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4 years ago

Write the prime factorization of each number in e-g. e. 25 f. 100g. 16

Mathematics

1 answer:

kipiarov [429]4 years ago

8 0

Answers:

25 = 5*5 which is the same as 25 = 5^2

100 = 2*2*5*5 which is the same as 100 = 2^2*5^2

16 = 2*2*2*2 which is the same as 16 = 2^4

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Explanation:

To find the prime factorization of 25, we divide by prime numbers. We see that 25/2 = 12.5 isn't a whole number, and neither is 25/3 = 8.33 (approx). But 25/5 = 5 is a whole number. The result is a prime number so we can stop here. This shows that 25 = 5*5 = 5^2

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We'll do the same for 100 as well. Start with dividing over 2

100/2 = 50

50/2 = 25

we can't do 25/2 as mentioned earlier, but we can say 25/5 = 5

So basically 100 = 2*2*25 = 2*2*5*5 = 2^2*5^2

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The same will happen with 16 as well. We divide by 2 until we arrive at a prime number result

16/2 = 8

8/2 = 4

4/2 = 2

We have three 2's as denominators and that last result 2 is included in the set of prime factors as well to say 16 = 2*2*2*2 = 2^4

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The factor tree for each is shown below. For something like 100, there are a few ways to draw out the tree. The same applies for 16 as well.

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alexandr1967 [171]

Answer:

Here's what I get.

Step-by-step explanation:

1. Rotate 180° about origin

The formula for rotation of a point (x,y) by an angle θ about the origin is

x' = xcosθ - ysinθ

y' = ycosθ + xsinθ

If θ = 180°, sinθ = 0 and cosθ = -1, and the formula becomes

x' = -x

y' = -y

The rule is then (x, y) ⟶ (-x, -y).

H: (-3, -5) ⟶ (3, 5)

J: (-5, -3) ⟶ (5, 3)

Q: (0, -1) ⟶ (0, 1)

The vertices of H'J'Q' are (3, 5), (5, 3), and (0, 1).

2. Rotation 90° counterclockwise about origin

cos90° = 0 and sin90° = 1

x' = xcos90° - ysin90° = -y

y' = ycos90° + xsin90° = x

The rule is then (x, y) ⟶ (-y, x).

B: (4, 5) ⟶ (-5, 4)

L: (5, 0) ⟶ (0, 5)

S: (2, 2) ⟶ (-2, 2)

The vertices of B'L'S' are (-5, 4), (0, 5), and (-2, 2).

3. Rotation 90° clockwise about origin

cos(-90°) = 0 and sin(-90°) = -1

x' = xcos(-90°) - ysin(-90°) = y

y' = ycos(-90°) + xsin(-90°) = -x

The rule is then (x, y) ⟶ (y, -x).

F: (1, -5) ⟶ (-5, -1)

H: (-2, -3) ⟶ (-3, 2)

U: (-4, -5) ⟶ (-5, 4)

The vertices of F'H'U' are (-5, -1), (-3, -2), and (-5, 4).

4. Rotate 180° about origin

The rule is (x, y) ⟶ (-x, -y).

J: (1, -1) ⟶ (-1, 1)

V: (2, 0) ⟶ (-2, 0)

Y: (5, -3) ⟶ (-5, 3)

R: (4, -3) ⟶ (-4, 3)

The vertices of J'V'Y'R' are (-1, 1), (-2, 0), (-5, 3), and (-4, 3).

The figures below show your shapes before and after the rotations.

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Write the prime factorization of each number in e-g. e. 25 f. 100g. 16​

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