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LekaFEV [45]
3 years ago
14

The polynomial equation x3+x2=-9x-9 has complex roots +-3i . What is the other root? Use a graphing calculator and a system of e

quations. –9 –1 0 1
Mathematics
1 answer:
Scilla [17]3 years ago
3 0

Answer:

x=-1

Step-by-step explanation:

x3+x2=-9x-9

add 9x +9 on each side

x^3+x^2+9x+9=-9x-9+9x+9

x^3+x^2+9x+9=0

factor out an x^2 from the left  2 terms and a 9 from  the right 2 terms

x^2 (x+1)  +9(x+1) = 0

factor out x+1

(x+1) (x^2+9) = 0

using the zero product property

x+1 =0    x^+9 =0

x=-1    x^2 =-9

x=-1     sqrt(x^2) = sqrt(-9)

x=-1     x = ±3i

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Is -0.3 a rational number? is 3.14144144414444... a rational number?
Ainat [17]

I will try to make this as simple as possible.

First off, we need to know what a rational number is: A rational number is any number that can be made by dividing 2 integers. For example:

1.5 would be a rational number because 1.5 = 3/2 (3 and 2 are both integers)

With that being said, let's begin.

First off, let's start with -0.3, let's ask ourselves, can we make this number by dividing 2 integers, the answer is yes, we can, by doing \frac{-3}{10} we have the equivalent of -0.3, so now we know it's a rational number.

As for the second one, it can't be a rational number because it can't be made by dividing to integers, so the answer is:

-0.3 is a rational number, but 3.14144144414444 is not.

Hope this helped! c:

3 0
3 years ago
Louann and Carla received equal scores on a test made up of multiple choice questions and an essay. Louann got 14 multiple choic
alexgriva [62]
Each multiple choice question would be 5 points. For Louann she got 14 of the questions correct so 5 x 14 = 70 and 70 + 24 would be 94. For Carla she got 16 of the questions correct so 5 x 16 = 80 and 80 + 14 = 94. You're answer would be 5, hopefully this helps :)
5 0
3 years ago
Let the region R be the area enclosed by the function f(x)=ln(x) and g(x)= 1/2x-2. Find the volume of the solid generated when t
Neporo4naja [7]

Answer:

V=61.66

Step-by-step explanation:

This problem can be solved by using the expression for the Volume of a solid with the washer method

V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx

where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).

Before we have to compute the limits of the integral. We can do that by taking f=g, that is

f(x)=g(x)\\ln(x)=\frac{1}{2}x-2

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)

x1=0.14

x2=8.21

and because the revolution is around y=-5 we have

R=ln(x)-(-5)\\r=\frac{1}{2}x-2-(-5)\\

and by replacing in the integral we have

V=\pi \int \limit_{x1}^{x2}[(lnx+5)^2-(\frac{1}{2}x+3)^2]dx\\

V=\pi [28x+\frac{1}{x}+xln^2x-12xlnx-6lnx]  

and by evaluating in the limits we have

V=61.66

Hope this helps

regards

3 0
3 years ago
Determine the vertex of the function f(x) = 3(x − 2)2 + 1.
anastassius [24]

The vertex point of the function f(x) = 3(x - 2)² + 1 is (2 , 1) ⇒ answer A

Step-by-step explanation:

Any quadratic function represented graphically by a parabola

1. If the coefficient of x² is positive, then the parabola open upward

  and its vertex is a minimum point

2. If the coefficient of x² is negative, then the parabola open

   downward and its vertex is a maximum point

3. The standard form of the quadratic function is: f(x) = ax² + bx + c

    where a, b , c are constants

4. The vertex form of the quadratic function is: f(x) = a(x - h)² + k,

     where h , k are the coordinates of its vertex point

∵ The function f(x) = 3(x - 2)² + 1

∵ The f(x) = a(x - h)² + k in the vertex form

∴ a = 3 , h = 2 , k = 1

∵ h , k are the coordinates of the vertex point

∴ The coordinates of the vertex point are (2 , 1)

The vertex point of the function f(x) = 3(x - 2)² + 1 is (2 , 1)

Learn more:

You can learn more about quadratic function in brainly.com/question/1357167

#LearnwithBrainly

6 0
3 years ago
Read 2 more answers
The sum of all but one interior angle of a heptagon is 776°. The final angle must have a measure of
shutvik [7]
A heptagon has 7 sides.

Sum of all interior angles = (7 - 2) x 180 = 900°

900 - 776 = 124°

Answer: The final angle must be 124°
5 0
3 years ago
Read 2 more answers
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