Mathematics Middle School

How do I find the prime factorization of 40? And what is prime factorization?

Answers

Answer 1
Prime factorization is a way of showing which prime numbers (numbers that can only be divided by one and itself) can go into a number. For instance, the prime factorization of 4 would be 2 x 2. Two can only be divided by one and itself, so it is a prime number, and 2 x 2 = 4. For larger numbers, divide by a prime number until the number that is being divided is a prime number. Each divisor will be used as part of the prime factorization. The final dividend will also be used. Add the dividend, order each divisor from least to greatest, and then you're done. Therefore, the prime factorization of 40 would be 2 x 2 x 2 x 5.
Answer 2
Final answer:

Prime factorization is finding the prime numbers that multiply to create the original number. The prime factorization of 40 is 2³ × 5.

Explanation:

Prime factorization is the process of breaking down a composite number into the prime numbers that, when multiplied together, give the original number. To find the prime factorization of 40, you would start by finding two numbers that multiply to give you 40. You could start with 4 × 10. Since 4 is not a prime number, it can be further broken down into 2 × 2. The number 10 can also be broken into prime factors 2 × 5. Therefore, the prime factorization of 40 is 2 × 2 × 2 × 5, or 2³ × 5.

Related Questions

The sum of r and t is equal to 42. Let r = 25. What is the value of t?

Answers

r + t = 42
r = 25

Plug in 25 for r

(25) + t = 42

Isolate the t by subtracting 25 from both sides

t + 25 (-25) = 42 (-25)
t = 42 -25
t = 17

Hope this helps
Since r = 25, t must equal a number that, when added to 25, equals 42.

42 - 25 = 17. t must equal 17.

17 + 25 = 42.

456 000 has been rounded to the nearest thousand. What was the smallest possible number this could have been?

Answers

The smallest possible number could have been 455,500

Answer:

The smallest possible number this could have been = 455500

Step-by-step explanation:

456000 has been rounded to the nearest thousand.

If the value is more than 456500 the value rounded to the nearest thousand is 457000.

If the value is less than 455500 the value rounded to the nearest thousand is 455000.

In between 455500 and 456500 the value rounded to the nearest thousand is 456000.

So,  The smallest possible number this could have been = 455500

18m-9v+6v-7m hope you can help

Answers

Here, you have to combine like terms. So, it is 11m-3v.
by combining 18m and -7m you get 11m. then you combine -9v and 6v to get -3v. the answer is 11m-9v.

To make an ice-cream cone, employees at an ice-cream shop completely fill the cone and then add one scoop of ice cream on top. The cone has a height of 6 inches and a diameter of 2 inches. To the nearest cubic inch, how much ice cream is in the cone before the scoop is added on the top?
A 6 in³
B 19 ​in³​
C 25 ​in³​
D 75 ​in³​

Answers

It is B I believe have a nice day

Answer:Its probably A

Step-by-step explanation:

PLEASE HELP ME IM IN A BIG HURRY

The price of a pair of headphones is $49.99 before tax. Ron bought the headphones for a 50% discount. He then paid sales tax of 8% on the discounted price.

Part A: How much did Ron pay in sales tax? Show all work and steps in your solution.
Part B: What is the total amount that Ron paid for the headphones? Show all work and steps in your solution.

Answers

Part A:
Price before tax: $49.99
Discount: 50% of $49.99 = 50% * $49.99 = 0.50 * $49.99 = $25.00
Discounted price: $49.99 - $25.00 = $24.99
Tax on discounted price: 8% of $24.99 = 8% * $24.99 = 0.08 * $24.99 = $2.00

Part B:
Total price: $24.99 + $2.00 = $26.99

A carpenter is creating a circular wooden table with a radius of 4 feet and needs to know the area of the table to purchase the correct amount of stain to finish it.

What is the area of the table?

Use 3.14 for π .

Enter your answer, as a decimal, in the box.

(?) ft²

Answers

Answer: The area of the circular wooden table = 50.24 ft²

Step-by-step explanation:

Given: The radius of the circular table = 4 feet

We know that area of a circle is given by :-

[tex]\text{Area}=\pi r^2[/tex]

Therefore, the area of circular wooden table is given by :-

[tex]\text{Area}=3.14(4)^2\\\Rightarrow\ 3.14\times16\\\Rightarrow\text{Area=}50.24\ ft^2[/tex]

The area of the circular wooden table = 50.24 ft²

Answer: 50.24

Step-by-step explanation:

We know: The radius = 4 feet and that the area of a circle = πr^2

Next: (π) 3.14 (4)^2

which we can simplify to be 3.14 * 16

= 50.24

(just took the test hope this helped)

what term should be added to create a perfect square trinomial ??

x^2+18x
i think it’s +81 but i’m not positive.

Answers

Yes you are correct. You take half of the x coefficient 18 to get 9, then you square 9 to get 81

x^2+18x+81 is a perfect square trinomial which factors to (x+9)^2

Combine any like terms in the expression. If there are no like terms, rewrite the expression. 4s^2 + t^3 + 3s^2 – 7s^2

Answers

[tex] 4s^2 + t^3 + 3s^2 - 7s^2[/tex]
=[tex] t^3 [/tex]

Mr. Stuart has 12 girls and 10 boys in his math class. He writes each of their names on a separate sheet of paper and puts all of the names in a bag. He selects one name without looking. What is the probability that Mr. Stuart will select a boy’s name?

Answers

The probability of Mr. Stuart pulling a boys name is very likely. Although there is slightly more girls it is still as many boys.

the sun of 3 times a number and 5 is 2 times the number plus 15. what is half the number

Answers

3x+5=2x+I5
-5. -5
3x. =2x+10
-10 -10
3x-10=2x
-3x. -3x
-10= -1x
-1 -1
10=x

Dennis can load the car in 28 min. If Andy helps him it takes 21 min to load the car how long will it take Andy alone?

Answers

let the load car = y , and Andy will take time x (min.) to load the car
So,
    The rate of Andy to load the car = y/x

And we given that: Dennis load the car in 28 min.
So,
    The rate of Dennis to load the car = y/28

If both are loading the car in time = t = 21 min
then:
         y = (y/x) t + (y/28) t     ⇒ divide all equation by y and substitute with t
∴      1 = (21/x) + (21/28)     ⇒ multiply all equation by 28x
        28x = 21*28 + 21x
        28x - 21 x = 588
        7x = 588
∴      x = 84 min.

Which mean Andy will take 84 min. to load the car alone.

While attending a college football game, you think you can guess the attendance within 10% of the actual value. If the announced attendance is 65,000, within what number of people would your guess have to be in order for you to support your claim?

Answers

Answer:

13,000 People

Step-by-step explanation:

65,000 (0.1) = 6500

6500 (2) = 13,000

You multiply by 2 to get 10% above or below the announced attendance.

Answer:

6,500

Step-by-step explanation:

If you think you can guess the attendance within 10% of the actual value, then your guess would have to be within 6,500 of the actual attendance of 65,000 in order for you to support your claim. This is because 10% of 65,000 is 6,500. So if your guess is within 6,500 of the actual attendance, then you can support your claim.

The data below shows the average of text messages a group of students sends per day. Which histogram could represent the data?

Answers

The answer should be B

What is 534.076 rounded to the nearest hundredth? A. 534.07 B. 534 C. 500 D. 534.08

Answers

its going to be obviously D

D 534.08 this would help

58 people attend a banquet at Disney residents paid 13.00 and non residents paid 17.50. If Disney made 925.00 from ticket sales for the event how many residents and non residents attended

Answers

x= # of residents
y= # of non residents

QUANITY EQUATION
x+y= 58

COST EQUATION
$13.00x + $17.50y= $925.00

SOLVE FOR 1 VARIABLE
x+y= 58
subtract y from both sides
x= 58-y

SUBSTITUTE IN 2nd EQUATION
$13.00x + $17.50= $925.00
13(58-y) + 17.50y= 925.00
multiply 13 by all in parentheses
(13*58)+(13*-y)+17.50y= 925.00
754-13y+17.50y= 925.00
combine like terms
754+4.50y= 925.00
subtract both sides by 754
4.50y= 171
divide both sides by 4.50
y= 38 number of non residents

SUBSTITUTE TO FIND X
x+y= 58
x+38= 58
x= 20 number of residents

ANSWER: 20 residents and 38 non residents attended.

CHECK:
$13.00(20) + $17.50(38)= $925.00
260 + 665= 925
925 = 925

Hope this helps! :)

Answer:

$925.00

Step-by-step explanation:

If mJK=(7x-39) and mML)=87, find x

Answers

If two chords of a circle are congruent, then their intercepted arcs are congruent
7x-39 = 87
7x = 87 + 39
7x = 126
x = 126/7
x = 18

The value of X calculeted in the circle is equal to 18.

What is the 2 parallel lines?

Parallel lines are basically two straight lines that do not have a point in common. In other words, they are two lines that do not meet, but that necessarily have the same direction.

If two chords of a circle are paralles, then their intercepted arcs are congruent:

[tex]7x-39 = 87\\7x = 87 + 39\\7x = 126\\x = 126/7\\x = 18[/tex]

See more about circle at brainly.com/question/11833983

What is the area of the figure?
Please explain how you got your answer!
(the missing length is 25)

Answers

 232.5 (Triangle)
+320.  (Rectangle)
=------------
342.5 (area)

What is the value of h when the function is converted to vertex form?

Answers

y = x^2-14x+29
a = 1, b=14, c =29

h = b/2a
h = 14 / 2*1 = 14/2 = 7
 h = 7

what is the intersection points of f(x)=2x+7 and g(x)=x^2-1

Answers

intersecting means f(x)=g(x)
2x+7=x²-1
x²-2x-8=0
(x-4)(x+2)=0
x=4, or x=-2
when x=4, f(x)=g(x)=15
when x=-2, f(x)=g(x)=3
so the intersecting points are (4, 15) and (-2, 3)

is 15\16 already in its simplest form?

Answers

Hi!

Yes, this fraction is in its simplest form because you cannot factor this anymore then it already is. I tried to factor out a 3 and a 2, but it still does not work.

The simplest form is [tex] \frac{15}{16} [/tex]

-ASIAX Frequent Answerer

14x-5(-2x+3)

Distributive and combine

Answers

Multiply parenthesis by -5

14x+10x-15 ( Collect the like terms)

The answer will be:
24x-15

Will give brainliest please help asap

Answers

Translation, rotation, reflection do not affect congruence. Dilation destroys congruence.

C
NC
C

The graph of a system of two linear equations has no solution . What is true about the lines

Answers

They are parallel lines.
They are parallel. This means that they will never intersect and they have the same slopes.

How much compound interest is earned on $2050 at 4% interest for 3 years, compounded annually? Give your answer in dollars and cents. Don’t forget to subtract P from A.

Answers

To solve for the amount + interest for compounding interest you will use this formula:
[tex]A = P ( 1 + \frac{r}{n}) ^{nt} [/tex]

Where A = Accrued amount
           P = Principal amount
           r = rate in decimal
           t = number of years
           n = compounding periods per unit of time
Your given:
P = $2050
r = 4% or 0.04
t = 3 years
n = 1 per yr
Now we insert that into your formula:
[tex]A = P ( 1 + \frac{r}{n}) ^{nt} [/tex]
[tex]A = 2050 ( 1 + \frac{0.04}{1}) ^{1.3} [/tex]
[tex]A = 2050 ( 1 + 0.04) ^{3} [/tex]
[tex]A = 2050 ( 1.04) ^{3} [/tex]
[tex]A = 2050 (1.124864 ) [/tex]
[tex]A = $2305.97 [/tex]

Now to get the interest just remember that:
I = A - P
I = $2,305.97 - $2,050
I = $255.97
So that is equal to 255 dollars and 97 cents


 $255.97 is the correct answer

The cost of 7 drinks is $16.38. What is the cost of each drink?

$1.54
$1.88
$2.34
$2.73

Answers

the answer to thus question is $2.34

The cost of each drink if 7 drinks cost $16.38 is $2.34.

What is Division?

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that the cost of 7 drinks is $16.38. Therefore, the cost of each of the drink will be:

Cost of each drink = Cost of all the drinks / Number of drinks

                               = $16.38 / 7

                               = $2.34

Hence, the cost of each drink is $2.34.

Learn more about Division:

https://brainly.com/question/369266

#SPJ3

On Saturday, you spend $33, give $15 to a friend, and receive $20 for mowing your neighbor’s lawn. You have $21 left. Use two methods to find how much money you started with that day.

Answers


21+20-15-33=x

x=-7

Hope this helped☺☺

I need help on Q #6-10 show all work please

Answers

6. 
x = x/a + b
x - b = x/a
ax - ab = x
ax - x = ab
x(a - 1) = ab
x = ab/(a - 1)

7. x/3 + x/a = 1
x + 3x/a = 3
ax + 3x = 3a
x(a + 3) = 3a
x = 3a/(a + 3)

8. x/a + bx = c/a
x(1/a + b) = c/a
x = c/a(1/a + b)
x = c/(ab + 1)

9. x/a - 2x = c
x(1/a - 2) = c
x = c/(1/a - 2)
x = ac/(1 - 2a)

10. x/a = b + 3x
x/a - 3x = b
x(1/a - 3) = b
x = b/(1/a - 3)
x = ab/(1 - 3a)

Add the two expressions.

−6.3x+4 and 1.5x−6

Enter your answer, in simplified form, in the box.

Answers

-4.8x + -2 (don't combine those because aren't like terms)
Is your answer correct

I’ve been looking at this for a while, and I can’t figure out the answers. Can someone walk me through it?

Answers

A , B and E - not a solution
C is a solution 6x+4x^3
D is a solution as well
It could be E,D,and B

If the circumference of a circle measures 3/2 π cm, what is the area of the circle in terms of π?

Answers

Final answer:

The area of the circle with a circumference of 3/2 π cm is 9/16 π cm².

Explanation:

The question is asking about finding the area of a circle when the circumference is given. The formula to find the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle. Given that the circumference is 3/2 π cm, we can use this information to find the radius.

From the circumference equation, r = C/2π = (3/2π)/ 2π = 3/4 cm. Having the radius, we can then use the formula for the area of a circle, which is A = πr². As a result, the area of the given circle is π(3/4)² cm² which simplifies to 9/16 π cm².

Learn more about Area of Circle here:

https://brainly.com/question/28642423

#SPJ12

Other Questions
A spaceship orbiting earth flies to the moon. How is the gravitational force pulling on the spaceship related to the distance that the spaceship is from the earth? Question 25 options: As the distance from the earth decreases, the gravitational pull on the spaceship would decrease. There is no gravity on the moon and therefore only the earth will exert gravitational force on the spaceship. As the distance from the earth increases, the gravitational pull on the spaceship would decrease. The gravitational pull of the earth is constant and therefore the gravitational pull on would not change. 10 POINTS + BRAINLIEST ANSWER!!!65x + y = 455A grocery store receives a shipment of oranges and consistently sells the same number of oranges each day. The equation above models the number of oranges, y, that remain x days after the shipment is received. What does it mean that (7, 0) is a solution to the equation?A. It takes 7 days after the shipment until none of the oranges are remaining.B. There are 7 oranges in the shipment.C. It takes 7 days for orange to be sold to 455 customers.D. After the shipment, 7 oranges are sold each day. Which statements are true based on the diagram? Check all that apply. Which best describes a cause of US imperialism during the late 19th century? A. Businesses made more goods than domestic consumers were able to buy. B. Political leaders wished to block the spread of Communism around the globe. C. Military leaders believed that spending on warfare would encourage economic growth. D.Industrial producers needed new sources of immigrant labor. which equation has (2, -1) as a solution?A. y = 2x - 1B. y = x + 3C. y = x - 3D. y = -2x + 1If someone could explain this to me it would be greatly appreciated. Thank you. A mini-cube measures 1.5 in. wide. A mega-cube is 5 times as wide. What is the volume of the mega-cube, rounded to the nearest tenth? true? and false? At the end performance actors come out and bow in order from largest role to smallest Taiwan is located south of south koreaTrue or false? The left hemisphere of the brain processes information _________, while the right hemisphere of the brain processes information ________. reflecting on it as a whole; sequentially globally; sequentially sequentially; one piece of data at a time sequentially; globally Liver and muscle tissue store readily available energy as a starch called Which organelle is responsible for autophagy and autolysis? Hurry I'm TIMED!!!! The following graph shows the low temperatures for the past six nights. What was the range of temperatures for the six nights?34F22F12F8F As an MA, how can you professionally ask a patient about birth control? How would the patients age alter the questions or discussion? How might an individuals economic status impact the use of contraceptives? How can this issue be addressed with patients? Which invention allowed the greatest personal freedom of travel? How can tobacco affect the body?A. Yellow teeth B. Makes working out easierC. Improves immune system D. Prevents dizzinessPlease give correct answer! Can someone please help me and check over my answers (S/A stands for student answers) 1.In which of the following is the word agreeable divided correctly into syllables?A. AgreeableB. AgreeableC. AgreeableD. AgreeableS/A: B2. Three of the following words are synonyms. One word doesn't belong with the other three. Which worddoesn't belong?A. PromiseB. VowC. PledgeD. Createstudent Answer:D3. Each of the following words has the suffix -ed. Which word is spelled correctly?A. DuckkedB. PreennedC. PlottedD. CleannedS/A:C4. Each of the following words has a root ending in y. To each, the suffix -ed has been added. Which wordis spelled correctly?A. ConveyedB. DefyedC. FerryedD. SpyedS/A:A5. Read each of the following words aloud. Which has a silent consonant?A. PlaneB. CrestC. KneeD. CringeS/A: C6. When reading a newspaper, you come across the word subterranean. You guess the meaning of theword by breaking it into its parts. You know that sub- is a prefix meaning "under," and the word terraoften refers to "earth" or "ground." The suffix -an means "relating to." You guess that subterranean means"underground." The process you've just used is calledA. structural analysis.B. phonetic analysis.C. context clues.D. dictionary skill.S/A: A7. The words who's and whose areA. homonyms.B. antonyms.C. context clues.D. synonyms.S/A: A8. Which of the following words is spelled correctly?A. BelievibleB. UnpredictibleC. PerfectibleD. IncomparibleS/A: C9. The words disclosure and concealment areA. antonyms.B. homonyms.C. equivalents.D. synonyms.S/A:D10. Which of these words is spelled incorrectly because it violates the rules for ie versus ei words orexceptions to those rules?A. SurfeitB. SiegeC. SlieghtD. SovereignS/A:?11. Which one of the following sentences contains a synonym for distortion?A. His misrepresentation of the facts was caught by the lawyer.B. The distraction caused a minor accident in the parking lot.C. Her truthfulness paid off in the end.D. The two parts of the sphere created a symmetrical whole.S/A: B12. While reading a magazine, you ask a friend the meaning of the word suffragette. Although she says thatshe's never used this word in speaking or writing, she knows what it means if it's part of her _______vocabulary.A. writtenB. oralC. recognitionD. underscoredS/A:C13. While reading a story, you come across the following sentence:Although Mary was often unfriendly, she established rapport quickly with Jane.By contrasting the word rapport with the word unfriendly, you realize that rapport means "friendlyrelations." The skill you've just used is calledA. context clues.B. phonetic analysis.C. structural analysis.D. dictionary skill.S/A:A14. You're using a dictionary to look up unfamiliar words. Which of these words is least likely to be anentry word?A. StreamerB. FrigateC. ExpediteD. SoberlyS/A:A15. To figure out how to correctly speak the word onomatopoeia, you look up the word in your dictionary.You then refer to a chart that explains the dictionary's symbols for how to say the word. This chart iscalled the dictionary'sA. vocabulary.B. pronunciation key.C. table of contents.D. entry word.S/A:B16. Which one of the following words is spelled correctly?A. RelayedB. JustifyedC. ApplyedD. WorryedS/A:A17. A synonym for preparedness isA. readiness.B. punctuality.C. procrastination.End of examD. cooperation.S/A:A18. Speak aloud each of the following words. Which word has stress on its first syllable?A. DetestB. ObtainC. RenewD. FollowS/A:D19. All of the following words are misspelled. Which one of them is misspelled due to the dropping of asilent e?A. MangmentB. MasagingC. ManeuvorD. MessynessS/A:A20. The following words each contain the letters c, i, and e. Which word is spelled correctly?A. ConcieveB. RecieveC. DecieveD. ScienceS/A: D WILL MARK AS BRAINLIEST ON THE SPOT!!!!!!!!!! what is a creative title for brave new world in conditioning? where are commas needed ? Oncethelargestportionofthefoodpyramid,grainsarestillanimportantpartofahealthydiet.Grainscomeintwoforms:wholeandrefined.Wholegrainscontaintheentiregrainkernel,whichincludestheoutermostlayertheinnerlayer,andthesmallestpartofthegrain.Thesearethebran,germandendosperm.Togethertheymakeawholegrain.Wholegrains,whichincludewhole-wheatflour,wholecornmeal,oatmeal,andbrownricearegreatnutritionalchoices.Refinedgrainssuchaswhitebreadandwhiterice,arenotasnutritionallypowerfulfortheylackthevitaminsandfiberthatthetwoouterlayersofgrainprovide.Inordertogetthemostoutofyourdailygrainconsumptionchooseoatmeal,popcorn,orwhole-graincrackers.Ageneralrecommendeddailyintakeofgrainsamountstoaboutonecupofcerealatbreakfasttwoslicesofwholegrainbreadatlunch,andonecupofpastaorriceatdinner.Ifyouwantto"easilycustomizeyourgrainintake"saysnutritionistEvaTomer,"consultMyPyramidatwww.mypyramid.gov. How do you solve 9x+2=8x+9 The area of a rectangular hotel room is 209 square feet. the perimeter is 60 feet. what are the dimensions of the room?