Prove: The square of a number that is two more than a multiple of 3 is one more than a multiple of 3.

Answers

Answer 1

Step-by-step explanation:

x is the number

x = 3y + 2

the square

x² = (3y + 2)² = 9y² + 12y + 4

9y² is a multiple of 3 (because of the factor 9)

12y is a multiple of 3 (because of the factor 12)

4 is 1 more than a multiple of 3 (1×3).

so, the sum of all 3 terms is 1 more than a multiple of 3.


Related Questions

2 1/3 x (-3 2/7) what does it equal I’m doing “multiplying signed fractions”

Answers

The answer to this question is -32

a bottle of orange juice holds for 4/6 quarts of juice. a bottle of pineapple juice holds 2/3 quarts of juice. which bottle has more juice ​

Answers

Answer:

the orange juice has more ounces than the pineepple juice

Step-by-step explanation:

Bonnie has 4 sharpened and 8 unsharpened pencils in her pencil case. She randomly selects 2 of the pebcils from the box without replacement. What is the probability that both pencils will be sharpened? A. 1/2 B.1/9 C. 4/33 D.1/11

Answers

Answer:

D. 1/11.

Step-by-step explanation:

There are 12 pencils in the case.

Prob( first one is sharpened) = 4/12 = 1/3

Prob(second is sharpened) = 3/11

Prob(both sharpened) = 1/3 * 3/11

= 3/33

= 1/11.

The probability is 1/11 that both pencils will be sharpened which is the correct option(D).

What is probability?

The probability is defined as the possibility of an event being equal to the ratio of the number of outcomes and the total number of outcomes.

Given that,

Bonnie has 4 sharpened and 8 unsharpened pencils

So, there is a total of 12 pencils in the pencil case.

Let, the probability first one is sharpened is P(E₁)

The probability second one is sharpened is P(E₂)

P(E₁) = 4/12 = 1/3

P(E₂) = 3/11

Required probability both sharpened P(E) = P(E₁)×P(E₂)

Required probability both sharpened P(E) = 1/3 × 3/11

Required probability both sharpened P(E) = 3/33

Required probability both sharpened P(E) = 1/11.

Hence, the probability is 1/11 that both pencils will be sharpened.

Learn more about probability here:

brainly.com/question/11234923

#SPJ2

what is the probability that the red shows a six or the green die shows a six?

Answers

Answer:

11/36

Step-by-step explanation:

On a map, Breanne measured the distance (as the crow flies) between Los Angeles, California and San
Francisco, California at 2 inches. The scale on the map is 1/4 inch = 43 miles. What is the actual
straight-line distance between Los Angeles and San Francisco?

Answers

the straight line distance is 344

HELP HOW DO I FIND THE VALUE OF X

Answers

9514 1404 393

Answer:

  7.  118

  8.  27

Step-by-step explanation:

Make use of the fact that the sum of angles in a triangle is always 180°.

__

7. 33 + 29 + x = 180 . . . . . numbers in degrees

  x = 180 -62 . . . . . . . . . . . subtract 62 from both sides of the equation

  x = 118

__

8. 21 +x + 132 = 180

  x = 180 -153 . . . . . . . subtract 153

  x = 27

A rectangle has an area of 64 ft squared. If the length of the rectangle is x ft and the width of the rectangle is x to the 1/2 ft, find the length and width of the rectangle.

Answers

Answer:

I DONT KNOW BUT YOU HAVE TO CHECK OUT MY QUESTION NO OE CAN SOLVE IT I BET

Step-by-step explanation:

s2t-10
if s = -8 and
T= 3/4 please show how you got the answer

Answers

First substitute- (-8)(2)(3/4)-10// it goes to (-16)(3/4)-10// which goes to -12-10// which -12-10=-22

What is the value of y?
2y
Y+10
50°

Answers

Answer:

The question is incorrect. Please rewrite the question.

Miss Landry is getting married soon. She would like to hire a professional who will come to her house and do hair and makeup for the bridal party on her wedding day. She has narrowed it down to two possible choices. A woman from Springdale Salon charges an initial fee of $40 and then an additional $15 per hour. Alternatively, a team from Beauty by Dan offers a free consultation and then charges a higher hourly rate of $35. If it takes a certain amount of time to finish everyone's hair and makeup, Miss Landry will end up paying the same amount either way. How much would Miss Landry end up paying?

Answers

70

40+15=55+15=70(2 hours )

35+35=70(2 hours)

you are working to save money for a trip you need to save 1500 you already saved $250 saved, and make $10 an hour at your job whites and solve an equation to represent how many hours, h, you need to work to make the rest of the money

Answers

Answer:

125 hrs

Step-by-step explanation:

1500-250=10h

simplify

1250=10h

divide both sides by 10

h=125

125 hrs

Exit
Justin is going to the school dance. He went to the mall and bought two new shirts for $21.99 each and a new pair of dress shoes for $45.59. Which two operations would be used in order to figure out how much he spent at the store?
A. multiply and add
B. add and subtract
C. multiply and subtract
D. divide and add

Answers

Answer:

its letter A multiply and add

A) I believe is the correct answer

Given the points (-5,-7) and (-2,-8), calculate
the slope.
(I NEED THIS ANSWER ASAP!)

Answers

Answer:

Slope is -1/3

Step-by-step explanation:

(-5,-7)(-2,-8)

-8+7/-2+5

-1/3

m=-1/3

Answer:

Slope=-1/3

Step-by-step explanation:

Is (-4,-4) a solution of y> -6x - 1?
Choose 1 answer:
Yes
No

Answers

Answer:

no........... is not the answer

if the length of a box is 17 cm breadth is 6 cm and volume is 1020 cube find the height of the box​

Answers

Answer:

10 cm

Step-by-step explanation:

17×6×h=1020

102h=1020

h=1020/102=10

h=10 cm

81.04 x 0.010 answer please

Answers

Answer:

0.8104

Step-by-step explanation:

Answer:

0.8104

Step-by-step explanation:

Take the 0 out of the end of the 0.010 because there is no reason for it to be there.

Then you just multiply 81.04 by 1 because the rest of 0.01 is just zeros and the you get 81.04.

Then you count the decimal places in 0.01 which you get two so you move the decimal in 81.04 two times to the left.

Your answer should be .8104

I hope this helps!!!!

what is the solution for 5(m-3) ≥ 7m-2.4 ?

Answers

Answer:

Step-by-step explanation:

5(m-3)≥7m-2.4

5m-15≥7m-2.4

2m≤-12.6

m≤-6.1

Answer:

m>6.3

Step-by-step explanation:

There are 285 sixth graders going on a class trip to the museum.each bus can hold
25 students. How many buses will be needed to transport all the students? Will all the buses be fuller? If not how many students will be on the last bus.
the buses be filled? If not, how many stuc

Answers

Answer:

12 Busses

10 in the last bus

Step-by-step explanation:

275 in 11 busses and 10 in 12th bus

Suppose a student carryinga virus returns toan isolated college campus o 1000 students. Determine a differential equation for the number x(t) who have contracted the fluif the rate at which the disease spreads is proportional to the number of interactions between the number of students who have the fluand the number of students show have not been exposed to it.

Answers

Answer:

[tex]\frac{dx}{dt}[/tex] = k.x.[1000 - x] ;  

where k is the proportionality  constant

Step-by-step explanation:

Let

The number of people who are infected with the flu = x(t)

Total number of students = 1000

So,

Total number of student who do not expose with the flue = 1000 - x(t)

As given,

We have to find the differential equation such that

The rate at which the disease spreads is proportional to the number of interactions between the number of students who have the flu and the number of students show have not been exposed to it.

⇒[tex]\frac{dx}{dt}[/tex] ∝ x(t) . [ 1000 - x(t) ]

⇒[tex]\frac{dx}{dt}[/tex] = k.x.[1000 - x] ; where k is the proportionality  constant

Please help me in struggling with this

Answers

Answer:

Step-by-step explanation:

21

16

27

15

70

Answer:

Step-by-step explanation:

Hello!

I think I can help.

Lets use the first problem and walk through it and I think it could help you with the others.

3/7 = ?/49

So basically with these problems you are working backwards. You are working right to left and dividing to figure out what you will need to multiply the other part of the fraction by.

So here we have 49 and 7 that line up with each other. (Always look for the fractions that line up horizontally)

Going right to left and dividing :

49 / 7

= 7

So we know that it was 7 x 7 to get that 49

So now we used the number we just found by dividing (7) and multiply it left to right by the other number to find the missing number (?).

If we do this we do :

3 x 7

= 21

And that is the missing number !

We plug that in right where the blank is (?) and we get :

3/7 = 21/49

I am not sure if you have to simplify this but you cant anyways. If you have questions about simplifying ask in the comments.

To check this we can actually multiply the side that had two numbers to begin with (the left side numbers) and multiply it by the number we found by dividing (7).

So we do this with 3/7 :

3 x 7 = 21

7 x 7 = 49

if we plug this back in we get :

21/49 = 29/49 and we know this is correct.

I hope this helps you solve the other problems. If you have any questions or are still confused with others please message me or comment and I will do what I can to help.  :)

What is the square root of -24

Answers

The square root of a negative number does not exist in the set of real numbers so the answer is Undefined

Question Help
$
11.3.IP-8
John is knitting a blanket. He records the length he knits each day. How many more inches does
John need to knit so the blanket is 54 inches?

Answers

I'm not sure. Don't be angry but this is my first time on this app but it helps a lot and i would also like to help but it seems that I'm the one who needs help.

If you can answer these simple questions im giving brainly :)

Answers

Answer:

65   3    46

Step-by-step explanation:

Answer:

a² + 1 = 65

18/2a = 3

6(d + 8) - 10d = 46

Step-by-step explanation:

a² + 1 when a = 8

first, plug in 8 for a.

a² + 1 ⇒ 8² + 1

begin simplifying by finding , which is just 8 · 8.

+ 1 ⇒ 64 + 1

finish simplifying by adding 64 + 1.

64 + 1 = 65

therefore, when a = 8, a² + 1 = 65.

18/2a when a = 3

first, plug in 3 for a.

18/2a ⇒ 18/2(3)

begin simplifying by multiplying 2 · 3.

18/2(3) ⇒ 18/6

finish simplifying by dividing 18 ÷ 6.

18/6 = 3

therefore, when a = 3, 18/2a = 3.

6(d + 8) - 10d when d = 1/2

(i'm going to convert 1/2 to 0.5 because i prefer working with decimals rather than fractions)

so... 6(d + 8) - 10d when d = 0.5

first, plug in 0.5 for d.

6(d + 8) - 10d ⇒ 6(0.5 + 8) - 10(0.5)

begin simplifying by distributing 6 to 0.5 and 8, which is just 6 · 0.5 and 6 · 8.

6(0.5) = 36(8) = 48

after distributing, your expression is 3 + 48 - 10(0.5).

continue simplifying by multiplying -10 · 0.5.

3 + 48 - 10(0.5) ⇒ 3 + 48 - 5

add 3 + 48.

3 + 48 - 5 ⇒ 51 - 5

finally, finish simplifying by subtracting 5 from 51.

51 - 5 = 46

therefore when d = 1/2 or 0.5, 6(d + 8) - 10d = 46.

i hope this helps! have an amazing day <3


[tex] {a}^{2} {a}^{4} {a}^{5} answer \: a40 \: or \: a11 [/tex]

Answers

It’s a tiny the power of 11
2+4+5 = 11
Pls mark as brainliest

A group of football is formed a circle in the middle of the field to stretch out. The circle had a diameter of 30 yards. which measurement is close to the circumference of the circle in yards?

Answers

Answer: Solution

A=πr2=π·302≈2827.43339

Step-by-step explanation:

what duos e=mc² mean

Answers

Answer:

energy equals mass times the speed of light squared

Step-by-step explanation:

Energy equals mass times the speed of light squared

explanation : Albert Einstein was the one who made that!

the graph shows how many saketboards a company made over a period of time.How can you show that the slope is constant

Answers

Do you have a picture of the graph because we need to know how many skateboards.

find the measure of the missing angle​

Answers

Answer:

50

Step-by-step explanation:

40 plus 90 equals 130 and triangle must be 180 so we need 50 degree

50°

Let x be the missing angle.

90°(right angle) + 40°(given) + x = 180° ( the sum of degrees of interior angles of triangle)

x = 180°-130°

x = 50°

Carly purchased pints of ice cream for a party. If each guest will be served exactly
pint of ice cream, what is the greatest number of guests that Carly can serve?

Answers

Answer:

I do not understand the question I am so sorry :(

Step-by-step explanation:

Please help, this is due soon

Answers

Answer:

4

Step-by-step explanation:

If I remember correctly you can not have the arrows on the same y axis

Other Questions
The CDC offers guidelines for confirming a diagnosis of food-borne illness.TrueFalse (2a+5) is equal to 8a+60a+________? Eqiuvalent expressions5(x)(x)(x)(x) simplify the expression 4x+2-1/2x brainlist-brainlist-brainlist The Gulf Stream flows along the equator before turning north along Floridas east coast. How does the Gulf Stream impact Floridas climate? What is the answer The nucleus or large central vacuole containsgenetic material of a eukaryotic cell. Write a letter to your uncle in another town telling him how you enjoyed the holiday that you last spent with him Someone plz helppppA chemistry teacher needs to mix a 40% salt solution with a 70% salt solution to make 25 qt of a 52% salt solution. How many quarts of each solution should the teacher mix to get thedesired result?40% salt solution=?qt70% salt solution=?qt Will mark Brainlyist help me fill out the chart The ___________________________ ________________________ is the abbreviation for an element on the periodic table. Someone plz help been stuck on this question for the last 2 hoursPaul has $30,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 7% interest and part at 13% interest. How much does Paul need to invest in each option to make a total 11% return on his $30,000?7% interest =$?13% interest =$? Read this excerpt from an argumentative essay. National landmarks are popular tourist destinations, and some of them, such as bridges or dams, perform important functions. But it costs money to keep these places running and open for tourists, so who is going to pay? When the government pays, the money comes from people's taxes. Most people would rather pay lower taxes, so the government has to cut back on its spending. Maintaining national landmarks is a luxury we cannot afford. I think there are many more important things that the government can spend our money on, such as helping people who do not have enough food, making sure all children get a good education, and keeping all of us safe. Which claim does this excerpt make Which of the following could be the side measures of a right triangle? *1)6 ft, 5 ft, 4 ft2)8 ft, 7 ft, 6 ft3)10 ft, 8 ft, 6 ft4)12 ft, 10 ft, 8 ft Solve the equation, and choose the type of solution youfound.2x + 8 = 2(x + 4) Can someone let me know how this looks so far. (I still gotta add eyes) Which equation does the model below represent? pls help ! Describe the system of the assembly line. Jazzy goes to bed 3 h after dinner. Yesterday, she spent 1 1/2 h on her homework and 2/3 h on the telephone after dinner. How much time does she have before bed time?PLEASE SHOW YOUR WORK!!! What is the main idea of this text Atkins agreed to testify against Manson in exchange for avoiding the death penalty. Her grand jury testimony led to Manson being arraigned for the murders on Dec. 11, 1969. Atkins later recanted her testimony, and her deal was revoked by the prosecutors [source: Steffens and Staples]. Linda Kasabian, who hadn't entered any of the houses or committed any murders, was granted immunity and testified for the prosecution during the trial.