Mathematics Middle School

Factor completely 2x3 + 10x2 + 4x + 20.
2(x3 + 5x2 + 2x + 10)

2[(x + 5)(x2 + 2)]

(2x + 10)(x2 + 2)

(x + 5)(2x2 + 4)

Answers

Answer 1
2x^3 + 10x^2 + 4x + 20
= 2(x^3 + 5x^2 + 2x + 10)
= 2[x^2(x + 5) + 2(x + 5)]
= 2[(x+5)(x^2 + 2)]

answer
2[(x + 5)(x^2 + 2)] 
Answer 2

Answer:

Step-by-step explanation:

Alright, lets get started.

The given expression is :

[tex]2x^3+10x^2+4x+20[/tex]

taking 2 common factor

[tex]2(x^3+5x^2+2x+10)[/tex]

[tex]2(x^3+2x+5x^2+10)[/tex]

[tex]2[(x+5)(x^2+2)][/tex]

So, the correct answer is option B :    answer

Hope it will help :)

Related Questions

A board game that normally costs $30 is on sale for 25 percent off. What is the sale price for the game?

Answers

$22.50 is the answer because 25 percent of 30 is 7.5, 30 minus 7.5 is 22.5

Plz mark brainliest, glad to help.

Figure a’b’c’d’f is a dilation or figure abcdf by a scale factor of 1/2. The dilation is centered at (-4,-1)


Which statement is true?

Answers

What are the options?

5/8 0.67 1.2 3/5 Greatest to least

Answers

1.2
0.67
5/8
3.5

I think this is what it would be.

What does the phrase “took to It like a duck takes to water” mean in this sentence?

When the young woman started learning how to play the saxophone she “took to It like a duck takes to water”

A) she practiced often
B) she found It natural
C) she played for others
D) she improved gradually

Answers

The answer to this question would be B)She found it natural
Final answer:

The phrase means the young woman found it natural and quickly developed a liking for learning how to play the saxophone.

Explanation:

The phrase "took to it like a duck takes to water" means that the young woman found it natural and took a liking to learning how to play the saxophone effortlessly and quickly. It implies that she had a natural talent and aptitude for playing the instrument. This expression is often used to describe someone who picks up a new skill or activity easily and enthusiastically.

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need an answer as soon as possible.
asking for a friend.

Use the sequence: 1, –2, 4, –8, . . .
a. Find the common ratio in the sequence.
b. Write a rule for the sequence.
c. Find the next three terms

Answers

Part A

Answer: The common ratio is -2

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

Explanation: 

To get the common ratio r, we divide any term by the previous one

One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2

Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time

Side Note: each term is multiplied by -2 to get the next term

============================================================
Part B

Answer:
The rule for the sequence is 
a(n) = (-2)^(n-1)
where n starts at n = 1

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

Explanation:

Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio

The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)

============================================================
Part C

Answer: The next three terms are 16, -32, 64

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

Explanation:

We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms

-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64

showing that the next three terms are 16, -32, and 64

An alternative is to use the formula found in part B

Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier

Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier

Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier

while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)

The annual snowfall in a town has a mean of 38 inches and a standard deviation of 10 inches. Last year there were 63 inches of snow. Find the number of standard deviations from the mean that is, rounded to two decimal places

Answers

This is 2.5 standard deviations from the mean.

We find this by subtracting the mean from our value, and dividing by the standard deviation:
(63-38)/10 = 25/10 = 2.5

given the equation (x-a)^2(x-2)=x^3+bx^2+12x-72 find a and b

Answers

Final answer:

To find the values of a and b, expand the given equation and compare it with the cubic equation. The values of a and b are 2 and -10, respectively.

Explanation:

To find the values of a and b, we can expand the given equation and compare it with the cubic equation x³ + bx²+ 12x - 72 = 0. Expanding and comparing the coefficients, we get:

a = 2

b = -10

In the box, complete the first 4 steps for graphing the quadratic function given. (Use ^ on the keyboard to indicate an exponent.) Then print a sheet of graph paper and graph the quadratic function to turn in to your teacher. Be sure to label the axes and vertex.

y = -x2 - 4x - 3

hellllllllllllllp

Answers

Answer:

This was my answer, hopefully it helps!

Final answer:

To graph the quadratic function y = -x^2 - 4x - 3, find the vertex, plot additional points, and connect them with a curve.

Explanation:

To graph the quadratic function y = -x2 - 4x - 3, follow these steps:

Identify the coefficients and constant term: a = -1, b = -4, c = -3.Find the x-coordinate of the vertex using the formula x = -b/(2a):x = -(-4)/(2*(-1)) = -4/(-2) = 2Substitute the x-coordinate of the vertex into the equation to find the y-coordinate:y = -(2)2 - 4(2) - 3 = -4 - 8 - 3 = -15Plot the vertex at (2, -15) on the graph paper.Use the symmetry of the parabola to plot two additional points, equidistant from the vertex:If we move 1 unit to the right of the vertex (x = 3), we find y = -(3)2 - 4(3) - 3 = -9 - 12 - 3 = -24.If we move 1 unit to the left of the vertex (x = 1), we find y = -(1)2 - 4(1) - 3 = -1 - 4 - 3 = -8.Connect the three points with a smooth curve to complete the graph.Label x-axis, y-axis, the vertex, and any other relevant points or lines.

Find a irrational number between 7.7 and 7.9 explain why it’s irrational

Answers

7.77777777 repeating

Irrational numbers are:

Numbers that repeat 
7.7777777 repeats the number 7 after the decimal

Numbers that CANNOT be written as a simple fraction.
7.7777777 cannot be written as a fraction in simplest form.

Answer = 7.777777777 repeating

~Aamira~

Hope this helped :)
Yeah what he said :) lol yuhhr welcome

Please help (puppy eyes)

Answers

First we have to find the decimal equivalent by dividing.
5 / 8 = 0.625

It can't be an Integer because decimals can't be intergers, so that's ruled out

It can't be repeating as it does end, so that's also ruled out

Since the decimal does end it can't be non-terminating, non-repeating

So the answer is Terminating Decimal by process of elimination

The local volleyball team hosts a concession stand to raise money. They spend $120 to purchase popcorn, candy, and drinks. They buy 95 bags of popcorn at $0.75 each and 35 bags of candy at $1.20 each. How much money does the volleyball team have left to spend on drinks?

a. $7.25 b. $15.50 c. $6.75 d. $20.25

Answers

The answer is C. $6.75.

This is found by multiplying 95 by $0.75 and adding the product ($71.25) to the product of 35 times $1.20 ($42). Then subract $113.25 (sum of $42 and $71.25) from 120 to get your final answer.

I hope this helps!

The money left to spend on drinks is $6.75.

Correct option is (C).

What is Arithmetic?

The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations. The term "arithmetic" (which comes from the Greek word "arithmos," "number") often refers to the fundamental concepts in number theory, measurement, and computation (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

As per the given data:

Total money spend = $120

95 bags of popcorn at $0.75 each

35 bags of candy at $1.20 each

Money spend on popcorn = 0.75 × 95 = $71.25

Money spend on candy = 1.20 × 35 = $42

Money spend on popcorn and candy = $71.25 + $42 = $113.25

Money left to spend on drinks:

= Total money - Money spend on popcorn and candy

= $120 - $113.25

= $6.75

Hence, the money left to spend on drinks is $6.75.

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Which of these is an example of a random sample?
A.
The manager of a baseball team asks his team members about their views on the previous game they played.
B.
For a survey on air travel, 100 people are chosen randomly from five different airports.
C.
Five players from a basketball team are chosen for a game.
D.
Three members of a band are chosen for a concert.

Answers

The answer is B. The other answer choices are incorrect because they include only a certain group of people so it wouldn't be as random.

Answer:

b

Step-by-step explanation:

the others are incorrect because they talk about group so its not random.

Please help me!
How many possible outcomes are there when you roll four dice?

A. 1416
B. 1296
C. 24
D. 36

Answers

There are C. 1296 outcomes when you roll 4 dice. Hope this helps:)
Final answer:

When rolling four six-sided dice, there are 1296 possible outcomes. This is calculated by raising the number of outcomes for one die (6) to the power of the number of dice (4).

Explanation:

The subject of this question pertains to the probability in Mathematics, specifically focusing on the number of possible outcomes when rolling a die multiple times. In this case, we're looking at rolling four six-sided dice.

When you roll one die, there are indeed 6 possible outcomes, as a standard die has 6 faces. But if you roll two dice, the number of possible outcomes increases to 36 (6 outcomes for the first die times 6 outcomes for the second die).

Now in our case we are rolling four dice. Hence, the number of outcomes will be 6 to the power of 4, which means 6 * 6 * 6 * 6 = 1296. Therefore, the correct answer is B. 1296.

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john surveyed a random sample of 10 students in 7th grade seven of them they would vote for tammy as class president if there are 230 students in 7th grade what is the best estimate of the students who would vote for tammy

Answers

7 out of 10 would vote for Tammy so what value (x) would vote for her out of 230. Set up a proportion comparing the two.

x= # of people who vote Tammy

7 out of 10= x out of 230
7/10= x/230
cross multiply

(7*230)= (10*x)
1610= 10x
divide both sides by 10

161= x


ANSWER: 161 people in 7th grade would vote for Tammy.

Hope this helps! :)

please help50 points and brainliest to first one to answer

Answers

762 is the answer to the first one

a jar contains blue, red, yellow, and green marbles. p(blue) = 1/4. what type of probability isillustrated and why

Answers

I believe it's theoretical probability, because there are no experiments to base the probability from.
It is an theoretical probability :)



Hope I'm right!!





Give me 5 stars and brainliest if so.


Each side of ΔABC is 75 units in length. Point D is the foot of the altitude drawn from side A to side BC. Point E is the midpoint of segment AD. What is the length of BE

Answers

The first thing is to calculate the area of the triangle ABC using the Hero's formula. 
Area = √(s(s-a)(s-b)(s-c))
Where s is half the perimeter and a, b, and c are the lengths of the triangle.
s = 0.5(3×75) = 112.5
Since our triangle is equilateral, a=b=c
Area = √(112.5(112.5-75)³) 
        = √5,932,617.188
        = 2,435.696448 square units.
The same area can be found using the formula, 0.5(bh). Where b is the base length and h is the altitude from the base length.
In this triangle, b=75.

∴ 2,435.696448 = 0.5(75×h)

     h = 4,871.392896÷75
        =64.95190528 units

Since E is the midpoint of AD, then DE=h÷2=32.47595264 units

Now we have a right triangle BDE, where BE is the hypotenuse and BD=75/2. 

∴ BE = √((BD)²+(DE)²)
         =√(37.5²+ 32.47595264²)
         = √2,460.935815
         = 49.6078 units.
The answer is 49.6078 units.

SOlution:

Area = √(s(s-a)(s-b)(s-c)).s = 0.5(3×75) = 112.5So,Area = √(112.5(112.5-75)³)         = √5,932,617.188        = 2,435.696448 square units.
2. 2,435.696448 = 0.5(75×h)
     h = 4,871.392896÷75        =64.95190528 unitsDE=h÷2
=32.47595264 units


3. BE = √((BD)²+(DE)²)         =√(37.5²+ 32.47595264²)         = √2,460.935815         = 49.6078 units.

3/4 + 5/7 reduce to lowest term

Answers

3/4 + 5/7 = 3
_
5 is they answer

On the first day of the year you have $700 in your bank account you spend $35 per week your friend starts the year with 450 in his bank account he said to $15 per week solve the equation 700-35W equals 450+15 W to find out how many weeks W it will take for you and your friend to have the same amount of money in your bank account

Answers

700 - 35W = 450 + 15W
       +35W            +35W
700 = 450 + 50W
-450  -450
350 = 50W 

7 = W

It will take 7 weeks for their bank accounts to be the same. 

Put the two expressions 700-35w and 450+15w on either side of an equal sign. Solve. 
Hope this helps!

The Roman Empire began in 27 B.C. and ended in 476 A.D. The Persian Empire lasted approximately 5/11 as long as the Roman Empire. Based on this approximation, if the Persian Empire began in 550 BC, in what year did it end?
Round all years to the nearest whole number.

Answers

Step One
How many years did the Roman Empire Last?
Abs(27) + 476 = Roman Empire.
27 + 476 = 503 years.

Note the total number of years starts in BC. To add that to the AD number of years you have to take the absolute value of the 27. Otherwise you would be subtracting and that would make the total number of  years wrong by 54 years.

Step Two
Find 5/11 of the total number of years.
(5/11) * 503 = 228.6363 Hold off on rounding.

Step Three
Find the ending date.
Starting date = 550 BC
Ending date = ???
Number of years between Start and end = 228.6363
Ending date = starting date - 228.6363 you are working towards AD
Ending date = 550 - 228.6363
Ending date = 321.4 BC
Rounded that comes to 321 BC.

Answer:321

Step-by-step explanation:

see the difference between the roman empire numbers

find 5/11 of that

see how much there already is and subtract

jerry built a coffee table for his living room. His table, that also serves as storage bin, is in the shape of a trapezoid. He wants to build a shelf in the middle of the coffee table to separate his photo album storage from his magazines. the top opening of the box is 22 inches and the base of the box is 12 inches. How long should he make the shelf to fit in the middle?

Answers

Answer: The correct answer is 17 inches.

Answer:

17 inches

Step-by-step explanation:

Given that jerry built a coffee table for his living room. His table, that also serves as storage bin, is in the shape of a trapezoid. He wants to build a shelf in the middle of the coffee table to separate his photo album storage from his magazines. the top opening of the box is 22 inches and the base of the box is 12 inches.

To make the trapezium into two halves he can draw a middle line from the mid points of the two non parallel sides.

Since base I =22 inches and base II = 12 inches we get

the middle line would be the average of the two bases

(Recall mid point theorem on triangles extended to trapeziums)

Hence we have the length required

=[tex]\frac{1}{2} (22+12)\\\\=\frac{1}{2} (34)\\=17 inches[/tex]

find the value of x.

Answers

The figure has 4 sides, so we know that the interior angles add up to 360 degrees.

Make all the angles equal 360 degrees.

x + 92 + 82 + 47 = 360
x + 221 = 360
x = 139°

Juan added 3/5 gallon of gasoline into his car’s empty fuel tank on Sunday. He uses 1/5 gallon of gasoline on Monday to go to work. He uses 2/5 gallon of gasoline on Tuesday during a short trip. Is his fuel tank empty after he drives on Tuesday? Explain.

Answers

Juan tank is empty because if he added 3/5 of gasoline to fill up his tank, and used 1/5 of it one Monday, that would equal 2/5.On Tuesday he uses 2/5 of the gasoline such equals zero. Hope this helped :)

How much interest is earned in four years on a deposit of 10,000 if it is allowed to accumulate in an account paying 7% interest compounded annually

Answers

Equation for one year:
0.07(10000) + 10000
But for 4 years:
4(0.07(10000)) + 10000
0.28(10000)) + 10000
We can make it simpler:
1.28(10000)
Multiply:
12800
YOU WILL HAVE $12800

6xt3x -x+9 =33 solve the equatolion

Answers

I'm pretty sure it's 3 (I did it in my head)

Find the percent of decrease from 280 to 210. Round to the nearest tenth of a percent, if necessary.
a 0.3% b 25% C 33.3% D 133.3%

Answers

I got the answer c and if I am correct then it is repeating also
280n = 210
Isolate n:
n = 0.75
1.0 - 0.75
25% decrease, option b

Solve. 5x+10+7x=-3+13+7x+12

Answers

For this problem, we can move all the X's to one side and all the regular numbers to the other. 

7x comes over and become -7x 

10 goes over and becomes -10.

5x+7x-7x=-3-10+13+12.

-3-10=-13, which cancels out the positive 13.

-7x+7x=0 which cancels each other out. 

Now, 5x=12

Divide each side by 5.

x=2.4  <--- final answer. 
Hey there! :) 

5x + 10 + 7x = -3 + 13 + 7x + 12

Add like terms.

(5x + 7x) + 10 = (-3 + 13 + 12) + 7x

Simplify.

12x + 10 = 22 + 7x

Now, we have to isolate x. To do that, we must start out by subtracting 10 from both sides.

12x = 22 + 7x - 10

Then, subtract 7x from both sides.

12x - 7x = 22 - 10

Simplify.

5x = 12

Divide both sides by 5.

x = 12/5 OR as a decimal, x = 2.4

~Hope I helped!~

How to Factor out the coefficient of the variable 3n-24

Answers

Find the greatest common factor between 3n and 24. It's 3. 

Now divide each term by 3 inside the equation. 

3n / 3 = n
- 24 / 3 = - 8

So your new equation is 3(n - 8). 

Emanuel was charged $32\$32$32dollar sign, 32 for a 1429 km14\dfrac29 \text{ km}14​9​​2​​ km14, start fraction, 2, divided by, 9, end fraction, space, k, m taxi ride. What was the cost per kilometer?

Answers

 2 1/4, because you  have to divide 32 by 14 2/9 resulting in the the 14 2/9 to be 128/9 and then flipped, 9/128.Afterwards, cross out the the 32 and 128 since 32 is a factor of 128 to get 1 and 4.Then apply mutiplication 1/1 * 9/4= 9/4 or 2 1/4 

We are required to find the cost per kilometer of Emmanuel.

The cost per kilometre is $2.25 OR $2 and 25cents.

According to the question, the total cost of the journey = $32

The total distance covered during the journey =

14 2/9 km

Therefore, the cost per kilometre can be evaluated mathematically as follows;

Cost per kilometer = cost of the journey ÷ Distance of the journey

= 32 ÷ 14 2/9

By converting 14 2/9 to an improper fraction; we have;

= 32 ÷ 128 / 9

= 32 × 9/128

= (32×9) / 128

= 288 / 128

= 2 32/128

= 2.25 dollar per kilometer

Therefore, the cost per kilometer is $2.25

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Shavon is going to wrap a box that is shaped like a rectangular prism. The box is 12 inches long, 8 inches wide, and 3 inches high. What is the least amount of wrapping paper that Shavon will need to completely cover the Box?

Answers

It is given in the question that , the box is 12 inches long, 8 inches wide and 3 inches high .

We have to find the least amount of wrapping paper that Shavon will need to completely cover the box .

And for that we have to use the formula of surface area, which is

[tex] Area= 2(length*width+width*height+length*height) [/tex]

Substituting the values of length, width and height, we will get

[tex] Area= 2(12*8+8*3+12*3) =2(156)=312 [/tex]

Correct option is the last option .

Other Questions
Juan makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours Traits, conditions, or diseases that are passed down through families through one of the X or Y chromosomes. If sin (13y-5) = cos (2y+5), then what is the value of y? Read the following excerpt from the novel Pride and Prejudice and answer the question that follows. from Pride and Prejudice by Jane Austen "In vain I have struggled. It will not do. My feelings will not be repressed. You must allow me to tell you how ardently I admire and love you." Elizabeth's astonishment was beyond expression. She stared, coloured, doubted, and was silent. This he considered sufficient encouragement; and the avowal of all that he felt, and had long felt for her, immediately followed. He spoke well; but there were feelings besides those of the heart to be detailed; and he was not more eloquent on the subject of tenderness than of pride. 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