What is the leading coefficient of a third degree function that has an output of 221 when x=2, and has zeros of −15, 3i, and −3i?

Answers

Answer 1

Answer:

  1

Step-by-step explanation:

The function with the given zeros will factor as ...

  f(x) = a(x +15)(x^2 +9) . . . . with leading  coefficient 'a'

You have ...

  f(2) = 221 = a(2+15)(2^2+9) = a(17)(13) = 221a

Then a = 221/221 = 1

The leading coefficient is 1.

_____

Additional comment

As you know, a function with zero x=p has a factor of (x -p). The given zeros mean the function has factors (x -(-15)), (x -3i). and (x -(-3i)). The product of the last two factors is the difference of squares: (x^2 -(3i)^2) = (x^2 -(-9)) = (x^2 +9). This is how we arrived at the factorization shown above.


Related Questions

The equation `F=\frac{9}{5}C+32` relates temperature measured in degrees Celsius, `C`, to degrees Fahrenheit, `F`. Determine whether there is a proportional relationship between `C` and `F`. Explain or show your reas

Answers

Answer:

No, a Celsius temperature is not proportional to its equivalent Fahrenheit temperature.

Step-by-step explanation:

The formula is

F=(9/5) C+ 32

F increases as C increases and F decreases as C decreases, but the relation is not a direct proportionality.

In mathematics, a direct proportion has the form

y=mx

where m is a constant.

If the formula had been F=(9/5) C, it would have been a direct proportion.

However, the addition of the + 32 term makes the formula no longer a direct proportion

a hiking trail at a state park is 8.4 miles long a park ranger wants to place signs at the beginning and end of the trail and along the trail so that the signs are 1.4 miles apart how many signs will the ranger need?

Answers

Answer:

the ranger will need 6 signs

Step-by-step explanation:

The Finish Line paid Converse $24 for a new pair of basketball shoes. If the store sells the shoes for $48, what is the percent mark-up (increase)?

Answers

Answer:

Answer:Total revenue at breakeven is $1,508,042 Explanation:Breakeven point in units = Fixed cost / Selling price -Variable cost per unit Breakeven, and now i think u get it u can do alone! Hope i help you❤️!

A firm employs many clerical workers making near minimum wage salaries and a few executives making much higher
salaries, a report from this firm says in one place that a typical annual salary of an eemployee is $25,000 and in another
place that a typical salary is $30,000. Assuming one of these values is the mean annual salary and the other is the median
annual salary, which is which?.

Answers

Answer:

30000 is mean, 25000 is median

Step-by-step explanation:

Just a logical explanation

if you have a lot  of people making 25000, then chance are you'll find that value in the middle, in assuming that the executives make a lot more

and with executives making a lot more, the mean is 30000

sources: Compare the mean and median of a data set that has a distribution that is skewed right. Answer: The mean will have a higher value than the median

Gracy was running errands around her neighborhood. First she went to the doctors but they were closed. She then drove to her house stopping to grab her library books. She went to the library to drop them off then headed to the grocery story passing her house on the way.

In total, how far would Gracy have traveled once she returned home from the grocery store?

9miles
3 miles
18 miles
6 miles

Answers

Answer is 9 miles from your home

pls help me solve this​

Answers

Volume = Area of triangle x length


Area of triangle = 1/2 x base x height

Area of triangle = 1/2 x 5 x 4

Area of triangle = 10


Volume = area of triangle x length

Volume = 10 x 12

Volume = 120 cm^3

Cody and Lisa both went bowling last weekend, but not together. Cody went during open bowling time,
paying $7 for shoe rental and $1 per hour. Lisa went on family night, when each hour was $3 and shoe
rental was $1. As it turned out, they played for the same number of hours and spent the same amount.
How many hours did each one bowl?
Write a system of equations, graph them, and type the solution.

Answers

If both Cody and Lisa play for t hours, then Cody pays a total of $(7 + t), while Lisa pays a total of $(1 + 3t). If they both pay the same amount P, then

7 + t = P

1 + 3t = P

Solve for t :

7 + t = 1 + 3t

t - 3t = 1 - 7

-2t = -6

t = 3

So Cody and Lisa each bowled for 3 hours, and they both ended up paying P = $10.

pls answer quickly

which of the following measurement is the smallest?

A) kilogram

B) Gram

C) centigram

D) milligram​​

Answers

Answer:

D, milligram.

Step-by-step explanation:

In latin prefixes, kilo- means 1000, cent- means 1/10, and milli- means 1/1000. This means milli- is the shortest and therefore milligrams are the smallest measurement.

Answer:

Milligram I think

Step-by-step explanation:

I could be wrong however

Help help help help math math

Answers

Answer:

A = 192

Step-by-step explanation:

3 x 8^2

3 x 64 = 192

Simply the Expression.

Answers

32768
x
10
There’s something wrong with the question re check it

Which list is in order from least to greatest?

Answers

Answer:

6/10 , 5/8 , 2/3

Step-by-step explanation:

The 3rd one

6/10 , 5/8 , 2/3

if you simplify them into fraction it will be :

0.6 , 0.625 , 0.666

Hey y’all please help me with this question.

Answers

Answer:

-g-8>9 answer

since g is -18 and we have (-)g we will have +18

+18-8+10

now we have 10 and it will be bigger the the 9.

Answer:

-g-8≥9

Step-by-step explanation:

Just ask!

Hope this helps.

Please answer this, The question is below............................................................................. .........

Answers

Answer:

Area of a parallelogram = Base times Height

Step-by-step explanation:

For this parallelogram, the value for Height is 5cm. So Area = Base x 5. If you are given the value for base then just multiply that by 5 and you get the area. Hope this helps :)

PLEASE HELP ILL DO THE SAME PLEASE AND I NEED STEP BY STEP IM TRYING TO LEARN :(

Answers

Answer:

5)

Line 1: [tex]y=-x+3[/tex]

Line 2: [tex]y=3x-3[/tex]

6)

Line 1: [tex]y=\frac{1}{2}x-2[/tex]

Line 2: [tex]y=-\frac{5}{2}x+6[/tex]

7)

See below

Step-by-step explanation:

To write the system of equations on the graph, you just need to write the 2 equations of the 2 lines.

5)

The first thing to do is find the slope of the lines. Pick one of them, and start by finding 2 points on that line that land perfectly on the grid.

It's pretty hard to read that top graph in the photo, but I think I see these ones marked:

Line 1: (0, 3) and (3, 0)

Line 2: (0, -3) and (2, 3)

Make sure I got them correct, because the equations will be wrong otherwise. Same for problem 6. To find the slope, divide the change in y by the change in x. Starting with line 1, y went from 3 to 0, so a change of -3. x went from 0 to 3, so a change of 3.

Divide the change in y by the change in x:

[tex]m=\frac{y2-y1}{x2-x1}\\\\m=\frac{0-3}{3-0}\\\\m=\frac{-3}{3}\\\\m=-1[/tex]

The slope of line 1 is -1. That means every time x increases by 1, y decreases by 1. You can see that on the line.

Now for line 2:

[tex]m=\frac{3--3}{2-0}\\\\m=\frac{6}{2}\\\\m=3[/tex]

When x increases by 1, y increases by 3.

The last thing to do is find the y-intercept of both lines. That's just where the line intersects the y-axis, at x = 0, and it's clearly visible on the graph so there isn't much to do.

Line 1: 3

Line 2: -3

Now, you can write the equations for these lines in slope intercept form:

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept we found above.

Line 1: [tex]y=-x+3[/tex]

Line 2: [tex]y=3x-3[/tex]

In line 1, -1x can be simplified to just -x.

6)

I'll do the exact same process here, but with less explaining. Let me know if you have any questions.

Find 2 points:

Line 1: (0, -2) and (4, 0)

Line 2: (0, 6) and (4, -4)

Find the slope of line 1:

[tex]m=\frac{y2-y1}{x2-x1}\\\\m=\frac{0--2}{4-0}\\\\m=\frac{1}{2}[/tex]

and line 2:

[tex]m=\frac{-4-6}{4-0}\\\\m=\frac{-10}{4}\\\\m=-\frac{5}{2}[/tex]

Now, the y-intercepts:

Line 1: -2

Line 2: 6

Write the equations:

Line 1: [tex]y=\frac{1}{2}x-2[/tex]

Line 2: [tex]y=-\frac{5}{2}x+6[/tex]

7)

A system with 1 solution means 2 lines that intersect at 1 point. Problems 5 and 6 are both examples of this. A system with no solution means lines that never intersect, meaning that they have the same slope, they're parallel.

Example:

[tex]y=2x+1\\y=2x+2[/tex]

Those both have a slope of 2, and if you graph them, you'll see that they never intersect.

A system with infinitely many solutions means they intersect at every possible point. These would just be the same line.

Example:

[tex]y=2x+1\\y=2x+1[/tex]

That's what they are, graph them however you like.

the vertex angle of isosceles triangle is 110. what are the measures of the base angles

Answers

Two sides are equal in an isosceles triangle. This means that the angle both sides make with the third side must be the same. Since the angles in a triangle add up to 180°, you can subtract 110° from 180° and divide your answer by two. The resulting number will be the measure of each of the two unknown angles

Marking brainliest

What do you thinks this means and why does it matter

Answers

Answer:

You didnt put anything for me to see lol

Step-by-step explanation:

Two numbers x and y, have a sum of 23 and a difference of 7. x is greater than y
a. write two equations in x and y
b. solve your equations to find to values of x and y

please tell me the answer and explain how you got it thanks

Answers

Answer:

Below in bold.

Step-by-step explanation:

Use the elimination method:

a.   x + y = 23

     x - y = 7

b.  Adding the 2 equations eliminates y, so we have

     2x = 30

        x = 15.

     Substitute x = 15 in equation a:

      15 + y = 23

         y = 23 - 15

        y =  8.

       Answer x = 15, y = 6.

Step-by-step explanation:

this is what you are told in the problem

x+y=23............1 (the sum)

x-y=7.................2 (the difference)

PS make sure to number your equations

in equation 1 we can take x over so that we form a new equation labelled equation 3

y=23-x...........3

sub 3 into 2

x-(23-x)=7

x-23+x=7

2x=7+23

2x=30

x=15.........4

sub 4 into 1

15+y=23

y=23-15

y=8

what's 9 plus 10 and not 21

Answers

Answer:

19

Step-by-step explanation:

A sticker costs 25 cents. How many dollars is that?

Answers

Answer:

Boy.... Its one forth a dollar.

Step-by-step explanation:

1/4

The cylinder and the sphere below have the same radius and the same volume. What is the height of the cylinder?
a.6m
b.8m
c.9m
d.4m​

Answers

ANSWER:

9m is the answer

7/14 in its simplist form

Answers

Answer:

1/2

Step by step explanation:

Answer:

1/2

Step-by-step explanation:

i’m struggling with this question. can you please help me?

Answers

Answer:

50°

Step-by-step explanation:

∠ RST = (arc QC - arc RT) / 2

          = (150° - 50°) / 2

          = 50°

Find the x and y intercepts of each equation

Answers

Step-by-step explanation:

the y-intercept is the y value when x = 0.

the x-intercept is the x Banjul when y = 0.

now we only need to put the corresponding 0-value into the equations and calculate the other value.

a.

x = 0, y = 10

y = 0, x = 5 because

0 = 10 - 2x

2x = 10

x = 5

b.

x = 0, y = 2 because

9y = 18

y = 0, x = 18/4 = 9/2 because

4x = 18

c..

x = 0, y = -22 because

-2y = 44

y = 0, x = 44/6 = 22/3 because

6x = 44

3x = 22

d.

x = 0, y = -4/12 = -1/3 because

0 = 4 + 12y

y = 0, x = 4/2 = 2 because

2x = 4

x = 2

A football team caught the ball in 60% of the
plays during a game. Based on this information, if
the team caught the ball in 15 plays, how many
total plays did the team have?

Answers

Answer: 25 Plays Total.

60% of 25 is 15

10% of 25 = 2.5

2.5x6=15

Hope This Helps.

Find the volume of a cylinder whose radius is 2 cm and whose height is 6 cm (use ╥=3.14 and give the answer to the nearest hundredth).

Answers

V = πr²h

V = 3.14 · 2² · 6

V = 3.14 · 24

V = 75.36

Hope this helps!

Answer: 75.36

Step-by-step explanation:

Ed and Sally are taking a tour of Paris. There are 333 different types of tours (walking tour, bike tour, and trolley tour) and 222 different times each tour is offered (morning and evening). They each created a display to represent the sample space of randomly picking a type of tour and a time.
Whose display correctly represents the sample space?

Answers

Answer: the answer is sally only

What is the value of the expression below?

(8+1/8) divided by (2.5+3/4)
2.5
4.875
11.375
26.4

Answers

Answer:

2.5

Step-by-step explanation:

(8+1/8) = 8.125

(2.5+3/4) = 2.5 + 0.75 = 3.25

8.125 / 3.25 = 2.5

Help?please rnnnn………

Answers

Answer:

8,176

Step-by-step explanation:

You have to first do 8 × 5110 = 40,880

Then you divide 40,880 by 5

40,800 ÷ 5 = 8,176

Sally bought two shirts that cost $6.99 each. The sales tax rate was 7%. What was the total amount Sally paid?Question 3 options:$0.98$7.48$14.05$14.96

Answers

Answer: $14.96

Step-by-step explanation:

13.98 + .98 = 14.96

The total amount paid by Sally is $ 14.96

What is Sales Tax?

The Sales tax is calculated by the equation

Sales tax rate = Sales tax percent / 100

Sales tax = List price x Sales tax rate

Given data ,

List price of the shirt Sally bought = $ 6.99

Number of shirts Sally bought = 2 shirts

Total price of 2 shirts = 2 x 6.99

                                    = $ 13.98

So , List price = $ 13.98

Sales tax rate = 7 %

Total amount paid by Sally = List price + Sales tax

Now , Sales tax is calculated by

Sales tax = List price x Sales tax rate

                = 13.98 x 0.07

                = 0.9786

Therefore , total amount paid by Sally = List price + Sales tax

                                                               = 13.98 + 0.9786

                                                               = $ 14.9586

                                                               ≈ $ 14.96

Hence , the total amount paid by Sally is $ 14.96

To learn more about Sales tax click :

https://brainly.com/question/27092799

#SPJ5

What is the expression after applying the distributive property? −12(−2+(−3))

Answers

Answer:

60

Step-by-step explanation:

-5.-12=60

Hey there!

-12(-2 + (-3))

= -12(-2 - 3)

DISTRIBUTE -12 within THE PARENTHESES

= -12(-2) - 12(-3)

= 24 + 36

= 60

Therefore, your answer is: 60

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

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