Mathematics Middle School

f(x) is a cubic function whose roots are 2, 3, and 4. Find f(x) and also find the value of f(2).
Please give an explanation so I know how to do it next time :) Thank you!

Answers

Answer 1
If you successfully guess one root of the cubic equation, you can factorize the cubic polynomial using the Factor Theorem and then solve the resulting quadratic equation easily.

33−22−9−4=0
3
x
3
−
2
x
2
−
9
x
−
4
=
0


On inspection, =−1
x
=
−
1
is found to satisfy the equation. Now the cubic polynomial can be factorized.

33−22−9−4=0
3
x
3
−
2
x
2
−
9
x
−
4
=
0


⟹(+1)(32−5−4)=0
⟹
(
x
+
1
)
(
3
x
2
−
5
x
−
4
)
=
0


One root is −1
−
1
. The rest at the roots of the following quadratic equation.

32−5−4=0
3
x
2
−
5
x
−
4
=
0


⟹=−(−5)±(−5)2−4×3×(−4)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2×3
⟹
x
=
−
(
−
5
)
±
(
−
5
)
2
−
4
×
3
×
(
−
4
)
2
×
3


⟹=5±25+48‾‾‾‾‾‾‾‾√6
⟹
x
=
5
±
25
+
48
6


⟹=5±73‾‾‾√6
⟹
x
=
5
±
73
6


⟹∈{−1,5−73‾‾‾√6,5+73‾‾‾√6}
⟹
x
∈
{
−
1
,
5
−
73
6
,
5
+
73
6
}


Some cubic equations to be solved by students are deliberately made to have one simple root which can be guessed.
Answer 2

Adoes thi involve coding?

Step-by-step explanation:

Related Questions

help with this, i looked over the slides and they didn't help

Answers

Answer:

its A

Step-by-step explanation:

Answer:

answer is 17 from 9 to -8mit takes 17 counts.

hope it helps

Determine if the lines are parallel, perpendicular, neither or the same line: y = -2x + 1 and -2x + 4y = 5.

Answers

Answer: These lines are perpendicular

Step-by-step explanation:

Let's use slope intercept form, y=mx+b (m=slope, b=y intercept)

Parallel lines have the same slope, or m

y=3x+7 and y=3x+32 are parallel because they have the same m

Perpendicular lines have an opposite reciprocal slope

y=2x+13 and y= -1/2+2 are perpendicular because they are reciprocals

y=-2x+1 is already in slope intercept form. Let's change the other problem

-2x+4y=5isolate the y, 4y=2x+5make y by itself, y=2/4x+5/4 or y=1/2x+5/4

Here are the two problems: y=-2x+1 and y=1/2x+5/4

Look closer. These lines are actually perpendicular.

Take the second problem's slope, 1/2. Make it a negative reciprocal, which means -2/1 or -2. These lines are perpendicular.

They are perpendicular

help please :)))))))))))))))))))))

Answers

The answer to this is C

What is 2(n−3)=4n+1?
n=??

Answers

Answer:

n = -7/2

Step-by-step explanation:

2(n - 3) = 4n + 1

=> 2n - 6 = 4n + 1

=> -6 - 1 = 4n - 2n

=> -7 = 2n

=> n = -7/2

N= -7/2 would be the correct answer

Can someone please explain how you do these you don't have to answer though

Answers

Answer:

3 to the power of 10

Step-by-step explanation:

Add the exponents and subtract if you are dividing

write in exponential notation of 4x1000+9x100+0x10+7x1

Answers

Answer

4000

900

0

7

Step-by-step explanation:

Not so sure about the answer though

4907 is the exponential notation

True or false:
The distance formula can be used to calculate the midpoint of a segment.

Answers

The answer is true I’m pretty sure
Answer is true I’m could be wrong

Tell whether the given statement is true or false. Explain your choice.
7. All real numbers are rational.
8. All whole numbers are integers.

Answers

For number 7 since the rational number is countable, and the set of real numbers is uncountable, almost all real numbers are irrational. So you should choose false

8 yes! All whole numbers are integers. For an example 0 is a whole number, 0 Is ALSO a integer. So you should choose truth
7. False. Since the set of rational numbers is countable, and the set or real numbers is uncountable, almost all real numbers are irrational.
8.true. All whole numbers are integers, so since 0 is a whole number, 0 is also an integer

Your mom is repainting your younger brother’s room. She is going to project the image shown below onto his wall so that she can paint an enlarged version as a mural. The length of the image of the train measures 2 inches.



Determine how long the mural will be if the projector uses a scale where 1 inch of the image represents 2 1 half feet on the wall.

Answers

Answer:

5 feet

Step-by-step explanation:

Probably about five feet

What is the length of JK?

Answers

The length of JK is 5
The length of Jk is 5.

Explanation:
Just count the number of squares next to it to find the length or how long it is

Simplify to create an equivalent expression.

Answers

the answer is A (-12p - 6)

Answer:

a

Step-by-step explanation:

step 1: simplify the expression (parentheses)

2 (-2 - 4p) + 2 (-2p - 1)

-4 - 8p + -4p - 2

step 2: add similar number together

-6 - 12p

PLEASE HELP!!!
Lee can type 1 1/3 pages every 15 minutes. How many hours does it take him to type 10 2/3 pages? Complete the rate table to solve the proportion.

pages---> 4/3=32/3
hours---> 1/4 = x

Lee can type 10 2/3 pages in _________ hours.
a. 1 3/4
b. 2
c. 2 1/4
d. 2 1/2

Answers

Answer:

First, we know that:

1 1/3 = 4/3

10 2/3 = 32/3

15 minutes = 0.25 hours

Let's imagine that x (hours) is the time it takes Lee to type 32/3 pages.

From the information, we can tell that:

Lee can type:

4/3 pages in 0.25 hours

32/4 pages in x hours

So x should be:

x = (32/4 . 0.25)/4/3 = 2 (hours)

So it takes Lee 2 hours ro type 10 2/3 pages

Step-by-step explanation:

HELP ME NOW PLEASE, IM BEGGING.

Answers

1. $1.23 per pair
A dozen is 12 so you do 12x7=84

Then you do 103.32 divided by 84 which gives you 1.23

2. His error was doing 103.32 divided by 7 because he thought it was only 7 pairs but it’s 7 dozen.

a. What is the correct unit?

Answer: 7 dozen= 12 x 7

                           = 84

      correct price= 103.32 divided by  84

                           =1.23

b. What error did the contractor likely make??

Answer: HE THOUGHT the value of 7 shoes other than 7 dozend pair of shoes

What coins do I have?
One-sixth of my coins are nickels
One-third of my coins are dimes
My coins are _

Answers

Answer:

Nickels and dimes?

Step-by-step explanation:

Nickels and dimes? I don’t understand the question. I feel like there’s missing information

pwease help 1 more quesiton

Answers

The answer is (2,-6) look at the picture to see how to do it
The correct answer is 2, -6

Does the following table show a proportional relationship between the variables x and y?

Answers

I think it’s no I am pretty sure it’s no
No is the answer I hope this can help you

find a difference pwease :,D

Answers

Step-by-step explanation:

option A is correct answer

Answer:

[tex] \frac{5}{8} - ( - \frac{1}{4} ) \\ \frac{5}{8} + \frac{1}{4} \\ \frac{5 \times 1 + 1 \times 2}{8} \\ \frac{5 + 2}{8} \\ \frac{7}{8} [/tex]

Please find an answer and explain

Answers

H is -6 and k is 6. that should be right

What is the length of JL?

Answers

Answer: 8 Units



btw have a good day :)
8 units/ first answer

A soccer field is 99 meters long (x-axis) and 66 meters wide (y-axis). The field crew needs to find the midpoint of one of the diagonals so they can paint a new center circle. What are the coordinates of the midpoint?

Answers

The Soccer Ground is a lot That the People's can't even reach the Goal Post

Answer:

The Soccer Ground is a lot That the People's can't even reach the Goal Post

Step-by-step explanation:

please help me with this

Answers

What do you want me to do lol I do not know what to do

Answer en el primero es -48,9582el   3 es 0,16

l 2 es 3,75

el 4 es 0,026

How to do this? please don't Ignore this, this is the second time I posted this.

Answers

Answer:

J, K, E, and, N

Step-by-step explanation:

the segments that represent a corresponding height if the side m is the base are, J, K, N & E.

could someone explain how to do this for me? i'm currently struggling with transformations and stuff

Answers

1. Reflect from the y-axis first
2. Then reflect from the x-axis

Answer:

it's rotation to the right

Step-by-step explanation:

the best i can explain it is, imagine you have an object like a bottle or bag whatever and you move it in a circle only half way so it's upside down then when you continue the circle to finish it or move it to the right again it will be the same as you started.

PLZ HELP WILL MARK BRAINLIEST 50 POINTS

REAL NUMBER SYSTEM

Answers

Answer:

B and J switch because J is a repeating number and repeating numbers are irrational because they don't have a definte end. Other than that, you are good!

Step-by-step explanation:

Answer:

B and J would be the correct answer

Step-by-step explanation:

please help 14 points

Answers

Answer:

3 over 8 (0.375)

3/8 and then 4/8 or 1/2

(URGENT) Will give 25 points

Answers

Answer:

Step-by-step explanation:

you have 28 cubic ft every 10 cubic feet is 20 so that so far 40 cubic feet then you add the rest is will be 48 dollars

A farmer has a house at the point (0, 0). He has a corn field that can be found by driving 1 unit up, 2 units right, 3 units down, and then 3 units right. If he instead walks diagonally to his corn field, how far has he gone? Round to 2 decimal places.

Answers

Answer:

right 6 units

Step-by-step explanation:

Answer:

5 units to the right and 1 unit down

6 units

(5, -1)

I need some help please

Answers

Answer:

r=10

Step-by-step explanation:

y=rx

r equals 10

y equals r times x  

3x10=30

10x10=100

16x10=160

Hope this helps: when i solved I got r=10

Which expressions are equivalent to 4(42)?



Select each correct answer.




4(20+22)

4(4+20)

4(4+2)

4(40+2)

Answers

1st= 4(42) so that’s one

4th= 4(42) so that’s the other one
It’s b good question!

[tex]\frac{2}{9}x - \frac{1}{3} = -1[/tex]

Answers

[tex] \large \mathfrak{Solution : }[/tex]

let's solve for x :

[tex] \dfrac{2}{9} x - \dfrac{1}{3} = - 1[/tex]

[tex] \dfrac{2}{9} x = - 1 + \dfrac{1}{3} [/tex]

[tex] \dfrac{2}{9} x = \dfrac{ - 3 + 1}{3} [/tex]

[tex]x = \dfrac{ - 2}{3} \times \dfrac{9}{2} [/tex]

[tex]x = - 3[/tex]

I hope it helped...

Answer:

x= -3

Step-by-step explanation:   both sides +1/3 so that the -1/3 gone

2/9x-1/3= -1

= 2/9x= -1+1/3

=2/9x= -2/3

=-3

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