpful. Happy studying.

4 0
3 years ago
Pls help I don't understand this
Rudiy27
<h3>Answer:</h3>

<u>By angle bisector property</u>,

  • 11x + 23 = 8x + 35
  • 11x - 8x = 35 - 23
  • 3x = 12
  • x = 4°

So, <u>m∠ABD</u> = 8x + 35

  • 8 × 4 + 35
  • 32 + 35 = 67°

<u>m∠CBD</u> = 11x + 23

  • 11 × 4 + 23
  • 44 + 23 = 67°

<u>m∠ABC</u> = 67° + 67° = 134°

4 0
2 years ago
What are the values of x and y in PQRS? What are PR and SQ?
mamaluj [8]

Step-by-step explanation:

sol;

x+1=y...(1)

3y-7=2x....(2)

or, 3(x+1)-72x [from (1)]

or, 3x+3-7=2x

or, 3x-2x=7-3

     x=4

now,

putting the value of x in (1)

y=x+1

 =4+1

 =5

PR and SQ are the diagonal of PQRS.

4 0
2 years ago
A market analyst is hired to provide information on the type of customers who shop at a particular store. A random survey is tak
sveta [45]

Complete question:

A market analyst is hired to provide information on the type of customers who shop at a particular store. A random survey is taken of 100 shoppers at this store. Of these 100, 73 are women. The shoppers The data is summarized below. we grouped in three age categories, under 30, 30 up to 50 and 50 and over. Women under 30 are 30, Men under 30 are 8 Women 30 to 50 are 25 and Men are 14 Women 50 and over are 18 and Men are 5.

Let W be the event that a randomly selected shopper is a woman. Let A be the event that a randomly selected shopper is under 30. a.) Find the probability of W. W (women Shoppers) = Find the probability of A. b.) Find the probability of A and W. c.) P (A and W) (Shoppers) d.) Find the probability of A or W. P(A or W) (Shoppers) e.) Find the probability of A given W

Answer:

A) P(W) = 73/100; B) P(A) = 38/ 100 C) 30 / 100

D) 81/100 E) 30/73

Step-by-step explanation:

- - - - - - - - Women Men Total

Under 30 - - - 30 - - - 8 - - 38

30 to 50 - - - - 25 - - 14 - - 39

50 & over - - - 18 - - - 5 - - -23

Totals - - - - - - 73 - - -27 - - 100

Recall:

Probability : P= (required outcome / Total possible outcomes)

A) probability of women shoppers: P(W)

Number of women shoppers = 73; total shoppers = 100

P(W) = 73/100

B) Probability of under 30: P(A)

= number of shoppers under 30 = 38

Tital number of shoppers = 100

P(A) = 38/ 100

C) probability of A and W; This is the probability that the selected person is a woman and under 30.

(W n A) = 30

= 30 / 100

D) probability of A or W:

P(A) + P(W) - P(A n W) :

(38 / 100 + 73 / 100 - 30 / 100) = (38+73-30) /100

= 81/100

E) probability of A given W:

P(A n W) / P(W) = 30/73

5 0
3 years ago
How and what is the answer
lana [24]
C ) 131 is the answer

in the upside-vertex (not inverted) triangle, angle to your left hand side would be equal to x (as interior alternate angles) = 68

and the angle to the right would be 180-y= 180-117 = 163 (as linear angles)

so the angle at the vertex = 180 - (68 + 163) =49  (as angles in a triangle sum upto 180)

so the angle mz = 180 - 49 = 131 degrees (as linear pair of angles or angle in a straight line)
4 0
3 years ago
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