Prove: The square of a number that is
one more than a multiple of 3 is also one
more than a multiple of 3.
n +
(3n + 1)2 = [ ? ]n? +
1([ ]n2 +
=
)n) +
- 1 more than a multiple of 3

Answers

Answer 1

Let 3n + 1 denote the "number" in question. The claim is that

(3n + 1)² = 3m + 1

for some integer m.

Now,

(3n + 1)² = (3n)² + 2 (3n) + 1²

… = 9n² + 6n + 1

… = 3n (3n + 2) + 1

… = 3m + 1

where we take m = n (3n + 2).


Related Questions

PLZZ HELP !! Select the correct answer. What are the zeros of the function y= (x-4)(x^2 - 12x+36)
A. -6,4 and 6
B. 4 and 6
C. -6 and -4
D. 0, 4, and 6​

Answers

It’s B. 4 and 6
If I’m not wrong

The zeroes of any function are where the function touches or passes through the x-axis.

To find these zeroes, we can factor, and set each part equal to 0.

y = (x - 4)(x^2 - 12x + 36)

It looks like some of the factoring was already done for us! All we have to do is factor the quadratic. To do so, we need two numbers that multiply to equal (a * c) and add up to b. In this case those two numbers are -6 and -6.

y = (x - 4)(x - 6)(x - 6)

Finally, set each part equal to 0!

x - 4 = 0

x = 4

x - 6 = 0

x = 6

x - 6 = 0

x = 6

Therefore, the zeroes of the function are 4 and 6, option B.

Hope this helps!! :)

A ski are offers two vacation package plans. Plan A gives one person four nights lodging and three dinners for $467. Plan B gives one person five nights lodging and four dinners for $593. Assuming that the lodging and dinner costs per night are the same for both plans, how much does one dinner cost?

Answers

Answer:

$37

Step-by-step explanation:

Plan A: 4n + 3d = 467

Plan B: 5n + 4d = 593

4n + 3d = 467

4n = 467 - 3d

4n/4 = 467/4 - 3d/4

n = 116.75 - 3/4d

5n + 4d = 593

5(116.75 - 3/4d) + 4d = 593

583.75 - 3.75d + 4d = 593

0.25d = 593 - 583.75

0.25d = 9.25

0.25d/0.25 = 9.25/0.25

d = 37

A television cost $950, how much is a 7% tax?​

Answers

Answer:

950x7%=66.5

950+66.5=1016.5 with tax

not sure but here you go

Answer:

is 66.5

?/950= 7/100 7x950=6650 6650 división by 100=66.5

rewrite the expression 2+5×4-2 with parenthesis to equal the given value: 12

Answers

That would be 4-2+5*2

Please help me and I'll give you a Brainly star

Answers

Answer:

Step-by-step explanation:

The answer is (C)

<AEB is congruent to <BEC

Select the correct answer from each drop-down menu.
The
In a circle with a radius of 7 feet, the radian measure of the central angle subtended by an arc with a length of 4 feet is
area of the sector formed by the arc is
Assume T = 3.14, and round your answers to the nearest hundredth.
square feet.

100 POINTS

Answers

Answer:

87.9? maybe i am not sure

Step-by-step explanation:

Step-by-step explanation:

Circumference of circle = π2r = 14πft.

Angle subtended by arc

= 2π * (Arc length/Circumference)

= 2π * (4ft/14πft) = 0.18π. (2d.p.)

Area of sector = 0.5r²(Angle subtended by arc)

= 0.5 * (7)² * (0.18π)

= 14.00ft². (2d.p.)

Mia cycled 12 miles over two days.
She cycled 7 miles on one day.
How many miles did she cycle on the other day?

 19 miles?
7 miles?
5 miles?
12 miles?​

Answers

She cycled 5 miles on the second day
5 miles I think because

need help asap please

Answers

Answer:

[tex]\displaystyle yes[/tex]

Step-by-step explanation:

If the angle of elevation is congruent in both triangles, then both smaller legs are congruent.

I am joyous to assist you at any time.

can you please help me, I cannot find the answer I'm trying to do my homework so my teacher doesn't get mad at me​

Answers

Answer:

the answer is 9

Step-by-step explanation:

hope i helped :)

Answer:

9

Step-by-step explanation:

3 times 3 is 9

A political action committee wanted to estimate the proportion of county residents who support a change to the county leash law. They took a random sample of 600 county residents and found that the proportion who wanted to change the law was 33% with a margin of error of +/- 4% (with 95% confidence). This implies:_____

a. If we took another sample of 600 residents the sample proportion would definitely be between 29% and 37%.
b. If we take many other samples from this population 95% of them will have a sample proportion that is between 29% and 37%.
c. We can not conclude anything about the population parameter since this is only a sample.
d. We are 95% confident that the true proportion of county residents who want the law changed is between 29% and 37%.
e. There is a 95% chance that the true parameter is 33%.

Answers

Answer:

d. We are 95% confident that the true proportion of county residents who want the law changed is between 29% and 37%.

Step-by-step explanation:

Meaning of a confidence interval:

A x% confidence interval being between a and b means that we are x% sure that the true population proportion is between a and b.

In this question:

Sample of 600, proportion who wanted to change the law was 33% with a margin of error of +/- 4% (with 95% confidence). This implies:

From the concept of confidence interval above, the correct answer is:

d. We are 95% confident that the true proportion of county residents who want the law changed is between 29% and 37%.

Which rule explains why these triangles are similar?

SSS
SAS
AA
none of the above; the triangles cannot be proven similar
Submit


Answers

the correct answer would be Side Angle Side

Answer:

The correct answer is:

AA

EGH

~△

EFD

Step-by-step explanation:

I got it incorrect the first time. the person above or below me is wrong.

Please answer thank you

Answers

Answer:

y=10.2x

Step-by-step explanation:

x represents hikers

y represents total pounds

Y=10.2x because once the items are added all up you get the amount of the total weight

Working out Choose a person aged 19 to 25 years at random and ask, "In the past seven days, how many times did you go to an exercise or fitness center or work out?" Call the response Y for short. Based on a large sample survey, here is a probability model for the answer you will get:8Working out Choose a person aged 19 to 25 years at random and ask, "In the past seven days, how many times did you go to an exercise or fitness center or work out?" Call the response Y for short. Based on a large sample survey, here is a probability model for the answer you will get:8

Answers

Solution :

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

This is a valid probability distribution.

In the question it is given that call for a response of Y for short of a sample of people aged between 19 years to 25 years.

Also the event that describes the value of call for response greater than 3 i.e. (Y < 3) is a randomly chosen people between the age 19 to 25 years old who has gone to fitness center or did exercise fewer than 3 days.

Valid probability models add up to 1

The probability is a valid probability model

The probability model is given as:

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

To determine if the model is a valid probability model, or not

We make use of:

[tex]\mathbf{\sum P(x) = 1}[/tex]

So, we have:

[tex]\mathbf{0.68 + 0.05 + 0.07 + 0.08 + 0.05 + 0.04 + 0.01 + 0.02 = 1}[/tex]

Add the probabilities

[tex]\mathbf{ 1= 1}[/tex]

The above equations shows that:[tex]\mathbf{\sum P(x) = 1}[/tex]

Hence, the probability is a valid probability model

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A 30 -foot ladder is leaning against a building. The base of the ladder is 18 feet from the side of the building. How high does the ladder reach along the side of the building?

Answers

Answer:  24 feet

========================================================

Explanation:

Refer to the diagram below. We have a right triangle with known horizontal leg 18, and unknown vertical leg x. The hypotenuse is 30.

Let a = x, b = 18, c = 30.

Apply the Pythagorean theorem to solve for x

a^2 + b^2 = c^2

x^2 + 18^2 = 30^2

x^2 + 324 = 900

x^2 = 900-324

x^2 = 576

x = sqrt(576)

x = 24

The top of the ladder reaches 24 feet high.

A 40-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. If x
represents the length of the first piece, find the lengths of all three pieces.
What is the length of the first piece?
What is the length of the second piece?
What is the length of the third piece?

Answers

Answer:

The first piece is 5 inches long, while the second is 15 inches and the third one is 20 inches.

Step-by-step explanation:

To determine the length of the 3 pieces, knowing that the total of the board is 40 inches, and that the second measures 3 times more than the first and the third measures 4 times more than the first, the following equation must be performed:

X + 3X + 4X = 40

8X = 40

X = 40/8

X = 5

Therefore, the first piece is 5 inches long, while the second is 15 inches and the third 20 inches.

What is the value of the expression 5ab−7b+c when a=3, b=3, and c=4?

13

24

28

39

Answers

Answer: the value of the expression is 28

Step-by-step explanation:

we simply substitute the letters in for the numbers.

5(3)(3) - 7(3) + (4)

we just multiply all of those together.

45 - 21 + 4

answer: 28

Answer:

the value of the expression is 28

Step-by-step explanation:

since we have already been given the values of a, b and c ,we must substitute them in the expression like this:

5(3)(3)-7(3)+4

28

2(5-6f)= 34
I need to find the value of f pls help

Answers

Answer:

f=-2

Step-by-step explanation:

2(5-6f)= 34

(5-6f)= 34/2

5-6f= 17

-6f=17-5

-6f=12

f=12/-6

f=-2

Step-by-step explanation:

2(5-6f)= 34

(2*5)-(2*6f)=24

10-12f=34

-12f=34-10

-12f=24

-f=24/12

-f=2

f=-2

A mother gives birth to a 6 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.

Y = _____________________

Answers

Answer:

Equation: (6x2)x5=?

Step-by-step explanation:

Well, lets see: (x times y), which is (6x2)x5=?

Equation: (6x2)x5=?

I think?

A single chocolate muffin has 260 calories, and a blueberry muffin has 240 calories. Both muffins can be bought at the local cafe. Jane goes to the local cafe to have breakfast. Their fruit platter has 210 calories and the french toast is 350 calories. A glass of orange juice is 40 calories and milk is 102 calories. The hashbrowns and eggs are twice the calories of the fruit platter. If Jane has half a blueberry muffin with a whole fruit platter and a third of a glass of milk for breakfast, how many calories did she consume during breakfast?

Answers

Answer:

364 calories

Step-by-step explanation:

1/2 of 240=120 calories

fruit platter =210 calories

1/3 of 102=34

120+210+34=364 calories

The amount of calories she consumes during breakfast is 364 calories.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a single chocolate muffin has 260 calories, and a blueberry muffin has 240 calories. Both muffins can be bought at the local cafe. Jane goes to the local cafe to have breakfast. Their fruit platter has 210 calories and the french toast is 350 calories. A glass of orange juice is 40 calories and milk is 102 calories.

The total amount of calories consumed in breakfast will be:-

1/2 of 240=120 calories

fruit platter =210 calories

1/3 of 102=34

Total calories = 120+210+34=364 calories

Therefore, the amount of calories she consumes during breakfast is 364 calories.

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sam counted his heart beats while resting his heart beat 220 times in 4 minutes Sam heart beat at the same rate for the 4min .complete the ratio of beats to min​

Answers

Answer: 220:4 or 220 to 4

Step-by-step explanation:

Answer:220:4

Step-by-step explanation:

aight anybody help me man lol

Answers

Answer:

10 4/6 -> 10 2/3

Step-by-step explanation:

simpliest form is the second option :)

Please answer quick!!! Will Mark BRAINLIEST!!!

Answers

Answer:

picture 1 : 360 cm2

picture 2:  sorry I don't really know

picture 3: 11.25 cm2

Step-by-step explanation:

hope this helps

A countertop is 11 feet long and 8 feet wide.

Part 1 out of 2
What is the area of the countertop in square meters? Use the conversion 1 foot = 0.305 meter. Round your final answer to 2 decimal places.

The countertop is
square meters.
Part 2 out of 2
Tile costs $28 per square meter. How much will it cost to cover the countertop with new tile?

It will cost $
to cover the countertop with new til


PLZZZZZ
HELPPPPPP
MEEEEEE
PLZZZZZ

Answers

part 1 8.19 meters
11 * .305 = 3.355
8 * .305 = 2.44
3.354 + 2.44 = 8.19

it will cost $252 to cover it
you need 9 square meters to cover 8.19 meters of area
so 9 * 28 = 252

chau made $270 for 18 hours of work. At the same rate, how many hours would he have to work to make $105​

Answers

Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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what am i supposed to put in that chart?

Answers

Answer:

as explained

Step-by-step explanation:

as in the photo i've shown :

i've shown the table for you both

i've shown the graph for one only the second one hope you can complete it if you have any questions you can ask.

for first one

if x=2 replace x=2 in f(x) you will get f(2)=4

f(3)=1

f(4)=0

f(5)=1

f(6)=4

Why did I start with x=2 and not x=1 because f(1)=9 in the graph provided there is no marking for y=9 but when drawing the graph extends it (as in photo 3 not as in photo 4)(graph in photo 3 is better)

Hope you understand(you can also put(2,4) ,(3,1) and so on in the graph as in photo 5

What is the value of a2 + 36 2c when a = 3, b = 8, and c = 2?​

Answers

Answer: 21 +4c

Step-by-step explanation:

Answer:

what is in between 36 and 2c?

List the angles from least to greatest! URGENT
(BETTER IMAGE)

Answers

Answer: Y<W<Z? Im not exactly sure but it looks right to me. Correct me if im wrong though.

Step-by-step explanation:

Answer:

W<Y<Z

Step-by-step explanation:

the side WZ is longer than side ZY, so the angle W is smaller.

can u pls help me with this question asap ​

Answers

Answer:

$14670

Step-by-step explanation:

Selling price of the house = $326000

Commission rate of the agency = 4.5%

Commission amount earned by the agency = 326000 × 0.045

                                                                        = $14670

Commission rate of the agent = 20% of commission earned by the agency

= [tex]\frac{20}{100}\times 14670[/tex]

= $2934

Therefore, agency made $14670 on the house.

4(b-3)=6 put the steps in Oder to solve the equation from first to last

Answers

Answer:

B= 9/2 Hope this helped

Let's solve your equation step-by-step.

4(b−3)=6

Step 1: Simplify both sides of the equation.

4(b−3)=6

(4)(b)+(4)(−3)=6(Distribute)

4b+−12=6

4b−12=6

Step 2: Add 12 to both sides.

4b−12+12=6+12

4b=18

Step 3: Divide both sides by 4

The value of b in the expression 4(b - 3) = 6 is 4.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, 4(b - 3) = 6 and we have to solve for b.

4(b - 3) = 6.

4b - 12 = 6.                              (distributive law a(b+c) = ab + ac).

4b = 6 + 12.           (constants change sign when moved to the other sides).

4b = 16.

b = 16/4.

b = 4.

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25.7,24.1,---------,20.9,19.3

Answers

Answer:

You just have to subtract 1.6 so the missing number is 22.5

Step-by-step explanation:

25.7 ,24.1, 22.5 , 20.9 , 19.3 , 17.7 , 16.1

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