Let $f(x) = x^3 + 3x ^2 + 4x - 7$ and $g(x) = -7x^4 + 5x^3 +x^2 - 7$. What is the coefficient of $x^3$ in the sum $f(x) + g(x)$?

Answers

Answer 1

Answer:

6

Step-by-step explanation:

Adding the two polynomials gives

(x^3 + 3x^2 + 4x - 7) + (-7x^4 +5x^3 + x^2 - 7) =

-7x^4 + (x^3 + 5x^3) + (3x^2 + x^2) + 4x + (-7-7) =

- 7x^4 + 6x^3 + 4x^2 + 4x -14

The x^3 term is 6x^3, so the desired coefficient is 6.


Related Questions

Find the area of a room that is 8-feet-wide and 9-feet-long.

Answers

Step-by-step explanation:

Area = l × b

= 9ft × 8ft

= 72ft²

Answer:

72 feet

Step-by-step explanation:

8 (length) • 9 (width) = 72 sq ft

Select all the expressions that represent the large rectangle's total area can't find the answer please help

Answers

where are the expressions. you didn’t attach anything

Find the area of the rectangle

Answers

Answer:

40 mi

Step-by-step explanation:

area= width*length  

Answer:

40 mi

Step-by-step explanation:

probally a jok e

[tex]A=l*w[/tex]

[tex]A = 5*8[/tex]

[tex]A=40[/tex]

please help me i only have 30 mins to an hour to finish

Answers

Answer:

D. 105 students

Step-by-step explantation: 11+10+21+6+2=50. So, 21 times 250 is 5250 and divided by 50 is 105.

Last one I need help in will give BRAINLY (don’t send me links)

Answers

Answer:

x=11

Step-by-step explanation:

4x+11=5x (angle adb and edf are the same)

11=5x-4x

11=x

x=11

if you want you can check by doing...

(14*11-29)+(5*11)=180

Guys what will be the population in five years.

I don’t know what i did wrong please help

Answers

Answer:

4990

Step-by-step explanation:

Multiply 638 by 5 then add 1800 and that's your answer

Answer:

4990

Step-by-step explanation:

638 x 5 = 3190

There is already a population of 1800, so then you add 3190 and 1800 to get 4900. The reason you add these numbers is because the population grows by 638 every year. They want to know how much it will grow in 5 years. You you multiply n (number) by y (year) to get t ( total).

Hope this helps!

Yours Truel, TheAnimeCatUwU

Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^1+c is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term My^1.01. If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?

Answers

Answer:

The doomsday is 146 days

Step-by-step explanation:

Given

[tex]\frac{dy}{dt} = ky^{1 +c}[/tex]

First, we calculate the solution that satisfies the initial solution

Multiply both sides by

[tex]\frac{dt}{y^{1+c}}[/tex]

[tex]\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}[/tex]

[tex]\frac{dy}{y^{1+c}} = k\ dt[/tex]

Take integral of both sides

[tex]\int \frac{dy}{y^{1+c}} = \int k\ dt[/tex]

[tex]\int y^{-1-c}\ dy = \int k\ dt[/tex]

[tex]\int y^{-1-c}\ dy = k\int\ dt[/tex]

Integrate

[tex]\frac{y^{-1-c+1}}{-1-c+1} = kt+C[/tex]

[tex]-\frac{y^{-c}}{c} = kt+C[/tex]

To find c; let t= 0

[tex]-\frac{y_0^{-c}}{c} = k*0+C[/tex]

[tex]-\frac{y_0^{-c}}{c} = C[/tex]

[tex]C =-\frac{y_0^{-c}}{c}[/tex]

Substitute [tex]C =-\frac{y_0^{-c}}{c}[/tex] in [tex]-\frac{y^{-c}}{c} = kt+C[/tex]

[tex]-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}[/tex]

Multiply through by -c

[tex]y^{-c} = -ckt+y_0^{-c}[/tex]

Take exponents of [tex]-c^{-1[/tex]

[tex]y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]

[tex]y = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]

[tex]y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]

i.e.

[tex]y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]

Next:

[tex]t= 3[/tex] i.e. 3 months

[tex]y_0 = 2[/tex] --- initial number of breeds

So, we have:

[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]

-----------------------------------------------------------------------------

We have the growth term to be: [tex]ky^{1.01}[/tex]

This implies that:

[tex]ky^{1.01} = ky^{1+c}[/tex]

By comparison:

[tex]1.01 = 1 + c[/tex]

[tex]c = 1.01 - 1 = 0.01[/tex]

[tex]y(3) = 16[/tex] --- 16 rabbits after 3 months:

-----------------------------------------------------------------------------

[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]

[tex]16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}[/tex]

[tex]16 = [-0.03 * k + 2^{-0.01}]^{-100}[/tex]

[tex]16 = [-0.03 k + 0.9931]^{-100}[/tex]

Take -1/100th root of both sides

[tex]16^{-1/100} = -0.03k + 0.9931[/tex]

[tex]0.9727 = -0.03k + 0.9931[/tex]

[tex]0.03k= - 0.9727 + 0.9931[/tex]

[tex]0.03k= 0.0204[/tex]

[tex]k= \frac{0.0204}{0.03}[/tex]

[tex]k= 0.68[/tex]

Recall that:

[tex]-\frac{y^{-c}}{c} = kt+C[/tex]

This implies that:

[tex]\frac{y_0^{-c}}{c} = kT[/tex]

Make T the subject

[tex]T = \frac{y_0^{-c}}{kc}[/tex]

Substitute: [tex]k= 0.68[/tex], [tex]c = 0.01[/tex] and [tex]y_0 = 2[/tex]

[tex]T = \frac{2^{-0.01}}{0.68 * 0.01}[/tex]

[tex]T = \frac{2^{-0.01}}{0.0068}[/tex]

[tex]T = \frac{0.9931}{0.0068}[/tex]

[tex]T = 146.04[/tex]

The doomsday is 146 days

1 point
2) What should come in the place of question mark (?) in the following
letter series based on the English alphabetical order CF HK MP RU? *
O WZ
OEF
GH
OHJ​

Answers

Answer:

A) WZ

Step-by-step explanation:

B,C, and D, come before RU

The ratio of the perimeters of two squares is 2:3. If the
area of the larger square is 324 square feet, what is the length, in feet, of the side of the smaller square?

Answers

2:3 would be the right feet.

Where the above ratio are given, the length of the side of the smaller square is approximately 14.7 feet.

How to compute the above

The area of a square is calculated by squaring the length of its side. Given that the area of the larger square is 324 square feet, we have:

(3/2)x² = 324

To solve for x, we can rearrange the equation and take the square root of both sides  -

x² = (324 * 2) / 3

x² = 216

x ≈ √216

x ≈ 14.7

Hence , the length of the side of the smaller square is approximately 14.7 feet.

Learn more about ratio at:

https://brainly.com/question/12024093

#SPJ2

A certain field is a rectangle with a perimeter of 818 feet. The length is 175 feet more than the width. Find the width and length of the rectangular field.

Answers

9514 1404 393

Answer:

width 117 feetlength 292 feet

Step-by-step explanation:

Let w represent the width of the field. Then w+175 is its length. The perimeter is ...

  P = 2(L+W)

  818 = 2((w+175) +w) . . . . . fill in given values

  818 = 4w +350 . . . . . . . . . simplify

  468 = 4w . . . . . . . . . subtract 350

  117 = w . . . . . . . . divide by 4

  w+175 = 292 . . . . find the corresponding length

The width of the field is 117 feet; the length is 292 feet.

I only need an equation for this. Plz help me

Answers

481 + 4m = 352 + 5m
m is equal to miles travelled

OMG PLEASE PLEASE PLEASE HELP!!!! I NEED THISS DONE ASAP!! Pleaseeee giving brainlest!!

Answers

Answer:

triangular prism

Answer:

it will be triangular prism

Is (9, 2) a solution to the system below?
x−4y=1, 2x−3y=3
1. Yes. (9, 2) is a solution to the system
2. No. (9, 2) is only a solution for the equation
3. No, (9, 2) is only a solution for the equation
4. No. (9, 2) is not a solution for either equation.

Answers

c sorry if i’m wrong btw

Helps please is for nooooowwwww

Answers

Answer:

The correct answer is the tor mar nada tor buda tor buni ami chai

5+10+15+20 in stigma notation

Answers

You mean Sigma notation not stigma ^^

Answer:

Look the attachment

help ill give extra poihts

Answers

Answer:

19 / (19+19+13) = 0.37254901... = ~ 37%

Step-by-step explanation:

19 is self-explanatory

(19+19+13) = 52

19 / 52 = 0.37254901...

0.37254901... = ~37%

brainliest plz

What does ''a over 3'' or a/3 mean?

Answers

Step-by-step explanation:

It means "a divided by 3". You need to divide a by 3. You can also write it as "1/3a".

Answer:

the answer is above me or below me

what is the answer in fraction form: 2(1/3+1/4)

Answers

Answer:

7/6 or 1*1/6

Step-by-step explanation:

Answer:

the answer is in the picture

PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!

Answers

Answer: Find the volume of cone, whose radius is 8 cm and height is 5 cm. Thus, the volume of the cone is 334.93 cm3.

Answer:

251.33cm^3

Step-by-step explanation: Use the formula V= π • (d/2)^2 • H

HOPEFULLY THIS HELPS


How many solutions does the system of linear equations represented in the graph below have?

No Solution

One Solution

Infinitely many solution

None of the above

Answers

Answer:

No solutions

Step-by-step explanation:

There are no solutions because the two lines have the same gradient (they are parallel)

Have a great day <3 and pls love me

HELP ME PLSSSSSSSSSSS IF I FAIL I M Screwed

Answers

Answer:

41

Step-by-step explanation:

What is the area of an equilateral triangle that has the base 12 cm,
and height of 10 cm? *
A 72.4 square centimeters
B 120 square centimeters
C 62.4 square centimeters
D 60 square centimeters

Answers

Answer:

C 62.4square centimetres

What is the area of the triangle?

Answers

40 right? Because base times height divided by two is area of a triangle

Answer:

52

Step-by-step explanation:

Write each percentage as a fraction in simplest form.
1. 50% 2. 99% 3. 15%
4. 200%

Answers

Answer:

1. 1/2

2. 99/100

3. 3/20

4. 2

Which number is a perfect cube?
A. 8
B. 9
C. 16
D. 25

Answers

C. 16
2^3 = 16
2x2=4
4x2=8
8x2=16

8 is a perfect cube number. So, option A.) is correct.

A number is said to be a perfect cube if it can be multiplied by itself three times. X must equal [tex]y^3[/tex] if it is a perfect cube of Y. As a result, a natural integer, not a fraction, is obtained when we take the cube root of a perfect cube. Therefore, [tex]3\sqrt{x}[/tex] equals y.

Let, a be a integer number then for a number to be perfect cube

Number= [tex]a^3[/tex]..............................................where a is integer number

8= [tex]a^3[/tex]

So, a=2

9= [tex]a^3[/tex]

No, integer value exist, whose cube is 9.

16= [tex]a^3[/tex]

No, integer value exist, whose cube is 16.

25= [tex]a^3[/tex]

No, integer value exist, whose cube is 25.

Thus, 8 is a perfect cube number. So, option A.) is correct.

Learn more about cubes, here:

https://brainly.com/question/1634952

#SPJ6

The following expression represents the profit made by John as he mows
lawns: P = 20L - 100
Which description correctly interprets each part of the expression?

Answers

Answer:

P is price per lawn, 20 is the money made per lawn, L is the number of lawns mowed, 100 is his initial cost.

Step-by-step explanation:

4. What is the slope of the graph of x – 2y = 8?

Answers

Answer:

The slope is 1/2

Step-by-step explanation:

Use the slope-intercept form  y  =  m x + b  to find the slope  m

Hope this helps:)

Which expression is equivalent to 64y18 – 1000z6?

Answers

Answer:

8 * (2y⁶ - 5z²) ( 4y¹² +10 y⁶z² + 25z⁴)

Step-by-step explanation:

64y¹⁸ – 1000z⁶ = 8 * (8y¹⁸ - 125z⁶) = 8 * ((2y⁶)³ - (5z²)³)

= 8 * (2y⁶ - 5z²) ( 4y¹² +10 y⁶z² + 25z⁴)

PLZ ANSWER I REALLY NEED IT

A student is asked to simplify the given expression. The student's response demonstrates which common misconception?
Simplify: x^4/ x^4 Student's response: 0
A) add exponents when dividing B) dividing by zero is undefined C) subtract exponents when dividing D) a number raised to the zero power is equal to 0

Answers

The answer to this question is D

find the volume of a right circular cone that has a height of 4.2 m and a base with a radius of 3.4 m. Round your answer to the nearest tenth of a cubic meter.

Answers

Answer: 50.8

Step-by-step explanation:

The volume of the given cone is 50.8 m³.

What is cone?

A cone is a shape created by connecting all the points of a circular base (which does not contain the apex) to a common point known as the apex or vertex using a series of line segments or lines.

Given that,

Height = h  = 4.2 m

Radius  of base = r  = 3.4 mm

Since we know that,

volume of cone = πr²h/3

now put the values

we get,

volume of cone =  π(3.4)²(4.2)/3

                          = 50.8 square m

Hence,

The volume = 50.8 m³

To learn more about cone visit:

https://brainly.com/question/30253224

#SPJ2

Other Questions
Is healthy care a delivery a business venture? Please help I was on this for a while What is the slope of the line 2x+8y=16 can anyone help D1||D2, x=??? Please helpI dont understand it Which of the following is equal to 2/3/7 When we look at a plant we notice that the leaves are green this is due to the Cost standards for one unit of product no. C77: Direct material 3 pounds at $2.50 per pound $ 7.50 Direct labor 5 hours at $7.50 per hour 37.50 Actual results: Units produced 7,800 units Direct material purchased 26,000 pounds at $2.70 $ 70,200 Direct material used 23,100 pounds at $2.70 62,370 Direct labor 40,100 hours at $7.30 292,730 Use the information to compute the following variances. The direct-material quantity variance is: What is the measure of an exterior angle of a regular hexagon?Enter your answer in the box. what digestive processes occur in the oral cavity the expression (x^12)(x^25)^2 is equivalent to x^p . what is the value of p What is herd immunity, and why are vaccines important for achieving herd immunity? Now that you have researched and gathered data. It is time to create a short outline for your paragraph. Be sure to define This note is:A. the note BB. the note GC. the note AD. the note C Which is the quotient of 154? A. 415 B. 223 C. 334 D. 4415 What 3 parts of the water cycle are a result of gravity? please help will give brainliest need fast Point out any instances of deadwood and pointless repetition in the followingsentences.1. At this point in time, we have no travel plans.2. In my opinion, I think depression is a terrible kind of illness.3. We have ignored and neglected the basic fundamental essentials for toolong a period of time.4. Men and women of both sexes must join the combat to fight for a betterworld.5. Sleepy and tired, he looked drained and exhausted. According to a physician in the 1500s, which of the following was a result of adding sugar to diet?(1 Point)strengthening body & mindcleans the blooddecays the teethall of the abovenone of the above make an equivalent fraction with the denominator 10,100, or 1000