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3 years ago

Find a third-degree polynomial equation with rational coefficients that has roots –5 and 6 + i.

Mathematics

1 answer:

Vitek1552 [10]3 years ago

8 0

The coefficients of the polynomial are rational, which means that any non-real roots occur alongside their complex conjugates. In this case, 6+i is a root, so 6-i is also a root.

So the simplest polynomial you can build with these roots is

(x - (-5)) (x - (6 + i )) (x - (6 - i )) = x ^3 - 7x ^2 - 23x + 185

(first choice)

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PLEASE HELP ME!

kotegsom [21]

Answer:

Bottom left graph

Step-by-step explanation:

We have to use what is called the zero-interval test [test point] in order to figure out which portion of the graph these inequalities share:

−2x + y ≤ 4 >> Original Standard Equation

+ 2x + 2x

_________

y ≤ 2x + 4 >> Slope-Intercept Equation

−2[0] + 0 ≤ 4

0 ≤ 4 ☑ [We shade the part of the graph that CONTAINS THE ORIGIN, which is the right side.]

$\displaystyle y > x + 2 \\ \\ 0 ≯ 2$ [We shade the part of the graph that does not contain the origin, which is the left side.]

So, now that we got that all cleared up, we can tell that the graphs share a region in between each other and that they both have POSITIVE RATE OF CHANGES [SLOPES], therefore the bottom left graph matches what we want.

** By the way, you meant $\displaystyle y > x + 2$ because this inequality in each graph is a dashed line. It is ALWAYS significant that you be very cautious about which inequalities to choose when graphing. Inequalities can really trip some people up, so once again, please be very careful.

I am joyous to assist you anytime.

7 0

3 years ago

After you finish school, your average monthly income is $1,600. You want to spend no more than 30% of that amount on a place to

Luba_88 [7]

3 other people + you

so 4 total which would come to about 480$

7 0

3 years ago

The moon has a radius of 1,079 miles. What is the circumference of the moon? Express your answer in terms of

MatroZZZ [7]

Answer:

gvhgfcbvhgfc

Step-by-step explanation:

yee

4 0

2 years ago

You and a friend go out to dinner. The cost of the meal is $45.22. You leave a 20% tip. The sales tax is 6% what is the total co

Doss [256]

Answer:

$57.52 I believe that is the correct answer.

7 0

2 years ago

AnimeBrainly PleaseHelp!

jekas [21]

Platinum Gym charges a one-time registration fee of $60, and membership is $20 a month.

Super Fit charges a one-time registration fee of $150, and membership is $10 a month.

(a) Write a expression to represent the membership cost of Platinum Gym for x months.

Let x = months

20x + 60 is your expression

(b) Write an expression to represent the membership cost of Super Fit for x months

Let x = months

10x + 150 is your expression

One month: Plug in 1 for x.

20(1) + 60 = 20 + 60 = 80

10(1) + 150 = 10 + 150 = 160

Platinum Gym is cheaper overall for one month by $80

One year: There are twelve months in a year. Plug in 12 for x.

20(12) + 60 = 240 + 60 = 300

10(12) + 150 = 120 + 150 = 270

Super Fit is cheaper than Platinum Gym overall for one year by $30

(d) Set the two expression equal to each other.

20x + 60 = 10x + 150

Isolate the x. Subtract 10x and 60 from both sides

20x (-10x) + 60 (-60) = 10x (-10x) + 150 (-60)

20x - 10x = 150 - 60

Simplify

20x - 10x = 150 - 60

10x = 90

Isolate the x. Divide 10 from both sides

10x/10 = 90/10

x = 9

It takes 9 months for the cost to be the same.

(e) It really depends on how long you want to work out at a gym. If you are working out for less than a year, than Platinum Gym is the better choice. If more than a year, then Super Fit is the better choice.

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hope this helps

5 0

3 years ago

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