Mathematics High School

30+ points need it asap! :) pls show work.
Write a polynomial function f of least degree with the following zeros: 3, 4 + i

Answers

Answer 1

Answer:

[tex]f(x)=(x-3)(x^2-8x+17)[/tex]

Or:

[tex]f(x)=x^3-11x^2+41x-51[/tex]

Step-by-step explanation:

To find our factors, we can work backwards.

We know that 3 is a zero. This means that:

[tex]x=3[/tex]

Subtract 3 from both sides:

[tex](x-3)=0[/tex]

So, (x-3) is one of our factors.

We also know that (4+i) is a zero. So:

[tex]x=4+i[/tex]

First, let’s isolate the imaginary. So, subtract 4 from both sides:

[tex](x-4)=i[/tex]

Now, let’s square both sides:

[tex](x-4)^2=(i)^2[/tex]

Expand the left. Evaluate the right:

[tex](x^2-8x+16)=-1[/tex]

Add 1 to both sides. So, our factor is:

[tex](x^2-8x+17)=0[/tex]

Hence, our polynomial function is:

[tex]f(x)=(x-3)(x^2-8x+17)[/tex]

This is also the least degree since we did the most minimum we can do to solve backwards.

Further Notes:

If we want to convert this to standard form, we can distribute:

[tex]f(x)=(x^3-8x^2+17x)+(-3x^2+24x-51)[/tex]

Combining like terms will yield:

[tex]f(x)=x^3-11x^2+41x-51[/tex]

Related Questions

Jim is building a model airplane. The scale is 1 in : 40 ft. The actual wingspan of the plane is 211 feet. How long will the wings of the model be?

Answers

Answer:

422 that's how long the wingspan will be.

Please Help Me I will give you 100 Points

Answers

Answer:

twoendndbdsjwu

Step-by-step explanation:

Answer:

a. x represents the 1$ rides and y represents the 2$ rides.

b. they represent the rides that she has taken.

c. (4, 11) or  x = 4 and y = 11

Step-by-step explanation:

What answer it is . Will mark brainliest

Answers

The correct answer is the one you have clicked on:)

Add and reduce: 1 1/2 + 2 2/3

Answers

the answer is  2 13/5 you cant reduce it its not a proper equation

Answer:

4 1/6

Step-by-step explanation:

1 1/2 + 2 2/3

1 3/6 + 2 4/6

= 4 1/6

hope this helps

have an amazing day!

Find the equation of the linear function represented by the table below in slope-intercept form.

x- 0 1 2 3 4

y- 9 18 27 36 45

Answers

Question: Where is the y2? Please be more specific!

1/2-1/4

help?:) uhhhh thankssss

Answers

1/2 - 1/4 = 2/4 - 1/4 = 1/4

I hope this helps!

plsssssssssssssss help with 11

Answers

Answer:

1 = $3.50

( I tried my best)

Solve the equation. Determine the number of solution. -8(x - 3) = -8x-24
No solution
O One solution
0 Infinitely many solutions

Answers

The answer is no solution

Whitney has £265 Nancy has £180 They each spend the same amount of money. Whitney has twice as much money as Nancy left now. How much money did they each spend?

Answers

Answer:

£95

Step-by-step explanation:

Given that:

Whitney's initial amount = £265

Nancy's initial amount = £180

Let amount each spent = x (amount is the same)

After spending Whitney has twice as much money as Nancy.

Amount spent by each?

(Whitney's initial amount - x) = 2(Nancy's initial amount - x)

265 - x = 2(180 - x)

265 - x = 360 - 2x

-x + 2x = 360 - 265

x = £95

Hence, they both spent £95

Mia has 20 markers, Noah has 25 markers, and Michael has 85 markers. Use the GCF and the
Distributive Property to find the total number of markers Mia, Noah, and Michael have.
Write each number as a product using the GCF as a factor, and apply the Distributive Property.
20 + 25 +85 =
(Use the operation symbols in the math palette as needed.

Answers

Answer:

130

Step-by-step explanation:

Factoring the given numbers:

20 = 2*2*525 = 5*585 = 5*17

CGF(20,25,85) = 5

The sum of given numbers:

20 + 25 + 85 = 5*4 + 5*5 + 5*17 = 5*(4 + 5 + 17) = 5*26 = 130

If you want to buy an item in a store that costs $32.50 and is on sale for 30% off, then how much would the item actually cost you after the discount? Round to the nearest cent.​

Answers

Answer:

22.80

Step-by-step explanation:

100% - 30% = 70% that you'll be paying

70% = [tex]\frac{70}{100}[/tex]  = 0.7

0.7 * 32.50 = 22.75

Round to nearest cent: 22.8

Find each unit rate. Determine which is lower. Drag and drop the correct rate or letter into each of the boxes to complete the sentences. Ingredient C: 1/5 cup for 3/4 serving or Ingredient D: 1/4 cup for 4/5 serving.

Answers

Answer:

4/15 < 5/16

Ingredient C < Ingredient D

Hence ingredient C has a lower cup per serving than ingredient D

Step-by-step explanation:

Given the unit rates :

C: 1/5 cup for 3/4 serving or Ingredient

D: 1/4 cup for 4/5 serving

C : 1/5 cup for 3/4 serving

1/5 ÷ 3/4

1/5 * 4/3

= 4 / 15

= 0.2667

D: 1/4 cup for 4/5 serving

1/4 ÷ 4/5

1/4 * 5/4

= 5 / 16

= 0.3125

5/16 > 4/15 ;

Ingredient C < Ingredient D

Hence ingredient C has a lower cup per serving than ingredient D

a. Each day, your teacher randomly calls on 5 students in your class of 30. What is the
probability you will be called on today?

Answers

Answer:

The probality is 5/30 or in simpliest form it is 1/6!

Step-by-step explanation:

Hope this helps! Plz give me brainliest

Which best represents 3=x/6 -2

Answers

Answer:

30

Step-by-step explanation:

Answer: x = 30

Step-by-step explanation: To solve for x, first you’ll have to make sure that your result will equal to 3. ( x/6 -2). Next, look for a numerator that can make a fraction that equals to 5. Then, you would have to multiply 6 x 5, which equals to 30, so 30 will be x. 3 = (30/6 - 2) 3 = 5-2.

State the slope and y-intercept of the graph of y=−25x+2

Answers

Answer:

slope=-25  y-intercept=2

Step-by-step explanation:

Answer: Slope=-25

y-int=2

Step-by-step explanation: y=mx+b, m is the slope and b is the y-int. The slope is the number in front of x like -25x that is -25. The y-int is the next to the slope which is 2.

The area model shows 2 and one-third. What is 2 times 2 and one-third?

Answers

Answer:

14/3 or 4.6

Step-by-step explanation:

I need help solving for x

Answers

X=-10

That’s the answer

Can anyone answer these
(simplify to find the quotients)

Answers

Here you go!! Hope this helps

Factoring the following Difference of Two Perfect Squares.
X^2– 16

Answers

hi

x²-16  =  (x+4)  (x-4)

"Shaquille, Lyle, and Amanda collect stamps. Shaquille has one-half the number of stamps that Lyle has. Amanda has two-thirds as many stamps as Lyle. Together they have 364 stamps. How many stamps does Amanda own?" Please help me :c

Answers

Answer:

112 stamps

Step-by-step explanation:

Shaquille and Amanda's stamps are described in terms of Lyle's, so:

Lyle's = 6x                     6x+3x+2x=364

Shaquille's = 3x                       13x=364

Amanda's = 4x                            x=28

Lyle has 168 stamps, Shaquille has 84, and Amanda has 112. 168+84+112=364

112 stamps hope this helps

hospital pays $9 for each set of scrubs plus a delivery fee of $13 per order the total cost for the scrub order was $463. how many sets of scrubs did the hospital order?

Answers

They ordered 50 sets of scrubs

Answer: 50 sets

Step-by-step explanation:

Scrubs=9x fee=13 total=463

463-13 dollar fee =450 450/9 equals 50 sets of scrubs to check it do 9x+13=463 x=50 so 9(50)+13=463 then 450+13=463 463=463 :) you're welcome hope it's the right type of math you need!

Can you guys plz help me

Answers

Answer:

[tex]\frac{20}{12}[/tex]

Step-by-step explanation:

Answer:

20/12 since 3*4 is 12 u do 5*4

Step-by-step explanation:

Please mark brainliest and hope this helps ya!!

​​ What is the area of a rectangle with vertices at ​(0, −4)​, ​(−1, −3)​ , (2, 0), and (3, −1)? Enter your answer in the box.
( ) units²

Answers

Answer:

?

Step-by-step explanation:

Answer:

Step-by-step explanation:

What is the value of the expression below when x=10x=10 and y=4y=4? 8x-7y 8x−7y

Answers

Answer:

X=10x =10

means here value of X is 1

y = 4y = 4

means here value of y is also 1

now substitute the values of X and y in the equation

8×1-7×1×(8×1-7×1)

8-7(8-7)

64-49

15

5 2/5 as a decimal number

Answers

Answer:

27/5 = 5,4

Step-by-step explanation:

5 2/5 = 27/5 = 5,4

Question
Help me -.8+ 2X = .3 - x

Answers

Step-by-step explanation:

2x+x=.3+.8

3x= 1.1/:3

x=0.366

Answer:

x = -2.566667

Step-by-step explanation:

simplify both sides

8 + 2x = 0.3 - x

8 + 2x = 0.3 + - x

2x + 8 = - x + 0.3

add x to both sides

2x + 8 + x = - x + 0.3 + x

3x + 8 = 0.3

subtract 8 from both sides

3x  + 8 - 8 = 0.3 - 8

3x = -7.7

divie both sides by 3

3x/3 = -7.7/3

x = -2.566667

help with math hw please

Answers

Answer:

x = 4

Step-by-step explanation:

All of the sides are the same so every angle is 17x-8.

Every triangle adds up to 180 degrees.

3(17x-8)=180

51x-24=180

    +24  +24

51x=204

 x= 4

An ice cream shop sells large cones for $2.50 and small cones for $1.50. Jack has enough money to buy 21 large cones. How many small cones could Jack buy?


plz healp

Answers

Answer:

the answer is 35 small cones

Step-by-step explanation:

2.50 x 21 = 52.50

52.50 / 1.50 = 35

The answer is 14 because 21 divided by 1.50 equals 14

first 10 didgts of pi

Answers

I guess I did not know how to answer sorry

Answer: thefirst ten didgets of pi are .1415926535

Step-by-step explanation:

Hellppppppppppppppppp

Answers

Answer: im pretty sure its option 2

Step-by-step explanation:

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