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seraphim [82]
3 years ago
5

Please help me answer this question. Show steps and explain

Mathematics
1 answer:
salantis [7]3 years ago
3 0

Your problem statement makes no reference to p or q, so we can only guess that "p/q" refers to the ratio of the lowest- and highest-degree coefficients:

... -6/1

Then the factors of p/q are the factors of 6, with either sign.

Factors of p/q: ±1, ±2, ±3.

There are a number of ways the factors can be tested. To test 1, simply add the coefficients. (The sum is -8.) To test -1, subtract the sum of odd-degree coefficients from the sum of even-degree coefficients. (The difference is 0.)

Knowing that -1 is a root of the function, you can use synthetic division to find the quadratic factor. (See the first attachment for the work.) Then you have ...

... f(x) = (x +1)(x² +x -6)

You can continue to test the factors of p/q, or you can factor the quadratic to get ...

... f(x) = (x +1)(x -2)(x +3)

Another way to test the factors is to program your graphing calculator to evaluate the function f(x) for those factors. The result from my TI-84 is shown in the second attachment. That shows f(x) = 0 for x = -3, -1, and +2.

Test the factors: f({-3, -2, -1, 1, 2, 3}) = {0, 4, 0, -8, 0, 24}

This tells you the x-intercepts.

X-intercepts: -3, -1, 2

Of course, the y-intercept is just the constant in the function—the value of the function when x=0.

Y-intercept: -6

As with any odd-degree polynomial with a positive leading coefficient, the overall behavior looks like "/". That is ...

End behaviors: f(x) goes to -∞ as x goes to -∞; f(x) goes to +∞ as x goes to +∞.

_____

A graph of f(x) is shown in the third attachment. (Graphing calculators make it easy to use graphing to find x-intercepts.)

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Equation of the line that passes through the points (0,6) and (-5,2)?
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Answer:

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Step-by-step explanation:

5 0
2 years ago
The vertices of a triangle ABC are A(7, 5), B(4, 2), and C(9, 2). What is measure of angle ABC? 30° 45° 56.31° 78.69°
GenaCL600 [577]

The measure of angle ABC is 45°

<em><u>Explanation</u></em>

Vertices of the triangle are:   A(7, 5), B(4, 2), and C(9, 2)

According to the diagram below....

Length of the side BC (a) =\sqrt{(4-9)^2+(2-2)^2}= \sqrt{25}= 5

Length of the side AC (b) = \sqrt{(7-9)^2 +(5-2)^2}= \sqrt{4+9}=\sqrt{13}

Length of the side AB (c) = \sqrt{(7-4)^2 +(5-2)^2} =\sqrt{9+9}=\sqrt{18}

We need to find ∠ABC or ∠B . So using <u>Cosine rule</u>, we will get...

cosB= \frac{a^2+c^2-b^2}{2ac} \\ \\ cos B= \frac{(5)^2+(\sqrt{18})^2-(\sqrt{13})^2}{2*5*\sqrt{18} }\\ \\ cosB= \frac{25+18-13}{10\sqrt{18}} =\frac{30}{10\sqrt{18}}=\frac{3}{\sqrt{18}}\\ \\ cosB=\frac{3}{3\sqrt{2}} =\frac{1}{\sqrt{2}}\\ \\ B= cos^-^1(\frac{1}{\sqrt{2}})= 45 degree

So, the measure of angle ABC is 45°

7 0
3 years ago
Read 2 more answers
What is the circumference of the given circle in terms of pi
Nezavi [6.7K]
The formula for finding the circumference is pi times the diameter so If your giving it in terms of pi then you're just finding the diameter which is 15
3 0
3 years ago
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Given the parent function f(x) = x3 give the best description of the graph of .
Reil [10]

Answer:

Answer: A

Step-by-step explanation:

4 0
2 years ago
PLEASE HELP ME!<br> I have to find the measurement of the angle but i can't figure it out.
Vadim26 [7]

<u>Answer:</u>

  • The value of ∠TMV is 45°.

<u>Step-by-step explanation:</u>

<u>We know that:</u>

  • ∠VTM + ∠TMV + ∠MVT = 180°
  • ∠VTM = 92
  • ∠MVT = 43

<u>Work:</u>

  • ∠VTM + ∠TMV + ∠MVT = 180°
  • => 92 + 43 + ∠TMV = 180°
  • => 135 + ∠TMV = 180°
  • => ∠TMV = 180 - 135
  • => ∠TMV = 45°

Hence, <u>the value of ∠TMV is 45°.</u>

Hoped this helped.

BrainiacUser1357

3 0
2 years ago
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