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just olya [345]
3 years ago
12

Prove step by step that 5^20-5^19 is an even number with out using a calculator Please can you tell me the steps and why?

Mathematics
1 answer:
hammer [34]3 years ago
8 0

9514 1404 393

Answer:

  factor out 5^19

Step-by-step explanation:

a) Reason from parity:

  both 5^20 and 5^19 are products with only odd numbers (5) as factors. Hence each is an odd number. The difference of odd numbers is always even.

__

b) Factor:

  5^20 -5^19 = 5^19(5 -1) = 5^19×4

This product has an even factor (4), so is even.

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Answer:

Cot(theta) = - 0.75 or -3/4

Step-by-step explanation:

The hypotenuse is 5

The y value is 4

We need to find the corresponding x value.

x^2 + y^2 = z^2

X = ?

y = 4

z = 5

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 9

Now in this case, you are in quadrant 2, so the x value is - 3

sqrt(x^2) = sqrt(9)

x = - 3

The cot value is the adjacent (x value) / the opposite ( y ) value

Cot(theta) = -3/4

cot(theta) = -0.75

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3 years ago
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3 years ago
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B)

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