Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 4 and 3 - I.

f(x)=

Answers

Answer 1

Answer:

f(x) =  x³ - 6x² + 5x + 12

Step-by-step explanation:

Given polynomial function f(x) with:

a = 1, r₁ = 4, r₂ = 3, r₃ = -1

With the least degree it is:

f(x) = 1*(x - 4)(x - 3)(x - (-1)) =         (x² - 7x + 12)(x + 1) =          x³ - 6x² + 5x + 12

Related Questions

Which equations are true equations?

Select all correct answers.


62−22=4+7⋅22

54 ÷ 6 + 3² = 4 + 4²

8042=10−22−1

19−2⋅5=9⋅73−9

Answers

We want to see which ones of the given equations are true equations. Here we will see that the only true equation is the second one:

54 ÷ 6 + 3² = 4 + 4²

We define a true equation as an equation where the thing at the left is equal to the thing on the right, so we need to check that for all the given equations.

1) 62 − 22 = 4 + 7⋅22

We just solve each side, we will get:

40 = 158

This is not a true equation.

2) 54 ÷ 6 + 3² = 4 + 4²

   9 + 9 = 4 + 16

   18 = 18

This is a true equation.

3) 8042 = 10 − 22 − 1

Clearly, this is not a true equation.

4) 19 − 2⋅5 = 9⋅73 −9

   19 - 10 = 657 - 9

           9 = 648

This is not a true equation.

Then the only true equation is the second one:

54 ÷ 6 + 3² = 4 + 4²

If you want to learn more, you can read:

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What Is the value of x?
A: x = 2.25
B: x = 11.25
C: x = 13
D: x = 22

Answers

Step-by-step explanation:

I have shown all the steps of obtaining the value of X in the picture above therefore the value of x is 22 which means the answer iisD

When William had one cat, he needed to serve 1/8 of a can of cat food each day. Now that William has adopted a second cat, he needs to serve a total of 2 7/8 cans each day. How much extra food is needed to feed the second cat?

Answers

2 7/8 - 1/8 = 2 6/8 cans of cat food

Which of the numbers below is greater than 0.75? Select all that apply. A) 32 B) −0.5 C) 1.2 D) −14 E) −2.4

Answers

Answer:

A and B

Step-by-step explanation:

becuz

Is that the correct answer for it please help me. I want to past my ecam

Answers

Answer:

No answer is be 28%

5+9+7+4=25

7/25 + .28 =28%

Step-by-step explanation:

HELPPP IM BEGGING U LOOK AT THE PIC BABES

Answers

Answer:

2nd option

Step-by-step explanation:

in the figure below red points are for ΔC"D"E"

we have to go in reverse order

to convert ΔC"D"E" to ΔC'D'E'

we have to scale the given triangle to a scale factor of 2

by multiplying vertices with 2

which gives blue points in the figure

next for 90° counter clockwise of ΔC'D'E' we get ΔCDE

for that we have to interchange x and y in the vertices

(2,2), (4,6), (-2,6) initial

(-2,2), (-6,4), (-6,-2) after

2nd option

10 Jim was thinking of a number. Jim subtracts 14 from it and gets an answer of 43.9. What was the original number?

Answers

57.9 add 14 to the answer and you get your number

Two numbers have a sum of 24 and a difference of 5. Use and algebraic method to find the two numbers.

Answers

Step-by-step explanation:

x, y are the 2 numbers

x + y = 24

x - y = 5

x = y + 5

and that in the first equation

y + 5 + y = 24

2y = 19

y = 9.5

x = y + 5 = 9.5 + 5 = 14.5

the 2 numbers are 9.5 and 14.5.

A rectangle of dimensions 60 units x 40 units is drawn on grid paper with vertices in
the nodes of the grid. A cell of the grid is 1 unit * 1 unit. A diagonal of the rectangle is
drawn. How many cells have been cut into two (not necessarily equal) parts?

Answers

The number of cells which have been cut into two parts is approximately ; 72 units

According to the question;

The rectangle has dimensions 60 units x 40 units.

Provided a cell of the grid is 1 unit * 1 unit.

When a diagonal of the rectangle is drawn;

The number of cells which have been cut into 2 pieces is the length of the diagonal of the rectangle.

Diagonal, D² = 60² + 40²

D² = 3600 + 1600

D² = 5,200

D = √5200

D = 72.11 units

Read more;

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Answer: 80

see attached

Step-by-step explanation:

If you do a 3x2 units, and draw a diagonal line, you'll see 4 units are cut.  because it's 60x40, then means BOTH lengthwise & widthwise you'll repeat 20 times, so 20*4 units = 80 units.

Yall i need help asap! please help​

Answers

3) 1010000

4) 1582

I helped

Solve. −4x−21=91 Enter your answer in the box. x =

Answers

Answer:

X = -27

Explain your answer:

Answer:

x = -28

Explanation

K12

The lenght of a rectangle exceeds it width by 2cm. If area of the rectangle is 80 cm The lenght of the rectangle is ?​

Answers

Answer:

[tex]x4 - (9x5)[/tex]

yan npo wag puro brainly

Answer:

The answer is l =40cm

How do you solve for x?

2(x - 3)^2 - 32 = 0

Answers

[tex] \: \: \: \: \: \: \: \: [/tex]

[tex]x = - 1 \\ x = \: 7[/tex]

Step-by-step explanation:

[tex]2(x - 3 {)}^{2} - 32 = 0[/tex]

divide both sides

[tex](x - 3 {)}^{2} - 16 = 0[/tex]

use - b² =(a - b ) (a + b) to factor the expression

[tex](x - 3 - 4) \times (x - 3 + 4) = 0[/tex]

calculate the difference and the sum

[tex](x - 7) \times (x + 1) = 0[/tex]

when the product of factors equals 0 ,at least one factor is 0

[tex]x - 7 = 0 \\ x + 1 = 0[/tex]

solve the equation for x

[tex]x = 7 \\ x + 1 = 0[/tex]

the equation has 2 solutions

[tex]x = - 1 \\ x = 7[/tex]

hope it helps

[tex] \: \: \: \: \: \: \: [/tex]

based on the information in the table is the cost of the pizza proportional to the number of toppings?

Answers

I could help you out but there is no table to go off of.

I NEED HELP please, take 50 points if you answer It and a 50/50 at a brainiest.

"The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario.

Which graph represents this wage increase for x < 12?"

-normally I'd just double-check this but. . . you get it.

Answers

Red dots are starting co-ordinates and whites are ending co-ordinates .

So the graph must have red dots at the start of line and not mandatory for at the end of line.

x<12

It should not be at end

Check option B

x ends at first point .

And also the interval is 2

so Option B is correct

There are 377 toys that Janet collected at the carnival. She wants to put them in 12 bags. After she splits them into bags, how many toys does she have left to give to her little brother?

Answers

Answer:

D. 31 toys

Step-by-step explanation:

377   ÷   12 =

31.41666666666667

given:

377 toys

12 bags

to find:

how many toys she'll have left to give her little brother.

solution:

[tex] \frac{377}{12} [/tex]

[tex] = 31.4166666667[/tex]

[tex]nearest \: whole \: number = 31[/tex]

hence, she'll have 31 toys left to give her little brother.

answer= option D

Mia bought 6 pounds of bananas for $3.54. How much does 1 pound of bananas cost?

Answers

Answer:

$0.59

Explanation:

$3.54 divided by 6 is $0.59. This concludes that 1 pound is $0.59. Hope this helps!

The cost of 1 pound of banana will be $0.59 per pound.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Mia bought 6 pounds of bananas for $3.54.

The cost of 1 pound of banana is given by the division of the total cost for 6 pounds and 6. Then we have

⇒ $3.54 / 6

⇒ $0.59 per pound

The cost of 1 pound of banana will be $0.59 per pound.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Diane has $12 to spend on a mixture of green and red grapes. What equation can she use to graph a line showing the different amounts of green and red grapes she can buy for $12. Green grapes cost $3/lb and red grapes cost $2/lb.

Answers

Answer:

y ≥ [tex]\frac{3}{2}[/tex]x + 6

Step-by-step explanation:

12 ≥ 3x + 2y

Money available ≥ cost of green grapes + cost of red grapes

To turn this into slope-intercept form,

12 ≥ 3x + 2y

2y ≥ -3x + 12

y ≥ [tex]\frac{3}{2}[/tex]x + 6

Graphed - see attached

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

12 times 3 divided 12 = time 2 by what u get

Sorry, ignore the other question I had on here, that was a typo. How do you find the positive/negative intervals of f(x) = 3/(x + 5) ? Please show in full detail!!

Answers

Answer:

Positive interval: x is in (-5, infty)

Negative interval: x is in (-infty, -5)

Step-by-step explanation:

A fraction is positive when the numerator and denominator have the same sign. Since the numerator is positive in this case, the fraction will be positive when it's denominator is also positive. Thus, we need to solve x+5>0. Subtracting 5 on both sides gives x>-5.

Positive interval: x is in (-5, infty)

A fraction is is negative when the numerator and denominator have the different signs. Since the numerator is positive in this case, the fraction will be negative when it's denominator is negative. Thus, we need to solve x+5<0. Subtracting 5 on both sides gives x<-5.

Negative interval: x is in (-infty, -5)

A fraction doesn't have an output when it's denominator is 0. That is, in this case when x+5=0 which is when x is -5.

what is (x-2) (3x-4)=
a.3x² - 6x-8
b.3x² - 2x - 8
c.3x² + 10x + 8
d.3x² - 10x + 8

Answers

Answer:

D. 3x^2-10x+8

Step-by-step explanation:

[tex] \: \: \: \: \: [/tex]

D. 3x²- 10x + 8

hope it helps

refer to the attachment

[tex] \: \: \: \: \: [/tex]

Mahmoud uses 3 cups of apple juice for every 4 cups of cranberry juice
.
to make a fruit drink.
a
How many cups of apple juice does Mahmoud use for 21 cups of the
combined fruit drink?

Answers

Answer:

9 cups of apple juice

Step-by-step explanation:

Y=6 z=7 h=0 what is y+h

Answers

Evaluate

[tex] \sf \longmapsto \: y + h[/tex]

When

[tex]y = 6[/tex][tex]z = y[/tex][tex]h = 0[/tex]

Let's start.

[tex] \sf \longmapsto \: y + h[/tex]

Put the values

[tex] \sf \longmapsto6 +0[/tex]

Answer

[tex] \sf \longmapsto6[/tex]

But there is no use of z = 7 . Z is excluded from y+h.

Snow fell for 9 hours at a rate of 12 inch per hour. Before the snowstorm began, there were already 8 inches of snow on the ground. The equation y=12x+8 models the depth y of snow on the ground after x hours. Explain what the slope and y-intercept mean in this snowstorm model.

Answers

Answer:

The slope of the model represents the amount of snow(in inches) added to the ground per hour

the y-intercept represents the beginning amount of snow already on the ground

Step-by-step explanation:

I’m really bad at math please help me

Answers

x=20

Hope this helps!!

Jean and Jericho who are playing in the school grounds decided to sit on a
seesaw. Jean, who is heavier, tends to raise Jericho on the other end of the seesaw.
They tried to position themselves in order to balance the weight of each other.

Questions: Underline the correct answer.

1. This situation illustrates (direct, inverse) variation.
2. The two quantities that must vary in this situation are (weight and
distance from the center, height and weight).
3. The heavier the kid, the (closer, farther) he/she should be at the
center to balance the seesaw?
4. When Jean moves farther from the center, Jericho tends to go (up,
down).
5. If Jericho moves closer to the center, Jean tends to go (up, down).

Answers

We want to see underline the correct part in each statement.

1) This situation illustrates (direct, inverse) variation.2) The two quantities that must vary in this situation are (weight and distance from the center, height and weight).3) The heavier the kid, the (closer, farther) he/she should be at the center to balance the seesaw?4) When Jean moves farther from the center, Jericho tends to go (up, down).5) If Jericho moves closer to the center, Jean tends to go (up, down).

So, Jean and Jericho are playing on a seesaw.

Jean is heavier than Jericho.

Now, notice that a seesaw is a lever. So it "amplificates" the force that you apply in one end to lift the weight that is on the other end. Depending on the form of the lever and the weights, the force that you need to do changes.

If we define:

W₁ = Jean's weight.d₁ = Jean's distance to the center.W₂ = Jericho's weight.d₂ = Jericho's distance to the center.

We must have:

W₁*d₁ = W₂*d₂

Then:

1) This situation illustrates (direct, inverse) variation.

d₁, the position of Jean, varies inversely with respect to Jean's weight.

2) The two quantities that must vary in this situation are (weight and

distance from the center, height and weight).

(by the equation above)

3) The heavier the kid, the (closer, farther) he/she should be at the

center to balance the seesaw?

By the given equation, we see that d₁ must be smaller than d₂.

And the last two are trivial:

4) When Jean moves farther from the center, Jericho tends to go (up,

down).

5) If Jericho moves closer to the center, Jean tends to go (up, down).

If you want to learn more, you can read:

https://brainly.com/question/18320907

If -2 - 4x = -8x + 3x,
then what is X-2?

Answers

Answer:

-0.8

Step-by-step explanation:

-2 -4 = -8x + 3x

-6 =-5x

x = 1.2

so x-2 =

1.2 -2 = -0.8

Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points?

–1.5
–0.5
0.5
1.5

Answers

Answer:

1.5

1.5

Step-by-step explanation:

The steps are in the image above

The slope of the line through these two data points is 1.5.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

x represents the time and y represents the temperature in degrees Fahrenheit.

temperature of –2°F at 8 a.m. Hence:

-2 = 8m + b   (1)

it was 4°F at 12:00 p.m. Hence:

4 = 12m + b  (2)

Solving equations 1 and 2 simultaneously gives:

m = 1.5, b = -14

The slope of the line through these two data points is 1.5.

Find out more on linear equation at: https://brainly.com/question/14323743

Heyy help me do this question please and thanks

Answers

Answer:

[tex]2.757*10x^{-4}[/tex]

The average rate of change of g(x) between x = 4 and x = 7 is Five-sixths. Which statement must be true?.

Answers

What are the options, if 3 is up their then it would be 3

Jodie wants to raise money for a school trip by selling raffle tickets at a basketball game. She sells each ticket for 50 cents, and she sells two and a half rolls of tickets. If each roll of ticket has 200 tickets, how much money did Jodie make?

Answers

Answer:

250 dollars

Step-by-step explanation:

t = tickets

t = 200

Two and a half rolls tickets = (200 x 2) + 200/2) = 400 + 100 = 500

500 tickets x 50 cents = 25000 cents

convert cents to dollars (move decimole point over left 2 units)

25000 = 250 dollars

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