The quadratic function g(x)=ax^2+bx+c has the complex roots (10+i) and (10-i). You may assume that a=1.
What is the value of b?
What is the value of c?

Answers

Answer 1

The values are [tex]b=-20\text{ and }c=101[/tex]

The quadratic function, expressed in factored form is

[tex](x-(10+i))(x-(10-i))=g(x)[/tex]

Expanding and simplifying

[tex]g(x)=(x-(10+i))(x-(10-i))\\=x^2-x(10-i)-x(10+i)+(10+i)(10-i)\\=x^2-10x+xi-10x-xi+100-i^2\\=x^2-10x-10x+100+1\\=x^2-20x+101[/tex]

since

[tex]g(x)=ax^2+bx+c=x^2-20x+101[/tex]

we can equate coefficients of like-terms and conclude that

[tex]a=1,b=-20,c=101[/tex]

Learn more about quadratic equations here: https://brainly.com/question/12995618


Related Questions

which multiplication can be used to explain the solution to 15 divided by one over 3

Answers

Answer:

3x5=15

5x3=15

Step-by-step explanation:

what is the equation

Answers

Answer:

y = -2x+9

Step-by-step explanation:

To figure out equations of tile patterns simply count the initial value and the rate of change, then convert it into (slope intercept form) which is

y = mx+b

In this case the rate of change is -2x because each figure loses 2 blocks as it goes.

You can also see the the initial figure 1 has 9 blocks so this is our constant

With this information we can create the equation y = -2x+9

m = -2

x = x

b = 9

If more aid is needed a simple search of (Visual Pattern - Writing an Equation and Creating a Table) will help you with a video easily.

Write the slope-intercept form of the equation with the given point and slope. Through (2,5) and m=1/2

Answers

Answer:

y=1/2x+4

Step-by-step explanation:

y-y1=m(x-x1)

y-5=1/2(x-2)

y=1/2x-2/2+5

y=1/2x-1+5

y=1/2x+4

Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.

If you're satisfied with the answer, then please mark me as Brainliest. Thank you.

The population of a city, y, in thousands of people, measured x years after 1800 can be modeled by the regression equation
y = 187.6/1 + 29.4e^-0.03x

Which statement best interprets a value in the equation?

The city population in 1800 was 187,600 people.
The city population grows by 29,400 people per year.
The limiting value of the city population is 29,400 people.
The limiting value of the city population is 187,600 people.

Answers

Answer:

D. The limiting value of the city population is 187,600 people.

Step-by-step explanation:

I'm honestly not sure, but it's based on the 187.6 on top of the equation. Correct on Edge 2021

Solve for x when 4x+16/12=x-4

Answers

Answer:

In short, Your Answer would be either 1 or 7

Step-by-step explanation:

|4x + 12| = 16

As it is in modulus function, it could be either +ve or -ve

4x+12 = 16   OR   4x - 12 = 16

4x = 16-12    OR   4x = 16 + 12

4x = 4           OR   4x = 28

x = 4/4     OR  x = 28/4

Is it a expression 3x - 7

Answers

Answer:

It’s an expression.

Step-by-step explanation:

An expression is technically an equation but without the answer.

Answer:

yes

Step-by-step explanation:

The difference between an equation and an expression is that an equation as an equals sign. An equation shows that 2 expressions are equal to each other.

Expression:

[tex]3x-7[/tex]

Equation:

[tex]3x-7=5y[/tex]

what is -150 + -12 =?

Answers

Answer:

-162

Step-by-step explanation:

Answer:

your answer is -162

Step-by-step explanation:

if you owe someone 150 dollars and then you owe them another 12 dollars you'll owe them a total of 162 dollars. Your losing 162 dollars which is -162 form the amount that you have


If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books?

Answers

Answer:

23 days

Step-by-step explanation:

Given,

No. of days taken by Jenny to read 7 books

= 8

So,

No. of days taken by her to read 1 book

[tex] = \frac{8}{7} [/tex]

Therefore,

No. of days taken by her to read 20 books

[tex] = \frac{8}{7} × 20 [/tex]

[On Simplification]

[tex] = \frac{160}{7} [/tex]

[On dividing]

= 22.85.....

[On approximating]

= 23 days (approx. )

Hence,

Jenny will take 23 days to read 20 books (Ans)

Question:-

If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books?

Answer:-

22.85714 or 23 days

Explanation:-

[tex]GIVEN,[/tex]

Number of books Jenny can read in 8 days = 7

[tex]NOW,[/tex]

Number of days taken by Jenny to read 1 book = [tex] \frac{8}{7} [/tex]

Number of days taken by her to read 20 books =

→ [tex]20 \times \frac{8}{7} [/tex]

→ [tex] \frac{160}{7} [/tex]

22.85714 or 23 days

HELP ME PLEASE

WHAT IS THE VALUE OF X ?

Answers

Answer:

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X

Step-by-step explanation:

Question 34, the answer is C. I just need the working. Tysm

Answers

Answer:

C

Step-by-step explanation:

∠ ABC = 90° ( angle in a semicircle )

Using the cosine ratio in right triangle ABC and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{10}{AC}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

AC × [tex]\sqrt{3}[/tex] = 20 ( divide both sides by [tex]\sqrt{3}[/tex] )

AC = [tex]\frac{20}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ( rationalising denominator )

AC = [tex]\frac{20\sqrt{3} }{3}[/tex]

radius AO = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × [tex]\frac{20\sqrt{3} }{3}[/tex] = [tex]\frac{10\sqrt{3} }{3}[/tex] → C

Foundations in Algebra: Probability Assignment
1. Andrew claims:
A spinner has 4 sections -
red, yellow, green, and blue.
The probability of getting the
red section is 0.25.
Is he correct? Explain your answer fully:
I

Answers

Answer:

yes a 1/4 probability is 0.25

Read aloude The price of a cell phone was reduced from $450 to $225. By what percentage was the price of the cell phone reduced? ​

Answers

Answer:

50% 250x2=450

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

$225 x 2 = 450

this means the cell phones price was reduced by 50%

glad to help ;)

Graph: y = 3 * x + 5 ​

Answers

Answer:

2

Step-by-step explanation:

take the 3 put on the side

In a hypothetical economy, current inflation-adjusted economic output is rising and is expected to continue rising in the coming months. This economy is currently in the___

peak stage of the business cycle

trough stage of the business cycle

contraction stage of the business cycle

expansion stage of the business cycle

Answers

The economic output is rising and is expected to continue rising in the coming months, the economy is currently in the expansion stage of the business cycle.

The business cycle consists of the following stages which changes with time;

Expansion stage: continuous rise in economic output.Peak stage: maximum economic output.Contraction (recession) stage: a continuous decline in economic output.Trough stage: the point of lowest economic output.

Thus, when the economic output is rising and is expected to continue rising in the coming months, the economy is currently in the expansion stage of the business cycle.

Learn more about business cycle here: https://brainly.com/question/904465

Question 6 of 12
✓ 49
A. 8
O O
B. 14
C. 7
SUBMIT

Answers

Answer:

C. 7

Step-by-step explanation:

7 · 7 = 49

I hope this helps!

Factorise

3-x^2

Someone answer this question please

Answers

Answer:

No factors.

3 - x^2 is prime.

Step-by-step explanation:

HOPE I MADE YOU SMILE!!

Answers

Answer:

ok points

Step-by-step explanation:

Answer:

Thank You so much.....You made me smile lol :D

Write a multiplication equation that corresponds to each division equation.
10 divided by 5 =
4.5 divided by 3 =
3 ½ divided by 4

Answers

Answer:

1. 10/1×1/5

2.5/1×1/3

3.1/2×1/4

Step-by-step explanation:

to turn it into a multiplication problem, turn the second fraction into its reciprocal (flip the numerator and denominator )

A rectangle has a perimeter of 44 inches and an area of 72 square inches. What are the lengths of the sides of the rectangle?

A) 2 inches and 36 inches
B) 4 inches and 18 inches
C) 8 inches and 9 inches
D) 11 inches and 11 inches

IT IS NOT D, I TRIED IT AND IT DOESNT WORK!

Answers

A rectangle has a perimeter of 44 inches and an area of 72 square inches.Perimeter = 44 inches, area = 72 square inches.Let the length and breadth be l and b respectively.We know, perimeter of a rectangle = 2(l + b)Therefore,2(l + b) = 44

or, l + b = 22

or, b = 22 - l ...(i)

We know, area of a rectangle = lbTherefore,lb = 72Putting (i) in b, we getl(22 - l) = 72

or, 22l - l^2 -72 = 0

or, l^2 - 22l + 72 = 0

or, l^2 - 4l - 18l + 72 = 0

or, l(l - 4) - 18(l - 4) = 0

or, (l - 4)(l - 18) = 0

or, l = 4 or l = 18

Therefore, if the length is 4 inches, then the breadth is (22-4) inches, i.e., 18 inches.And if the length is 18 inches, then the breadth is (22-18) inches, i.e., 4 inches.

Answer:

B) 4 inches and 18 inches.

Hope you could get an idea from here.

Doubt clarification - use comment section.

calculate the state income tax owed on a $50,000 per year salary (answer is not 2500)

Answers

The total tax paid is $2,300 on the yearly salary of $50,000

What tax rate applies to the first $10,000 of salary?

The first $10,000 of the salary would be charged to tax at 3% whereas the next threshold beyond $10,000 up until $50,000, in other words, the difference between the first $10,000 and $50,000, which is $40,000 is taxed at 5%.

The tax on the first $10,000 is computed as shown below:

tax on the first $10,000=$10000*3%

tax on the first $10,000=$300

The tax on the remaining $40,000 is 5% of the amount

The tax on the remaining $40,000=5%*$40,000

The tax on the remaining $40,000=$2,000

In other words, the total tax paid on the $50,000 annual salary is the sum of $300 and the $2000

total tax paid=$300+$2,000

total tax paid=$2,300

Find out more about personal income tax on:https://brainly.com/question/13793671

#SPJ1

Name three equal ratios from the graph

Answers

250:10

125:5

100:4

Step-by-step explanation:

ratio of y to x

How is the key event in this paragraph illustrated?

Answers

I think C because it dose seem to be showing sometime of an historical event. But of course I could be wrong.

my Christmas present to you​

Answers

Answer:

THX santa

Step-by-step explanation:

convert 3 3/4 into a improper fraction

Answers

Answer:

3 3/4 = 15/4

Step-by-step explanation:

To turn a mixed number into an improper fraction, multiply the whole number with the denominator of the proper fraction. Add the numerator of the proper fraction to this product to obtain the numerator of the improper fraction.

Hoped this helped.

Jamal sold a total of $9,500 worth of clothing last week at his store.if his commission is 12% of sales,how much commission did he earn?

Answers

Answer:

9,500x12%= $1,140

He earned $1,140

Step-by-step explanation:

Determine the measure of the angles.

Answers

Answer:

121 for both

Step-by-step explanation:

if we split the shape in the middle, we get two congruent triangles.

divide each angle by 2, and you will get 24 and 35.

The rule of angles within a triangle is that all of them must equal 180.

so

180-(24+35)

180-59

=121 degrees for both k and m

:)

Answer:

The answer is 121 for both k and m!! Hope this helps

Step-by-step explanation:

Add 70 and 48 which is 118 then subtract it to 360(always) which is 242 then divide it by 2 since theres 2 sides which you get 121

you are going to wash a large glass window in a shape of a trapezoid. The lenghts of the bases of the window are 10 feet and 14 feet. the height is 8 feet. you can wash 6 square feet of the window in 1 minute. how long will it take you to wash the entire window

Answers

Answer:

16 minutes

Step-by-step explanation:

First we are going to want to find the area of the window. We then divide that by the amount of area you can wash per minute ( 6 square feet )

So first lets find the area.

We are told that the window is in a shape of a trapezoid.

The area of a trapezoid can be calculated using the formula A = [tex]\frac{a+b}{2} h[/tex]

Where a and b are the base lengths and h is the height

We are told that the length of the bases are 10 ft and 14ft so a and b = 10 and 14. We are also told that the window has a height of 8 so h = 8 .

We then plug these numbers into the formula to find the area

Recall formula: [tex]A=\frac{a+b}{2} h[/tex]

a = 10 , b = 14 and h = 8

plug in these values into formula

[tex]A=\frac{10+14}{2} 8[/tex]

add 10 and 14 to get 24

[tex]A=\frac{24}{2} 8[/tex]

simplify fraction : 24 / 2 = 12

[tex]A=(12)(8)[/tex]

multiply 12 and 8 to get 96.

A = 96 square feet.

To find how long it would take to wash the window we divide the total area of the window by the amount of area that can be washed per minute

Total area of window = 96

Area that can be washed per minute = 6

Time it would take to wash the whole window = 96 / 6 = 16 minutes

Leon has to drive 36 miles to work. If he can average a speed of 48 miles per hour, about how long does it take him to get to work each day? (Hint: Use the formula d = rt.)

1. a quarter of an hour
2. three-fourths of an hour
3. half an hour
4. more than an hour

Answers

Answer:

i think the answer is 45 mins sorry if im wrong

2) If it is 12° outside and the temperature is going to -7° drop 19º. What will the new temperature be? ​

Answers

Answer:

69 degrees

Step-by-step explanation:

yeah

It takes violet 3/5 hour to paint a chair. How much of the chair will be finished after 1/3 hour? Plz answer this plzzzzz!!

Answers

The anwser is c your welcome
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