What is the equation of a line with a slope of −4−4 and a point (−2,5)

1 answer:

7 0

Here, we can formulate the slope-intercept equation from the point and the slope:

Slope = -4/-4 = 1
x1 = -2
y1 = 5

By point-slope form:

(y-y1) = m (x - x1)
(y-5) = 1(x +2)

y-5 = x +2

Simplifying to slope-intercept form:

y = x + 7

Therefore, the slope-intercept form would be y = x+7

I hope my answer has come to your help. God bless and have a nice day ahead!

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You are given 1000 one dollar bills and 10 envelopes. Put the bills into the envelopes in such a way that someone can ask you fo

taurus [48]

Answer:

We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489

Step-by-step explanation:

Observe that, in binary system, 1023=1111111111. That is, with 10 digits we can express up to number 1023.

This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.

However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.

Observe that:

1+2+4+8+16+32+64+128+256+489=1000
Since each one of the first 9 envelopes represents a position in a binary system, we can represent every natural number from zero up to 511.
If we want to give an amount "x" which is greater than $511, we can use our $489 envelope. Then we would just need to combine the other 9 to obtain x-489 dollars. Since $x-489\leq511$ , by 2) we know that this would be possible.