Answer:
Since a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.
Step-by-step explanation:
Let a/b be the rational number in its simplest form. If we divide a/b by 2, we get another rational number a/2b. a/2b < a/b. If we divide a/2b we have a/2b ÷ 2 = a/4b = a/2²b. So, for a given rational number a/b divided by 2, n times, we have our new number c = a/2ⁿb where n ≥ 1
Since 
= a/(2^∞)b = a/b × 1/∞ = a/b × 0 = 0, the sequence converges.
Now for each successive division by 2, a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb and
a/2⁽ⁿ ⁺ ¹⁾b/a/2ⁿb = 1/2, so the next number is always half the previous number.
So, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.
Answer:
yes
Step-by-step explanation:
There are several ways to go at this.
My first choice is to use a graphing calculator. It shows the function has a zero at x=5, so x-5 is a factor.
Another good choice is to use synthetic division (2nd attachment). If the remainder is zero, then x-5 is a factor. It is and it is.
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You can also evaluate the function at x=5. The remainder theorem tells you that if the value is zero, then x-5 is a factor. Evaluating the polynomial written in Horner form is a lot like synthetic division.
(((x -4)x -15)x +58)x -40 for x=5 is ... (-10·5 +58)5 -40 = 40-40 = 0
The value of h(5) is zero, so x-5 is a factor of h(x).
Answer: 5
− 1 + 
Step-by-step explanation:
Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below. Thank you!
<u>Step 1:</u><u> </u><u><em>Collect like terms.</em></u>
(3 + 2) + (6 − 3 − 4) + (-6 + 7)
<u>Step 2: </u><u><em>Simplify.</em></u>
5 − 1 +
~I hope I helped you! :) Good luck!~
These are all linear equations:<span>y = 2x + 1
5x = 6 + 3y
<span>y/2 = 3 − x</span></span>
Answer:
y=mx+b
Step-by-step explanation:
mark brainliest
