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3 years ago

Which equation is represented by the number line?

Mathematics

1 answer:

zavuch27 [327]3 years ago

6 0

Answer:

Equation 1: 6 + (-10) = -4

Step-by-step explanation:

1st segment starts at 0 and goes 6 units right so: +6

Second segment starts at 6 and goes 10 units left, so: -10

Finally the second segment lands on -4, so all together:

+6 + (-10) = -4 or 6 + (-10) = -4

Hope this helps!

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Which function has the following characteristics?

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Using the asymptote concept, the function with a vertical asymptote at x = 3 and an horizontal asymptote at $y = -\frac{1}{2}$ is given by:

$f(x) = -\frac{x}{2(x - 3)}$

<h3>What are the asymptotes of a function f(x)?</h3>

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

The vertical asymptote at x = 3 means that x = 3 is a root of the denominator, hence:

$f(x) = \frac{g(x)}{x - 3}$

The horizontal asymptote at y = -1/2 means that:

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Which happens if $g(x) = -\frac{x}{2}$ , hence the function is:

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More can be learned about asymptotes at brainly.com/question/16948935

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2 years ago

what is the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube

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Let the least possible value of the smallest of 99 cosecutive integers be x and let the number whose cube is the sum be p, then

$\frac{99}{2} (2x+98)=p^3 \\ \\ 99x+4,851=p^3\\ \\ \Rightarrow x=\frac{p^3-4,851}{99}$

By substitution, we have that $p=33$ and $x=314$ .

Therefore, <span>the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.</span>

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3 years ago