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3 years ago

A change machine can accept $1, $5, $10, and $20 bills and returns quarters. What is the domain and range of this situation?

Mathematics

1 answer:

Svet_ta [14]3 years ago

5 0

Answer:

Domain {1,5,10,20}

Ranger {4,20,40,80}

Step-by-step explanation:

$1=4 quarters

$5=20 quarters

$10=40 quarters

$20=80 quarters

Domain {1,5,10,20}

Ranger {4,20,40,80}

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Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

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Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

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3 years ago

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alexandr402 [8]

Answer:

The answer is 4/7

Step-by-step explanation:

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2 years ago

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-The terminal side of the angle contains the following point. Find the values of the six trigonometric functions for the followi

bearhunter [10]

Answer: see attachments

<u>Step-by-step explanation:</u>

Use Pythagorean Theorem to find the missing side (x² + y² = h²)

Use the following formulas to find the trig functions:

$sin\theta=\dfrac{y}{h}\qquad \qquad csc\theta=\dfrac{h}{y}\\\\\\cos\theta=\dfrac{x}{h}\qquad \qquad sec\theta=\dfrac{h}{x}\\\\\\tan\theta=\dfrac{y}{x}\qquad \qquad cot\theta=\dfrac{x}{y}$

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3 years ago

Solve: 3(2x - 5) = 6x - 15

Levart [38]

$3(2x-5)=6x-15$

$3(2x-5) :$

$6x-15 = 6x-15$

add 15 to both sides:

$6x-15+15=6x-15+15$

$6x =6x$

subtract 6x from both sides:

$6x-6x=6x-6x$

$0=0$

Both sides are equal : true for all x

Answer D

hope this helps!

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2 years ago