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4 years ago

Prove that the value of the expression 12^5+12^4 is divisible by 13.

Mathematics

1 answer:

Leto [7]4 years ago

6 0

Answer:

20736

Step-by-step explanation:

Step 1: Simplify the exponents

12^5 = 248832

12^4 = 20736

Step 2: Add them together

248832 + 20736

269568

Step 3: Divide the number by 13

269568 / 13

20736

Answer: 20736

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3 years ago

The function y=-x^2+65x+256 models the number y of subscribers to a website, where x is the number of days since the website lau

Wittaler [7]

Answer:

$y = 30x+290$

Step-by-step explanation:

Given

$y=-x^2+65x+256$

Required

The linear function of a competitor's website

On day 1, both websites have the same subscribers.

This implies that:

$y=-x^2+65x+256$

Substitute: $x =1$

$y=-(1)^2+65*1+256$

$y=-1+65+256$

$y=320$

This implies:

$(x_1,y_1) = (1,320)$

On day 34, both websites have the same subscribers.

This implies that:

$y=-x^2+65x+256$

Substitute: $x =34$

$y=-(34)^2+65*34+256$

$y=-1156+2210+256$

$y=1310$

This implies:

$(x_2,y_2) = (34,1310)$

To calculate the linear function of the competitor, we have:

$(x_1,y_1) = (1,320)$

$(x_2,y_2) = (34,1310)$

Calculate slope (m)

$m = \frac{y_2 - y_1}{x_2 -x_1}$

$m = \frac{1310 - 320}{34-1}$

$m = \frac{990}{33}$

$m = 30$

The equation is then calculated as:

$y = m(x - x_1) + y_1$

This gives:

$y = 30 * (x - 1) + 320$

Open bracket

$y = 30x - 30 + 320$

$y = 30x+290$ --- This represents the linear function of the competitor's website

5 0

3 years ago