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2 years ago

If quadrilateral ABCD rotates 90° counterclockwise about the origin, what are the coordinates of A′ in quadrilateral A′B′C′D′ ?

Mathematics

2 answers:

Vesna [10]2 years ago

6 0

Answer:

Option B is correct.

The coordinate of A' is (-2 , -1)

Explanation:

The coordinates of ABCD are A = (-1,2) , B(1,1) , C =(1,-1) and D(-2,-2).

Rotation means moving the shape around a fixed point clockwise or anticlockwise, and by a certain number of degrees.

Rule for 90° counterclockwise rotation about the origin: $(x,y) \rightarrow (-y,x)$

or we can say that switch x and y in the coordinates and make y value opposite.

Then, the coordinate of A' :

$A(-1,2) \rightarrow A'(-2 ,-1)$

Therefore, the coordinate of A' in the quadrilateral A'B'C'D' is, (-2 ,-1)

Greeley [361]2 years ago

4 0

I believe the answer is (-2,-1) after the original point (2,1) goes through the change of -y,x

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Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base.

Tanya [424]

Answer:

The larger cross section is 24 meters away from the apex.

Step-by-step explanation:

The cross section of a right hexagonal pyramid is a hexagon; therefore, let us first get some things clear about a hexagon.

The length of the side of the hexagon is equal to the radius of the circle that inscribes it.

The area is

$A=\frac{3\sqrt{3} }{2} r^2$

Where $r$ is the radius of the inscribing circle (or the length of side of the hexagon).

Now we are given the areas of the two cross sections of the right hexagonal pyramid: $A_1=216\:ft^2\: \:\:\:A_2=486\:ft^2$

From these areas we find the radius of the hexagons:

$r_1=\sqrt{\frac{2A_1}{3\sqrt{3} } } =\sqrt{\frac{2*216}{3\sqrt{3} } }=\boxed{9.12ft}$

$r_2=\sqrt{\frac{2A_2}{3\sqrt{3} } } =\sqrt{\frac{2*486}{3\sqrt{3} } }=\boxed{13.68ft}$

Now when we look at the right hexagonal pyramid from the sides ( as shown in the figure attached ), we see that $r_1$ $r_2$ form similar triangles with length $H$

Therefore we have:

$\frac{H-8}{r_1} =\frac{H}{r_2}$

We put in the numerical values of $r_1$ , $r_2$ and solve for $H$ :

$\boxed{H=\frac{8r_2}{r_2-r_1} =\frac{8*13.677}{13.68-9.12} =24\:feet.}$

8 0

2 years ago

At 9am you have run 2 miles. At 9:24 you have run 5 miles. What is your running rate in minutes per mile?

Drupady [299]

Answer:

8minutes per mile

Step-by-step explanation:

You ran 3 miles since 9am divide 24 by 3 to get 8 minutes

3 0

2 years ago

In the parallelogram AXYZ, line segment AT = 4y – 2, line segment TY = 6x -12, line segment TX = 14, line segment ZT = 2x + 12.

Tpy6a [65]

In a parallelogram diagonals bisect each other,
=>AT=TX=>4y-2=14=>4y=14+2=>4y =16=>y=16/4=4
And ZT=TY=>2x+12=6x-12
=>12+12=6x-2x
=>24=4x
=>24/4=X
=>6=X
Hope this helps u...!!!

8 0

2 years ago

A pizza parlor offers 4 different pizza toppings. How many different kinds of 2-topping pizzas are available?

Galina-37 [17]

Order does not matter so use "n choose k" formula is used to find number of unique combinations.

c=n!/(k!(n-k)!) where n is total possible choices and k is number of selections.

c=4!/(2!(4-2)!)

c=4!/(2!2!)

c=24/(2*2)

c=24/4

c=6

So there are 6 different two topping options when there are four different toppings to choose from.

6 0

2 years ago

Read 2 more answers

You are working on an assignment for your statistics class. You need to estimate the proportion of students at your college who

Ede4ka [16]

Answer:

B, Work with the math instructors to create a list of students currently taking a math class. Randomly select

Step-by-step explanation:

Let's think of each scenario at a time.

(A) We select 100 students enrolled in college randomly that should be fine because we are taking only students that can take classes. this rules out faculty members and any other persons but also there may be students that will never take any math course as part of their study plan, this is ruled out on that basis.

(B)if we take 100 students from the list of math instructor, that will ensure that we have taken students that are taking math class now, and math is part of their study plan, seems fine.

(C) visiting cafeteria randomly on multiple days will give us random persons that may not even be enrolled in university. this can be ruled out on that basis.

(D)Ten class at random and surveying each student in every class will make sampling size large or small depending on students enrolled in each of the class this will not give us reliable results.

We can conclude that (B) is the beast method for obtaining reliable results.

6 0

2 years ago