I do not get question 11 please help me!

Mathematics

1 answer:

Inessa [10]3 years ago

7 0

Triangle QRS has 3 congruent sides, so it is equilateral and equiangular.

The sum of the measures of the angles of a triangle is 180 deg, so each angle of triangle QRS is 60 deg.

Angle RQS measures 60 degrees and forms a linear pair with angle PQS. Angles in a linear pair a supplementary. That makes the measure of angle PQS 120 deg. leaving only 60 degrees as the sum of the measures of angles PSQ and SPQ. Triangle PQS is isosceles since sides PQ and QS are congruent. The angles opposite congruent sides of a triangle are congruent, so angle PSQ is congruent to angle SPQ. That means angles PSQ and SPQ measure 30 deg each.

m<PSR = m<PSQ + m<QSR = 30 + 60 = 90

m<PQS = 120

m<PSR : m<PQS = 90 : 120 = 3 : 4

No choice shows the correct answer.

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Show all work to identify the asymptotes and state the end behavior of the function f(x)=5x/x-25

Nina [5.8K]

Using the asymptote concept, it is found that:

The vertical asymptote is of x = 25.

The horizontal asymptote is of y = 5.

Considering the horizontal asymptote, it is found that the end behavior of the function is that it tends to y = 5 to the left and to the right of the graph.

<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.

In this problem, the function is:

$f(x) = \frac{5x}{x - 25}$

Considering the denominator, the vertical asymptote is:

x - 25 = 0 -> x = 25.

The horizontal asymptote is found as follows:

$y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5$