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Elza [17]
3 years ago
9

Write functions for each of the following transformations using function notation. Choose a different letter to represent each f

unction. For example, you can use R to represent rotations. Assume that a positive rotation occurs in the counterclockwise direction.
translation of a units to the right and b units up
reflection across the y-axis
reflection across the x-axis
rotation of 90 degrees counterclockwise about the origin, point O
rotation of 180 degrees counterclockwise about the origin, point O
rotation of 270 degrees counterclockwise about the origin, point O
Mathematics
1 answer:
joja [24]3 years ago
5 0

Answer:

1. Translation: g(x) = f(x-a)+b.

2. Reflection around y-axis: h(x) = f(-x)

3. Reflection around x-axis: k(x) = -f(x)

4. Rotation of 90° : R_{90} (x,y)=(-y,x)

5. Rotation of 180° : R_{180} (x,y)=(-x,-y).

6. Rotation of 270° : R_{180} (x,y)=(y,-x).

Step-by-step explanation:

Let us assume that the transformations namely translation, reflection are applied to a function f(x) and the rotation is applied to the point ( x,y ).

So, according to the options:

We know that 'translation moves the image in horizontal and vertical direction'.

1. As we have to translate the function f(x) 'a' units to the right and 'b' units up. So, the new form of the function becomes g(x) = f(x-a)+b.

Further, we know that 'reflection means to flip the image around a line'.

2. As, we have to reflect the function f(x) around y-axis. The new form of the function is h(x) = f(-x).

3. As, we have to reflect the function f(x) around x-axis. The new form of the function is k(x) = -f(x).

Since, 'rotation turns the image around a point to a certain degree'.

4. As, we have to rotate ( x,y ) counter-clockwise to 90° about the origin, the new form of the function is R_{90} (x,y)=(-y,x).

5. As, we have to rotate ( x,y ) counter-clockwise to 180° about the origin, the new form of the function is R_{180} (x,y)=(-x,-y).

6. As, we have to rotate ( x,y ) counter-clockwise to 270° about the origin, the new form of the function is R_{180} (x,y)=(y,-x).

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Answer:

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2) The probability of niki drawing a green marble is likely and the probability of tom drawing a blue marble is unlikely.

Step-by-step explanation:

1) Since there is only one 3 out of 6 numbers, the probability of that outcome is 1/6, which is low. The same thing goes for throwing a 4.

2) The reason why it is equally likely for niki drawing a green is because there are more green marbles than the other marbles. You could see it as a fraction as well, which is 4/9 Which is very close to one half (4.5). For tom, there are less blue marbles which brings it down to the unlikely spot (fraction = 3/9)

Hopefully this helps, and hopefully it isn't too confusing.

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3 years ago
I really need help. Find a. Round to the nearest tenth.
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Answer:

a ≈ 1.8

Step-by-step explanation:

a / sin (180 - 105 - 15)° = 2 /sin 105°

a = (2 /sin 105°) x sin 60°

a = (2 / 0.97) x 0.87

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the ratio of men to women at a class is 6 to 5 how many women students are there if there are 3600 men
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4.5x+ 7/9 x+2 1/3 + 1/6 x=5 1/18<br> What is the answer?? How would you solve it?? Please help!!
Travka [436]
18 is the least common denominator of all the fractions, so you can eliminate fractions by multiplying the equation by 18.

(4.5*18)x +((7/9)*18)x + (2 1/3)*18 + ((1/6)*18)x = (5 1/18)*18
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Collect terms.
98x + 42 = 91
98x = 49 . . . . . . . . . subtract 42
x = 49/98 = 1/2

The solution is x = 1/2.

_____
You can also do the arithmetic with mixed numbers and fractions. The usual methods apply.
  (4.5 + 7/9 + 1/6)x + 2 1/3 = 5 1/18
  (49/9)x + 7/3 = 91/18
  (49/9)x = 49/18 . . . . . . . subtract 7/3
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This can be a little more tedious than the method above, but it works and it will give you the right answer. A calculator that works with fractions can make this solution as easy as the other one.
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