Write a polynomial f(x)that satisfies the given conditions,
Polynomial of lowest degree with zeros of - 4 (multiplety 1), 3 (multiplicly 3), and with f(0)= 216,

Answers

Answer 1

Answer:

[tex]\boxed{\sf \ \ \ -2(x+4)(x-3)^3 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's note k a real, we can write the polynomial as

[tex]k(x-(-4))^1(x-3)^3=k(x+4)(x-3)^3[/tex]

and we know that f(0)=216 so

[tex]216=k(0+4)(0-3)^3=k*4*(-1)^3*3^3=-27*4*k=-108k\\\\<=> k=-\dfrac{216}{108}=-2[/tex]

So the solution is

[tex]-2(x+4)(x-3)^3[/tex]

hope this helps


Related Questions

Peter makes a large amount of pink paint by mixing red and white paint in the ratio 2 : 3. Red paint costs £80 per 10 litres. White paint costs £5 per 10 litres. Peter sells his pink paint in 10-litre tins for £60 per tin. Calculate how much profit he makes for each tin he sells

Answers

Answer: £25

Step-by-step explanation:

Given the following :

pink paint production = mixing red and white paint in the ratio 2 : 3

Price of red paint = 80 per 10 Litre

Price of white paint = 5 per 10 Litre

Selling price of pink paint = £60 per 10 litre

Recall the ratio of red to white paint :

2 : 3 ; 2 +3 = 5

Therefore,

Amount of Red paint used:

= (2/5) × 10 ; 20/5 = 4,

Cost per Litre = 80 / 10 = £8

Cost of red paint = 4 × 8 = £32

Amount of white paints used:

= (3/5) × 10 ; 30/5 = 6

Cost per Litre = 5 / 10 = £0.5

Cost of white paint = 6 × 0.5 = £3

Total cost of production = £(32 + 3) = £35

Profit = selling price - product cost

Profit = £(60 - 35) = £25

2.2 units to the right of 0 horizontal number line

Answers

Answer:

2.2

Step-by-step explanation:

2.2 units to the right of zero indicates that the integer is positive on a horizontal number line.

0 + 2.2 = 2.2

Find the area of the regular polygon.
32

Answers

Answer: 45

Step-by-step explanation: that is correct

Helppp!!!! please!!!

Answers

Answer:

A) 120 ft^2

Step-by-step explanation:

The total surface area is the sum of the areas of the 4 congruent triangular sides and the area of the square base.

TA = 4 * area of triangle + area of square

TA = 4 * bh/2 + s^2

TA = 4 * 6 ft * 7 ft/2 + (6 ft)^2

TA = 84 ft^2 + 36 ft^2

TA = 120 ft^2

Answer:

A) 120 ft^2

Step-by-step explanation:

HELPPPPPPPPP ! In circle O, what is measure of Arc AE? A. 84 B. 96 C. 120 D. 168 BTW I HAVE MORE QUESTIONS UP IF YOU WANT TO HELP!!!!!1

Answers

Answer:

arc m AE = 120

Step-by-step explanation:

∠C = 1/2 (AE-BD)

We can fill most of that in with the info we were given:

36= 1/2(AE-48)

Multiply both sides by 2 to get

72 = AE - 48 so  

AE = 120°

How do you simplify:

[tex] \sqrt{(125 ^{2} } ) ^{ - \frac{1}{3} } [/tex]

Answers

Answer:

[tex]\huge\boxed{\sqrt{(125^2)^{-\frac{1}{3}}}=\dfrac{1}{5}}[/tex]

Step-by-step explanation:

[tex]\sqrt{(125^2)^{-\frac{1}{3}}}\qquad\text{use}\ (a^n)^m=(a^m)^n\\\\=\sqrt{\left(125^{-\frac{1}{3}\right)^2}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=125^{-\frac{1}{3}}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{125^\frac{1}{3}}\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\dfrac{1}{\sqrt[3]{125}}=\dfrac{1}{5}\qquad\text{because}\ 5^3=125[/tex]

Explain the significance of the equation y = 50x + 20 which represents the hourly cost of a car repair.

Answers

The questions doesn't really specify much here is as much I can say.

Since 50 is the slope we can say that this is the hourly cost of a car repair (as stated in the question).

20 represents the y-intercept so this could represent the cost for the technician to look at whats wrong with the car.

Best of Luck!

SOMEONE PLZZZ HELP ME WITH THIS QUESTION!! I'd be immensely grateful :/

Answers

Answer:

Step-by-step explanation:

First let's find the value of x :

We khow that the area of this triangle is 400 and it is given by the product of the base and the height over 2

the base is x the height is 2x Let A be the area : A= (2x*x)/2 =2x²/2  =x² so x²= 400 ⇒ x= 20≥ 0 because it's a distance

Let's find the hypotenuse :

The pythagorian theorem :

h²= x²+(2x)² h²= x²+ 4x²h²= 5x² x=20⇒ h²= 5*(20)²h²= 2000h= 20[tex]\sqrt{5}[/tex] ≥0 because it is a distance

A) Given the area of a triangle is

B•h/2

B= x and H= 2x

Therefore 2x • x /2 = 400

2x^2 = 800

x^2 = 400

x = - or + 20

However since it’s the area it cannot be negative therefore the x value is 20

So the height is 40 (2x) while the base is 20 (x)

B) Given that the base is 20 and the height is 40, you can use Pythagoras Theorem where:

a^2 + b^2 = c^2

So 20^2 + 40^2 = 400 + 1600 = 2000

C^2 = 2000

C = square root 2000 ( insert in calculator and round up)

That gives you the hypotenuse.

An interior angle of a regular convex polygon is 140°. How many sides does the polygon have?

Answers

Answer:

hope it will help uh.....

In the image, point A marks the center of the circle. Which two lengths must form a ratio of 1:2?
A.
A F:AE
B.
BC:EF
C.
EF:AI
D.
AI:EF
E.
AI:AD

Answers

Answer: AI:EF

Step-by-step explanation:

Answer:

D. ) AI:EF

Step-by-step explanation:

PLATO

You can do one or both if u do both I’ll give Brainlynest

Answers

Answer:

18) a. X

19) d. 69°

Step-by-step explanation:

18) A reflection is a transformation where an image is flipped over a line. So V will still be in the same place, it will just be flipped over line B. The only answer that makes sense in X.

19) All the angles in the picture are vertical angles. Vertical angles are angles that are across from each other when two lines cross and they are always equal.

The angle opposite the angle that is 78° is also 78°.

The angle opposite the angle that is 33° is also 33°.

The three angles form a straight line so:

78° + 33° + x = 180°

111° + x = 180°

x = 69°

Since the angle is a vertical angle and is opposite angle a, angle a will also be 69°.

Hope this helps. :)

2a + 5a x 4a - a simplify

Answers

Answer:

20a² + a

= a(20a + 1)

Step-by-step explanation:

2a + 5a × 4a - a

= 2a + 20a² - a

= 20a² + a

PLS HELP ASAP The following probability distribution table shows information collected from a survey of students regarding their grade level and the transportation they use to arrive at school. What is the probability that a randomly selected eighth grader takes the bus?

Answers

Answer:

44%

Step-by-step explanation:

For these types of problems, look at the totals. We know that there are 0.44 out of 1 eighth graders. Since it doesn't specify how the 8th grader is dropped off, we take 0.44 and divide it by 1 (the total). We get 0.44, but since it's most likely asking for percentages, multiply that by 100.

What value of n makes the equation true?
-1/5n + 7=2
n=​

Answers

Answer:

n = 25

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and is:

Parenthesis

Exponents & roots

Multiplication

Division

Addition

Subtraction

~

First, subtract 7 from both sides:

(-1/5)n + 7 (-7) = 2 (-7)

(-1/5)n = 2 - 7

(-1/5)n = -5

Next, multiply -5 from both sides:

(-1/5)(-5)n = (-5)(-5)

n = -5 * -5

n = 25

25 is your answer for n.

~

Answer: n = 25

Step-by-step explanation: In this equation, our first step is to isolate the n term by subtracting 7 from both sides.

On the left, +7 -7 cancels and we're left with -1/5n.

On the right, 2 - 7 simplifies to -5.

So we have -1/5n = -5.

In order to get n by itself, since it's being multiplied by a fraction,

we multiply both sides of the equation by the reciprocal of that fraction.

The reciprocal of -1/5 is -5/1.

So we multiply both sides of the equation by -5/1.

So we have (-5/1)(-1/5n) = -5(-5/1).

On the left, our 1's cancel and our 1's cancel.

Also, remember that a negative times a negative is a positive.

So on the left we are left with n.

On the right, -5(-5/1) is 25.

So n = 25.

What is the value of x in the equation 4x +8y=40, when y=0,8?

Answers

Answer:

x=8.4

Step-by-step explanation:

4x +8y=40

replace y as 0.8

4x+8*0.8=40

4x+6.4=40

subtract 6.4 from both sides

4x=33.6

divide by 4

x=8.4

Step-by-step explanation:

4x + 8y = 40

Simplify the equation

Divide all terms by 4

We have

x + 4y = 10

Make x the subject

x = 10 - 2y

When y = 0.8

Substitute the value of y into the equation

We have

x = 10 - 2(0.8)

x = 10 - 1.6

x = 8.4

Hope this helps you

HELP ME PLEASE ~ Thanks :)

Answers

Answer:

A

Step-by-step explanation:

99/479

formula: girls in action divided by everyone

PLEASE HELP!!!

Here are the prices of five new skateboards, in dollars: 75, 82, 100, 120, 140.
The standard deviation is about $27.
If a sixth skateboard is added to the sample that has a price of $450, what
happens to the standard deviation?

Answers

Answer:

standard deviation=143.527

C

Step-by-step explanation:

75, 82, 100, 120, 140.

if we add 450

75, 82, 100, 120, 140,450

standard deviation=143.527

find the mean=sum /count=967/6=161.167

then find the  √square difference between each sample and the mean, add up the differences²/6-1

find the square root of the differences=143.527

Answer:

C-the new standard deviation is greater the $27

Consider triangle ABC. Triangle A B C. Angle C is 80 degrees and angles B and A are y degrees. What is the value of y in the triangle? Angle y = °

Answers

Answer:

y is equal to 50 degrees.

Step-by-step explanation:

The sum of the angles of a triangle is always 180 degrees.  To find what y is, subtract 80 from 180 and divide the difference by 2.  This will give you 50 degrees.

Answer:

y= 50°

Step-by-step explanation:

∠A =∠B = y. So, ΔABC is an isosceles triangle.

Sum of angles of triangle = 180

∠A + ∠B + ∠C = 180

y + y + 80 = 180   {add like terms}

2y + 80 = 180  {Subtract 80 from both sides}

2y + 80 - 80 = 180 - 80

2y = 100   {divide both sides by 2}

2y/2 = 100/2

y= 50°

Draw the graphs of y=2x plus 1

Answers

Hey there! :)

Answer:

Graphed below.

Step-by-step explanation:

Graphing y = 2x + 1 can be done by finding points on the line. Find the y and x intercepts to make graphing more simple:

Solving for the y-intercept:

y = 2(0) + 1

y = 1, or (0, 1). This is the y-intercept.

Solving for the x-intercept:

0 = 2x + 1

Subtract 1 from both sides:

-1 = 2x

Divide both sides by 2:

x = -1/2, or (-1/2, 0). This is the x-intercept. We can graph the equation given these two points.

An oblique cone has a radius of 5 units and a height of 9 units. What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth. A)117.8 cubic units B)141.3 cubic units C)235.5 cubic units D)282.6 cubic units

Answers

Answer:

Option (C) 235.5 cubic units

Step-by-step explanation:

Data obtained from the question include:

Radius (r) = 5 units

Height (h) = 9 units

Pi (π) = 3.14

Volume (V) =..?

The formula for calculating the volume of an oblique cone is the same as the formula for calculating the right cone. The formula is given below:

V = 1/3πr²h

With the above formula, we can obtain the volume of the oblique cone as follow:

V = 1/3πr²h

V = 1/3 x 3.14 x 5² x 9

V = 3.14 x 25 x 3

V = 235.5 cubic units.

Therefore, the volume of the oblique cone is 235.5 cubic units.

in the function equation ff (xx ) = 1500 (1.43)^xx, is it growth or decay? what is the percent of the growth/decay? what is the initial value?

Answers

Answer:

The initial value is 1500

growth

43 % growth

Step-by-step explanation:

Exponential equations are in the form

y = a * b^x

a is the initial value

b is the growth or decay

b>1 is growth b-1 rate  of growth

b <1 decay  1-b rate of decay

f(x) = 1500 * 1.43 ^x

The initial value is 1500

1.43 > 1 so it is growth

1- 1.43 = .43

Change to percent

43 % growth


The temperature each hour in Elma, Texas on October 1 is modelled by the equation
t(h) = 10 cos(15h - 10)° + 30 where his hour of the day with 0 meaning midnight, and t is the
temperature in degrees Celsius. How hot did it get in Elma on October 1?

Answers

Answer:

[tex]39.8^{\circ} C[/tex]

Step-by-step explanation:

We are given that the temperature each hour in Elma Texas on October 1 is modelled by the equation

[tex]t(h)=10cos(15h-10)^{\circ}+30[/tex]

Where h=Hour of the day with 0 meaning midnight

t=Temperature in degree Celsius

We have to find the temperature on October 1.

Substitute h=0

[tex]t(0)=10cos(15(0)-10)+30[/tex]

[tex]t(0)=10cos(-10)+30[/tex]

[tex]t(0)=39.8^{\circ} C[/tex]

Hence, the temperature in Elma on October 1=[tex]39.8^{\circ} C[/tex]

A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some children take 5 pieces, and 1 child takes 7 pieces of candy. How many children take 3 pieces of candy?

Answers

Answer:

children take 3 pieces of candy are 6

Step-by-step explanation:

x+y=19-1          x+y=18

3x+5y=85-7    3x+5y=78

eliminate x by multiplying the first equation by 3:

3x+3y=54

3x+5y=85   subtract

(3x+3y)-(3x+6y)=54-78

3x-3y-3x-5y=-24

-2y=-24         y=-24/-2=12

y=12 , substitute for y:

x+y=18

x=18-12

x=6

check: 3x+5y=78

3(6)+5(12)=78

18+60=78 correct

What is the range of the function shown on the graph above?

Answers

Answer:

A.

Step-by-step explanation:

Since range is y-axis based, we are looking at the y-values. We see that the endpoints of the graphed segment are closed points, so they are included in the range. That eliminates B (exludes values) and C (Not infinity, it's a segment, not a line). Choice A is the best answer because when you identify the y-values, you get -8 to -3 included.

A line is defined by the equation y = two-thirds x minus 6. The line passes through a point whose y-coordinate is 0. What is the x-coordinate of this point? A coordinate plane.

Answers

Answer:

  9

Step-by-step explanation:

Put the given information into the equation and solve for x.

  y = (2/3)x -6

  0 = (2/3)x -6 . . . . . substitute for y

  0 = x - 9 . . . . . . . . multiply by 3/2

  9 = x . . . . . . . . . . . .add 9

The x-coordinate of the x-intercept point is 9.

Answer:

x=9

hope this helps :>

Find the probability that a student earns a grade D or F

Answers

Answer: P = 1/7

Explanation:
There 35 students total and there are 3 students with grade D and 2 students with Grade F

3/35 + 2/35 = 5/35 = 1/7

Answer:

P=.14 or 1/7

Step-by-step explanation:

P(d)=3/35

P(f)=2/35

P( D or F) = 3/35 + 2/35=

1/7 or .14

find the 7th term of the geometric progression which begins with -6250,1250,-250

Answers

Answer:

a₇ = - 0.4

Step-by-step explanation:

The n th term of a geometric progression is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = - 6250 and r = [tex]\frac{1250}{-6250}[/tex] = - [tex]\frac{1}{5}[/tex] , thus

a₇ = - 6250 × [tex](-\frac{1}{5}) ^{6}[/tex]

    = - 6250 × [tex]\frac{1}{15625}[/tex] = - [tex]\frac{6250}{15625}[/tex] = - 0.4

4x - 1
2.
= x + 7
Can someone help please?

Answers

Answer:

6[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

4x-12 = x+7

4x-12+12 = x+7+12

4x = x+19

4x-x = x+19-x

3x=19

x = 6[tex]\frac{1}{3}[/tex]

And if we substitute the value of x into the equation 4x-12 = x+7,

we will get 13[tex]\frac{1}{3}[/tex] = 13[tex]\frac{1}{3}[/tex] in the end.

Hope this helps :)

Answer:19/3 = [tex]6\frac{1}{3}[/tex]Step-by-step explanation:[tex]4x -12= x+7\\Collect-Like-Terms\\4x-x =7+12\\3x=19\\Divide -Both-Sides-Of-The-Equation-By ; 3\\\frac{3x}{3} =\frac{19}{3} \\\\x = \frac{19}{3}\\ \\x = 6.3\\[/tex]

Robyn saves up $204 and spends $32.50 on books. She wants to purchase more books from a sale where they cost $8.15 each. Which equation represents the situation? A. 204x=8.15+32.5 B. 8.15x+32.5=204 C. 8.15+32.5x=204 D. 32.5x=204⋅8.15

Answers

Answer: B

Step-by-step explanation:

If we assume the no. of books to be x.

Value of more books will be 8.15 x

The equation will be

8.15x + 32.5 = 204

Differentiate x^(-3)/3-2x^2-x^(-1)

Answers

Answer:

-2x^2

Step-by-step explanation:

Simplify

x^-1 - 2x^2 - x^-1

becomes

-2x^2

Other Questions
Use the graph to approximate the ordered pair where the exponential function begins to exceed the quadratic function.the graph of an exponential function f of x equals two and two tenths to the power of x minus 7 tenths and a quadratic function g of x equals one eighth times x squared plus 2 times x plus 8 -125>-135 divide each side by -5 what is the resulting true inequality Identify the advantages of using 6 tube passes instead of just 2 of the same diameter in shell-and-tube heat exchanger.What are the advantages and disadvantages of using 6 tube passes instead of just 2 of the same diameter? . The job of applications engineer for which Maria was applying requires (a) excellent technical skills with respect to mechanical engineering, (b) a commitment to working in the area of pollution control, (c) the ability to deal well and confidently with customers who have engineering problems, (d) a willingness to travel worldwide, and (e) a very intelligent and well-balanced personality. List 10 questions you would ask when interviewing applicants for the job. Pls help see the picture posted the graph of y=f(x) is shown on the grid (Blank) tells you that the exact momentum and position of a particle can't be known at the same time.A. The Schrodinger equationB. Quantum mechanicsC. The uncertainty principleD. Particle-wave duality In one of his most memorable summer vacations, Danny recalls traveling to South Korea where he met a host of interesting people and lifelong friends. He also, however, recalls feeling disoriented and out of place because of the different cultural norms and beliefs. This feeling of disorientation that Danny experienced is an example of what? i need helppppppppppppp What is the circumference of the circle below? (Round your answer to the nearest tenth.) helloo guysss pleaseeee help with this one Plz help me plzzzzzz!!!! Magnetic field lines exit out of the . Magnetic field lines enter into the . Magnetic field lines travel around a bar magnet in n order to identify information in your composition that may contradict your thesis, you should _____. hy my friend kia koe mujhay batahaan ga k jab koe barinly mein online hota hy humhay kaisay pata chalta hy In tennis, which of the following is the first score possible after a game has started?a) Love - 15b) 30 -30c) 30 - Loved) Deuce Which is the best source for learning about new words?O A. A newspaperB. A thesaurusOU A memoirO D. A novel Garrison Company adds direct materials at the beginning of the process and adds conversion costs throughout the process. The following data represents data in the Shaping Department WIP, April 1 7 comma 000 units Transferredminusin costs in WIP, April 1 $79,940 Direct materials (100%) in WIP, April 1 $24,420 Conversion costs (55%) in WIP, April 1 $23,400 Units transferredminusin 49 comma 000 Transferredminusin costs during April $550,900 Units completed 46 comma 000 April direct materials cost $155,500 April conversion costs $239,250 WIP, April 30 10 comma 000 units (100% for materials and 40% for conversion costs) What are the equivalent units for conversion costs? QUESTION 8Find Future Value Using Compound Interest Formula:You deposit $6,000 in an account earning 4% interest compounded monthly. How much will you have in the account in 5 years?A $9,677.95B. $6,100.67C. $7,325.98D. $7,200QUESTION 9Find Future Value Using Compound Interest Formula:You deposit $5,000 in an account earning 5% interest compounded quarterly. How much will you have in the account in 10 years?A $5,661.35B. $7,500C. $8,235.05D. $8,218.10 4 years ago, the population of a city was of "x" inhabitant, 2 years later, that is to say two years ago, the population of this same city was 81,000 inhabitants and today it is 65,610. Using this data, find the population of four years ago.