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natita [175]
3 years ago
14

Angie’s rotation maps triangle XYZ to triangle X’Y’Z’. X(3, –6) maps to X’(–3, 6) Y(1, –2) maps to Y’(–1, 2) Z(–1, –5) maps to Z

’(1, 5) Which describes the rotation? mc015-1.jpg rotation mc015-2.jpg clockwise rotation mc015-3.jpg counterclockwise rotation mc015-4.jpg clockwise rotation

Mathematics
2 answers:
Advocard [28]3 years ago
6 1

Answer with explanation:

Vertices of Triangle X Y Z →→ Pre-Image : X(3,-6),Y(1,-2),Z(-1,-5)

Vertices of Triangle X' Y' Z' →→ Image : X'(-3,6),Y'(-1,2),Z'(1,5)

→→Drawing the Triangle XYZ and X'Y'Z' on coordinate plane

→All sides are unequal in length, so it is a Scalene Triangle.

Joining Z and Z'

⇒And ,finding that , if we rotate Triangle X Y Z in Anti clockwise Direction  by an angle of 180°, it gives Triangle X'Y'Z'.

Option :Anti Clockwise Rotation by an angle of 180°

zhannawk [14.2K]3 years ago
7 0

Answer:

180° rotation about the origin

Step-by-step explanation:

Analysing triangles XYZ and X'Y'Z' it can be seen that coordinates of point X (3, -6) were changed to (-3,  6), that is, (x, y) were changed to (-x, -y). The relation between Y and Y', and between Z and Z' is the same. A 180° rotation about the origin translates point (x, y) to point (-x, -y). In a 180° rotation, clockwise or counterclockwise rotation doesn't make any difference.

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20)
ivolga24 [154]

Answer:

0 & 1

Step-by-step explanation:

3(1 + x) < x + 6

Distribute

3x+3 < x+6

Subtract x from each side

3x+3-x < x+6-x

2x+3 <6

Subtract 3 from each side

2x+3-3 <6-3

2x <3

Divide each side by 2

2x/2 <3/2

x <3/2

3 0
2 years ago
Tap A takes 6 minutes to fill a tank and tap b takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. H
jekas [21]

Answer:  approximately 4.7368 minutes

This decimal value is the result of computing 90/19

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

Explanation:

Let's find the LCM of 6, 9 and 15. First, list out the prime factorization of each value.

  • 6 = 2*3
  • 9 = 3*3
  • 15 = 3*5

The unique prime factors are 2, 3, and 5. We have 2 show up at most once, 3 show up at most twice, and 5 show up at most once. The LCM is 2^1*3^2*5^1 = 2*9*5 = 18*5 = 90.

We'll use this LCM value to set up an example below.

---------------

Consider the tank to be 90 gallons. If we only use tap A, keep tap B closed, and don't open pipe C, then tap A fills the tank at a rate of 90/6 = 15 gallons per minute since it needs 6 minutes to completely fill the tank.

If we have tap B do all the work (keep tap A and pipe C closed), then the rate is 90/9 = 10 gallons per minute for this tap.

Keeping pipe C closed, the two taps A and B work together to have a combined rate of 15+10 = 25 gallons per minute.

Now we consider pipe C being opened. This drains the tank and can do so in 15 minutes (assume the taps A and B aren't open). If we're dealing with a full 90 gallon tank, then its rate is 90/15 = 6 gallons per minute.

The net rate is 25-6 = 19 gallons per minute. We can think of it as a tug of war where the taps A and B ultimately win out despite the fact that pipe C is draining the water. The two taps fill the tank faster than the pipe can drain the tank.

In other words, the tank ultimately gets filled up rather than drained out over the long run. That net speed is at 19 gallons per minute.

The amount of time needed is approximately 90/19 = 4.7368 minutes.

Side note: you can start with any size tank. It doesn't have to be 90 gallons. I picked on this value because it works cleanly with the original given numbers 6, 9 and 15.

6 0
3 years ago
Read 2 more answers
Why is -csc^2 (pi/4) = -2 ?
sweet-ann [11.9K]
Sin(pi/4) = 1/sqrt(2)
csc(pi/4) = sqrt(2)
csc^2(pi/4) = 2
-csc^2(pi/4) = -2
8 0
2 years ago
An ice cream cone has a radius of 3 inches and a height of 6 inches. Which measurement is the closest to the volume in cubic inc
fomenos
56.52 cubic inches. Volume equals pi times the radius squared times the height divided by three.


4 0
3 years ago
Read 2 more answers
What the answer to this problem
Romashka [77]
2•2•2•2•2-7•7•7
32-343
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8 0
3 years ago
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