Mathematics High School

(2x4+x3−4x2+3)+(4x4−2x3−x2+10x+2)



Express the answer in standard form.

Enter your answer in the box.

Answers

Answer 1
Im assuming there is exponents so if im assuming correctly, then the answer would be 6x^4 - x^3 - 5x^2 + 10x + 5 because you would combine like terms. 
Answer 2

Answer:  The required sum is [tex]6x^4-x^3-5x^2+10x+5.[/tex]

Step-by-step explanation:  We are given to find the following sum:

[tex]S=(2x^4+x^3-4x^2+3)+(4x^4-2x^3-x^2+10x+2).[/tex]

To find the sum, we need to add the coefficients of the same exponents of the unknown variable x.

The summation is as follows:

[tex]S\\\\=(2x^4+x^3-4x^2+3)+(4x^4-2x^3-x^2+10x+2)\\\\=(2+4)x^4+(1-2)x^3+(-4-1)x^2+10x+(3+2)\\\\=6x^4+(-1)x^3+(-5)x^2+10x+5\\\\=6x^4-x^3-5x^2+10x+5.[/tex]

Thus, the required sum is [tex]6x^4-x^3-5x^2+10x+5.[/tex]

Related Questions

Dan has a flower shop. Each day he displays 24 roses. He gives away 10 and sells the rest. Each day he displays 36 carnations. He gives away 12 and sells the rest. What expression can you use to find out how many roses and carnations Dan sells in in a week.

evaluate the expression to find out how many roses and carnations dan sells in a week

Answers

24 × 7 - (10 × 7)
36 × 7 - (12 x 7)

Two angles of a triangle have the same measure and the third one is 39 degrees greater than the measure of each of the other two. find the measure of the largest angle in the triangle.

Answers

Answer:

Step-by-step explanation:

By the Triangle Angle-Sum Theorem, all the angles of a triangle have to add up to equal 180.  If two of the angles are the same, then we will call them x.  The third one is 39 more than the measure of each of the other angles, so the third angle measures x + 39.  In equation form,

x + x + x + 39 = 180 and

3x + 39 = 180 and

3x = 141 so

x = 47

That means that the largest angle measures 47 + 39 which is 86

Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product? Check all that apply.Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product? Check all that apply.

Answers

We have the expression:
3x(x-12x) + 3x^2 - 2(x-2)^2

First, we will expand the power 2 bracket as follows:
3x(x-12x) + 3x^2 - 2(x^2 - 4x +4)

Then, we will get rid of the brackets as follows:
3x^2 - 36x^2 + 3x^2 - 2x^2 + 8x - 8

Now, we will gather the like terms and add them as follows:
-32 x^2 + 8x - 8

We can take the 8 as a common factor:
8 ( -4x^2 + x -1)

Answer:

It's option

A) the term...

C) after multiplying

D) the parentheses

Step-by-step explanation:

EDG2021



Which one of the following statements is NOT true of a free-falling object? An object in a state of free fall ____.



falls with a constant speed of -10 m/s.



falls with a acceleration of -10 m/s/s



falls under the sole influence of gravity



falls with downward acceleration which has a constant magnitude

Answers

Hi! C and D are not the answers, because they do fall downward and with the force of gravity. It does fall with an acceleration of -10 m/s. The object actually falls faster as it gets closer to ground and above 10 m/s, so the speed is not constant. The answer is A.

The statement which is NOT true among the given options is the first option - falls with a constant speed of -10 m/s.

In order to the determine which of the statements is NOT true, we will study each of the options one after the other.

For the first option - "falls with a constant speed of -10 m/s"

When an object is in a state of free fall, the speed is not constant. The speed actually increases as it moves closer to the ground.

∴ The first option is NOT true

For the second option - "falls with a acceleration of -10 m/s/s"

An object that is falling freely, falls under the influence of gravity. Acceleration due to gravity is approximately 10 m/s/s (10m/s²).

Therefore, an object in a state of free fall, falls with an acceleration of -10 m/s/s (The negative sign indicates deceleration, because the object is moving towards the ground).

∴The second option is true

For the third option - falls under the sole influence of gravity

As stated earlier, an object in a state of free fall, falls under the influence of gravity.

∴ The third option is true

For the fourth option - "falls with downward acceleration which has a constant magnitude"

As stated earlier, an object in a state of free fall, falls under the influence of gravity and acceleration due to gravity is approximately 10 m/s/s (10m/s²). This value is constant.

∴ The fourth option is true

Hence, the statement which is NOT true among the given options is the first option, falls with a constant speed of -10 m/s

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1. Find a counterexample.

If two angles are complementary, then they are not congruent.

Answers

45 and 45 degrees.

45 = 45
45 + 45 = 90

Suppose a number from 1 to 100 is selected at random. what is the probability that a multiple of 4 or 5 is chosen?

Answers

the range 1-100 is 100 numbers, divide by 4 and 5 to find the number of multiples.
100/4 = 25
100/5 = 20

probability of choosing multiple of 4
25/100 = 1/4
probability of choosing multiple of 5
20/100 = 1/5

the probabilities are not mutually exclusive because there are duplicate numbers, (overlap) multiples of both 4 and 5 being counted twice. 5/100 = 1/20
20, 40, 60, 80, 100

when "or" is used, add the probabilities, subtract the duplicates.

1/4 + 15 - 1/20 =
5/20 + 4/20 - 1/20 = 8/20 = 2/5

The probability that a multiple of 4 or 5 is chosen is 2/5.

The range 1-100 is 100 numbers, divide by 4 and 5 to find the number of multiples.

100/4 = 25

100/5 = 20

The probability of choosing a multiple of 4

25/100 = 1/4

The probability of choosing a multiple of 5

20/100 = 1/5

The probabilities are not mutually exclusive because there are duplicate numbers, (overlap) multiples of both 4 and 5 being counted twice.

5/100 = 1/20

20, 40, 60, 80, 100

When or is used, add the probabilities, and subtract the duplicates.

1/4 + 15 - 1/20

=5/20 + 4/20 - 1/20

= 8/20

= 2/5

The probability that a multiple of 4 or 5 is chosen is 2/5.

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PLEASE HELP?

Caitlin Grasso is a salesperson in the kitchen and bath department at Morris Supplies, Inc. She makes 5.5% straight commission on her total sales. What were her total week's sales, if her gross pay was $560?

A. $10,741.82
B. $3,640.00
C. $3,080.00
D. $10,181.82

Answers

5.5% = 560

1% = 560 / 5.5

100% = 100(560/5.5) = 10,181.82
*rounded

Hope this helps? :)

Answer:

D


Step-by-step explanation:

If her pay is $560, her sales is "something" whose 5.5% is 560.

We can setup the equation below and solve (let total sales be [tex]s[/tex]):

[tex](0.055)(s)=560\\0.055s=560\\s=\frac{560}{0.055}\\s=10,181.82[/tex]


Answer choice D is right.

I flip a fair coin four times what is the probability that i get more heads than tails

Answers

it will always be 50% heads 50% tails

Logan has a change jar that contains only pennies and nickels. he has 64 coins which add up to a total of $1.52. how many of each type of coin does he have?

Answers

6 nickels 19 quarters

Jimmy made a 15% profit on the sale of a custom designed boat, and the original cost of the boat was $15,000. the boat sold for how much?

Answers

2250 is the answer problem 15% of 15,000

PLZ PLZ HELP
Which graph represents the solution set of the system of inequalities?

{y<2/3xy≥−x+2

Answers

It is the third one on the graph.

Answer:

it was the 3rd one. i took the test :)

Convert 9.46 x 10^12 to expanded form

Answers

Your answer would be

(01.02) given that f(x) = 2x + 5 and g(x) = x − 7, solve for f(g(x)) when x = −3. (1 point) −15 −8 10 25

Answers

hello : 
 f(x) = 2x + 5 and g(x) = x − 7
f(g(-3))=f (-3-7) =f(-10) = 2(-10)+5 = -20+5 = -15

Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x = 7.

y=15 when x=6

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ ----------------------------\\\\ \textit{we also know that } \begin{cases} y=15\\ x=6 \end{cases}\implies 15=k6\implies \cfrac{15}{6}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{15}{6}x}\\\\ ----------------------------\\\\ \textit{what's \underline{y} when x=7?}\qquad y=\cfrac{15}{6}\cdot 7[/tex]
Final answer:

To write a direct variation equation, we use the form y = kx, where k is the constant of variation. We can find the value of k by substituting the given values into the equation. Once we have the value of k, we can write the direct variation equation that relates x and y. Finally, we can find the value of y for a given value of x by substituting it into the equation.

Explanation:

To write a direct variation equation, we use the form y = kx, where k is the constant of variation. We are given that y = 15 when x = 6. To find k, we can substitute these values into the equation:

15 = k * 6

To find the value of k, we divide both sides by 6:

k = 15/6 = 2.5

Now we can write the direct variation equation that relates x and y:

y = 2.5x

To find the value of y when x = 7, we substitute x = 7 into the equation:

y = 2.5 * 7 = 17.5

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To which set of numbers does the number -12 belong?

Answers

that belongs to the integers set, also rational and real number set


integers are like -4,-3,-2,-1,0,1,2,3,4 etc
rational numbers are number that can be written in form a/b where a and b are integers and b≠0
real numbes include rational numbers


so integers, rational number and real numbers

$250 is discounted into $212.50 what is the percent decrease

Answers

450 all together I think
15%
250 - 15% = 212.50

Which fraction represents the decimal .12 repeating

Answers

The answer is c.) 4/33

A science teacher needs to choose 4 students from a class of 20 to go to the library to do some research. How many different groups can he select?

Answers

The number of groups the science teacher can make is 5.

What are arithmetic operations?

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The total number of students is 20.

And, the number of students in one group is 4.

Now, the number of groups can be found using the following operation as,

Number of group = Total students ÷ Number for each group

⇒ 20 ÷ 4 = 5.

Hence, the total number of groups can be obtained as 5.

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Mrs marks has 3/4 pound of cheese to use making sandwiches she uses about 1/32 pound of cheese on each sandwich how many sandwiches can she make with the cheese she has?

Answers

3/4 = 24/32 and if each sandwich uses 1/32 cheese then she can make 24 sandwiches
(3/4) / (1/32) ...when dividing fractions, flip what u r dividing by, then multiply
3/4 * 32/1 = 24....so she can make 24 sandwiches

Which expression represents the phrase "half the sum of 10 and a number"

Answers

the answer should be 10/n

i know this is very late but for future people its

1/2 (10 + x)

What did the math teacher say after spending 8 hours in the ice and snow worksheet answer key?

Answers

Part 1

Given the question 'A set of 8 desert dishes costs $20. What was the cost of eah dish?'

Let the cost of each dish be x, then

8x = 20

x = 20 / 8 = 2.5

Therefore, the cost of each dish is $2.5



Part 2

Given the question 'Ben and Jerry together owns 24 comic books. If Ben owns 6 comic books, how many does Jerry own?'

Let the number of comic books owned by Jerry be x, then

x + 6 = 24

x = 24 - 6 = 18

Therefore, Jerry owns 18 comic books.



Part 3.

Given the question: 'Hans Klobber sells vaccum cleaners. He gets to keep one eighth of his sales as commission. How much must he sell in order to earn $1,000?'

Let the amount of sales required to earn $1,000 be x, then

1/8 (x) = $1,000

x = 8 times $1,000 = $8,000

Therefore, the amount of sale he must make to earn $1,000 is $8,000.



Part 4.

Given the question: 'On first down, a football team lost 8 yd. After 2 downs, the team had an overall gain of 20 yd. How many yards were gained on secong down?'

Let the number of yards gained on second down be x, then

-8 + x = 20

x = 20 + 8 = 28

Therefore, the number of yards gained on second down is 28 yards.



Part 5.

Given the question: 'After she wrote a check of $240, May Bounce had a balance in her checking account of -$6. What was her balance before she wrote the check?'

Let her balance before she wrote the check be x, then

x - 240 = -6

x = -6 + 240 = 234

Therefore, the balance in her checking account before she wrote the check was $234.



Part 6.

A bank of 8 floodlights together use 1,000 watts of power. How much power is used by each bulb?

Let the amount of power used by each bulb be x, then

8x = 1,000

x = 1,000 / 8 = 125

Therefore, the amount of power used by each bulb is 125 watts.



Part 7.

Given the question: 'Between noon and midnight, the temperature dropped 20°F. If the temperature was -8°F at midnight, what was the temperature at noon?'

Let the temperature at noon be x, then

x - 20 = -8

x = -8 + 20 = 12

Therefore, the temperature at noon was 12°F.



Part 8

Given the question 'If a strawberry pie is divided into 6 equal slice, each slice has 240 calories. How many calories are in the whole pie?'

Let the number of calories in the whole pie be x, then

1/6 (x) = 240

x = 240 times 6 = 1,440

Therefore, the number of calories in the whole pue is 1,440 calories.



Part 9.

Given the question: 'A chest was resting on the ocean floor 1000 ft below the surface. It was lifted to the deck of a ship 8ft above the surface. How far was the chest lifted?'

Let the distance the chest was lifted be x, then

-1,000 + x = 8

x = 8 + 1,000 = 1,008

Therefore, the distance the chest was lifted is 1,008 ft.



Part 10

Given the question: 'When all the kids who tried out for Little League were divided into teams of 20 players, there were exactly 8 teams. How many teams tried out?'

Let the number of kids that tried out be x, then

1/20 (x) = 8
x = 20 times 8 = 160.

Therefore, the number of kids that tried out was 160 kids.

You are ordering a hamburger and can get up to 8 toppings, but each topping can only be used once. you tell the cashier to surprise you with the toppings you get. what is the probability that you get 2 toppings? express your answer as a fraction or a decimal number rounded to four decimal places.

Answers

Final answer:

The probability of getting 2 toppings on the hamburger is 1/28 or approximately 0.0357.

Explanation:

To calculate the probability of getting exactly 2 toppings on your hamburger, we need to consider the total number of possible combinations of toppings and the number of ways to choose 2 toppings out of those combinations.

There are 8 toppings in total, so the total number of possible combinations is 8 choose 2, which is calculated as 8! / (2! * (8-2)!), or 28.

Since you want exactly 2 toppings, the probability is the number of ways to choose 2 toppings out of the total combinations divided by the total number of possible combinations, which is 1/28 or approximately 0.0357 (rounded to four decimal places).

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What is the best first step for solving the given system using substitution while avoiding fractions?

2x+6y=7
6x+18y=24

a. Solve for x in the first equation.
b. Solve for y in the first equation.
c. Solve for x in the second equation.
d. Solve for y in the second equation.

Answers

solve with subsitution avoiding fractions

2x+6y=7
6x+18y=24

if we solve for x in first, we get x=-3y+7/2, has fractions so no
if we solve for y in first, we get y=-x/3+7/6, has fractions so no
if we solve for x in the 2nd, we get x=-3y+4, no fractions so yay
if we solve for y in the 2nd, we get y=-x/3+4/3, has fractions so no


answer is C
Well, it says to avoid fractions. So I did the math: 

Solving for x in the first equation get you: [tex]x= \frac{7}{2}-3y [/tex]

Solving for y in the first equation gets you:[tex]y= \frac{7}{6} - \frac{2}{6}x [/tex]

Solving for x in the second equation gets you: [tex]x=4-3y[/tex]

Solving for y in the second equation gets you:[tex]y= \frac{24}{18} - \frac{6}{18}x [/tex]

If you look you can see the only option that does not give you fractions is if you solve for x in the second equation. So your answer is c! I hope this helps! =) 

The north american and european continents are moving apart at a rate of about 3 cm/y. at this rate how long will it take them to drift 500 km farther apart than they are at present?

Answers

In this case, the continents are moving apart at a rate (velocity = 3 cm/y) and the distance for continent to move(distance= 500km). You are asked how long it will take(time). Then to answer this question you need to convert the 500km into the same unit as the velocity which was cm. The formula would be:

Distance = velocity x time
500km x 10^5 cm/km= 3cm/year x time
time= 5x 10^7 cm / (3cm/year)
time= 1.7 x 10^7 year or 17 million year
Final answer:

The North American and European continents will take approximately 166,667 years to drift 500 km farther apart than they are at present.

Explanation:

The North American and European continents are moving apart at a rate of about 3 cm/y. To determine how long it will take for them to drift 500 km farther apart than they are at present, we can use the formula:



Time = Distance / Rate



First, we need to convert the distance from kilometers to centimeters. There are 100,000 centimeters in 1 kilometer, so 500 km is equal to 500,000 cm.



Using the formula, the time it will take is:



Time = 500,000 cm / 3 cm/y



Calculating this, we find that it will take approximately 166,667 years for the continents to drift 500 km farther apart than they are at present.

Jon places a dot on a coordinate plane at (-10, -4). He wants to place another dot across the y axis, and it must be 14 points away. Where will Jon place the other dot?

Answers

At (4,-4). Because, the first value is the horizontal x-coordinate and the second is the vertical y-coordinate, so the direction of going across the y-axis is a horizontal movement. Therefore, you must add 14 to the x-coordinate. You add because positive is the opposite direction of the your first x-coordinate, -10. So the answer is (4,-4).

The coordinates of the other dot across the y-axis will be located at (4,-4).

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

If shift down by 4 units, subtract 4 from the function

Since the first value corresponds to the horizontal x-coordinate and the second to the vertical y-coordinate, moving horizontally across the y-axis is the result. As a result, you need to multiply the x-coordinate by 14. Since the direction of your first x-coordinate, -10, is positive, you must add. the solution is (4,-4).

Thus, the coordinates of another dot across the y-axis will be located at (4,-4).

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NEED HELP ASAP!!!!!!!

Solve the equation.

e² = 0.36

Enter your answer in the box.

e = ±

Answers

square root of 36 = +/-6   so  square root of 0.36 is +/0.6

Answer:

0.6

Step-by-step explanation:

took the test

Convert the equation (y + 2) = –1/3(x – 4) to the point-slope form. Then fill in the blanks below to describe how to graph the equation.

Plot the point _______, move _______ unit(s) down, and _______ unit(s) over to find the next point on the line. 

Answers

The point-slope form of the equation of the line is:

(y - y1) = m (x - x1)

So, (y + 2) = - 1/3 (x - 4) in the point-slope form is:

 [y - (-2) ] = (-1/3) [ x - 4 ]

You must, then realize that the line passes through the point (4,-2) and its slope is - 1 /3.

That slope, -1 / 3, means that the function is decresing (because the slope is negative),  and it decreases one unit when x increases 3 units.

Now you can fill in the blanks in this way:

Plot the point  (4, -2), move 1 unit down, and 3 units over to find the next point on the line.

There are 4 teams in a basketball league. Each team plays each of the other teams three times. How many games are played?

Answers

each team plays 9 games

 ( Team 1 plays team 2 3 times, team 3 3 times, team 4 3 times )


9 x 4 = 36 games total

What is the length of HN

Answers

hn is half the total length

38/2 = 19

HELP PLEASE The Appalachian Mountains had what effect on the people of the thirteen original colonies? A) they acted as a barrier to further settlement to the west B) they provided protection to the colonists from invading Indians C) they provided protection to the colonists from Spanish conquistadors D) animals lived there and were an important food source to major cities in the East

Answers

The answer is A they acted as a barrier to further settlement to the west. The Appalachians were the western outskirt of the states. They were an obstruction that kept them closer to the drift. The mountains stopped expansion of the colonies. To hard to go over to create new colonies

the answer is...



A) they acted as a barrier to further settlement to the west
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