What are consecutive integers?

QUESTION POSTED AT 10/10/2019 - 07:34 PM

Answered by answersmine AT 10/10/2019 - 07:34 PM

Consecutive integers are integers that follow each other in order. They have a difference of 1 between every two numbers. In a set of consecutive integers, the mean and the median are equal. If n is an integer, then n, n+1, and n+2 would be consecutive integers. Examples.
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Which set of integers is a Pythagorean triple? 3, 5, 6 5, 12, 13 15, 9, 17 6, 8, 12

Answer:

The set of integers which form a Pythagorean triple is:

5,12,13

Step-by-step explanation:

We are asked to find the set of integers such that they form a Pythagorean triplets.

Three integers a,b,c are said to form a Pythagorean triplets if they satisfy the property:

c^2=a^2+b^2

1)

3,5,6

6^2=36

and

3^2+5^2=9+25\\=34\neq 36

Hence option: 1 is incorrect.

2)

5, 12, 13

13^2=169

and

5^2+12^2=25+144=169

This means:

13^2=5^2+12^2

Hence, option 2 is correct.

3)

15,9,17

17^2=289

Also,

15^2+9^2=225+81=306\neq 289

Hence, option 3 is incorrect.

4)

6,8,12

12^2=144

and:

6^2+8^2=36+64=100\neq 144

Hence, option 4 is incorrect.

ANSWERED AT 17/10/2019 - 09:23 AM


QUESTION POSTED AT 17/10/2019 - 09:23 AM

Can somebody help me out please?!?!?!?!?! For a set of three consecutive odd integers, three times the largest integer is 7 less than twice the sum of the other two integers. What is the largest integer in the set?

The integers would be 15, 17, 19. 15+17=32x2=64 19x3+57 64-57= 7 Your answer would be 19

ANSWERED AT 17/10/2019 - 07:28 AM


QUESTION POSTED AT 17/10/2019 - 07:28 AM

1.24 belongs to what family of real numbers? A. Rational, integer, whole B. Rational, Integer, Whole, Counting C. Rational D. Irrational

Answer:

Rational.

Step-by-step explanation:

Rational number comprehends fractions and decimal numbers. But, in order to be decimal and rational, the number has to have a finite number of decimals or infinite but periodic decimals, on the contrary case they are irrational.

ANSWERED AT 17/10/2019 - 07:27 AM


QUESTION POSTED AT 17/10/2019 - 07:27 AM

The sum of three consecutive odd numbers is one hundred thrirty- five what is the smallest of the three numbers

The three numbers are 43,45,47
The smallest is 43.

please vote my answer branliest. Thanks!

ANSWERED AT 17/10/2019 - 07:20 AM


QUESTION POSTED AT 17/10/2019 - 07:20 AM

When positive integer n is divided by 167, the remainder is 35, and when positive integer k is divided by 167, the remainder is 17. what is the remainder when 2n+k is divided by 167?

Hey there! Can you express (using mathematics) what it means for the first statement? That is, when n is divided by 167 the remainder is 35.

ANSWERED AT 17/10/2019 - 06:02 AM


QUESTION POSTED AT 17/10/2019 - 06:02 AM

Find three consecutive odd integers such that the sum of the first and the third is 26

N, (n+2),  (n+4)  are the 3 consecutive odd integers.  Now we have
n+ (n+4) = 26
2n+4 = 26
2n = 22
n = 11.
So now the numbers are n, (n+2),  (n+4), or
11, 13, 15

ANSWERED AT 17/10/2019 - 05:21 AM


QUESTION POSTED AT 17/10/2019 - 05:21 AM

When positive integer N is divided by 167, the remainder is 35, and when positive integer K is divided by 167, the remainder is 17. What is the remainder when 2N+K is divided by 167?

N\equiv35\mod167\implies N=167n_1+35
K\equiv17\mod167\implies K=167n_2+17

for some integers n_1,n_2. So we have

2N+K=2(167n_1+35)+(167n_2+17)
=167(2n_1+n_2)+87
=167n+87

(where n is some integer)

\implies 2N+K\equiv87\mod167

i.e. the remainder upon dividing 2N+K by 167 is 87.

ANSWERED AT 17/10/2019 - 05:10 AM


QUESTION POSTED AT 17/10/2019 - 05:10 AM

PLZ HELP ASAP, I WILL MAKE BRAINLIEST What is the greatest possible integer solution of the inequality 8.904x < 18.037? -2 1 2 3

We are being asked what would be the greatest value of x that would satisfy the expression 8.904x < 18.037. Let us try both 1 and 2, the solution is shown below:
For x=1, we have:
8.904 *1 < 18.037 
8.904 < 18.037
For x=2, we have:
8.904*2 < 18.037
17.808 < 18.037

We could see the solution that the greatest possible value of x is 2.

ANSWERED AT 17/10/2019 - 05:03 AM


QUESTION POSTED AT 17/10/2019 - 05:03 AM

Write 45 in the form k squareroot 5 where k is an integer

45=k√5
times both sides by √5
45√5=5k
divide both sides by 5
9√5=k

ANSWERED AT 17/10/2019 - 03:39 AM


QUESTION POSTED AT 17/10/2019 - 03:39 AM

In the following equation, a and b are both integers. a(3x-8)=b -18x what is the value of a ? what is the value of b?

If a and b are two fixed integers this means the equations is a straight line where x values could be any number within (-∞,∞). So we can evaluate any two numbers to obtain a set of two different equations to solve the system for a and b. The number we will try are 0 and 1:

For 0 (Equation #1)

a(3(0)-8)=b-18(0)\\a(-8)=b\\b=-8a

For 1 (Equation #2)

a(3(1)-8)=b-18(1)\\a(-5)=b-18\\-5a+18=b\\b=18-5a

We can solve the system by replacing equation #1 in equation #2 like this:

-8a=18-5a\\-8a+5a=18\\-3a=18\\a=\frac{18}{-3} \\<strong>a=-6</strong>

Now we can replace the value of a in equation #1

b=-8(-6)\\<strong>b=48</strong>

ANSWERED AT 17/10/2019 - 03:38 AM


QUESTION POSTED AT 17/10/2019 - 03:38 AM

In the following equation, a and b are both integers. a(3x-8)=b -18x

A = -6
b = 48
Hope this helps :)

ANSWERED AT 17/10/2019 - 03:35 AM


QUESTION POSTED AT 17/10/2019 - 03:35 AM

The sum if three consecutive odd integers is -411. Find the three integers.

Odd integers are 2 apart

so they are
n,n+2,n+4
so sum is add

n+n+2+n+4=-411
3n+6=-411
mnus  both sides
3n=-417
divide both sides by 3
n=-139
n+2=-137
n+4=-135

the numbres are -139, -137, -135

ANSWERED AT 17/10/2019 - 03:33 AM


QUESTION POSTED AT 17/10/2019 - 03:33 AM

A hot air balloon descends at a rate of 320 feet per minute for 3 minutes. Use integers to calculate and represent the balloon's total change in altitude. (2 points)

That is
distance=rate times time
rate=320ft/m
time=3m


distance=320ft/m times 3m
distance=960ft

the total change is 960ft

ANSWERED AT 17/10/2019 - 03:33 AM


QUESTION POSTED AT 17/10/2019 - 03:33 AM

Which shapes apply to this statement ? Consecutive angles are congruent. A) parallelogram B) rectangle C) rhombus D) square

The answer is D hope it fits you well

ANSWERED AT 17/10/2019 - 03:16 AM


QUESTION POSTED AT 17/10/2019 - 03:16 AM

Compute the permutation. How many positive integers of 3 digits each can be formed with the digits 1, 8, 9, 2, 7, 6, 4, and 3, if no digit is repeated in a number? Answers: 27, 336, 512

So you have 8 digits (number available) to form 3 digit numbers (number selected).

Using the formula ^{a} P_{c} where a is the number of available digits, P is the permutation function and c is the number of digits to be selected.

The number of three digit numbers that can be formed = ^{8} P_{3}
                                                                                       = 336

                                                 O R

By using the formula Permutation =  \frac{a ! }{( a - c) !} where a is the number of available digits and c is the number of digits to be selected.

⇒  Permutation = \frac{8 ! }{( 8 - 3) !}

⇒  Permutation = \frac{40, 320 }{120}

⇒ Permutation = 336

ANSWERED AT 17/10/2019 - 01:43 AM


QUESTION POSTED AT 17/10/2019 - 01:43 AM

Compute the permutation. How many different positive integers of 2 digits each can be made with the digits 2, 4, 5, and 8, if no digit is repeated in a number?Answers:81216

We have two slots A and B
Slot A has 4 choices (2,4,5,8)
Once we make a choice, we can't reuse it. So we have 3 choices left for slot B

Multiply out the values mentioned above to get: 4*3 = 12

Alternatively you can use the nPr formula to get
n P r = (n!)/(n-r)!
4 P 2 = (4!)/(4-2)!
4 P 2 = (4!)/(2!)
4 P 2 = (4*3*2*1)/(2*1)
4 P 2 = 24/2
4 P 2 = 12
yielding the same answer

So no matter which method you use, the final answer is 12

ANSWERED AT 17/10/2019 - 01:43 AM


QUESTION POSTED AT 17/10/2019 - 01:43 AM

The Smith family wants to build a human pyramid when they go to the beach this summer. They will put one person on top and add 2 more people for each descending row. a.How many people will be in the seventh row? b.Find the total number of people in a pyramid with seven rows. c.Next summer, Jane Smith wants to build a pyramid with only the great-grandchildren. If they build it the same way, how many children are needed to make a pyramid with 10 rows? d.Suppose the cast of The Simpsons built a pyramid in which the bottom row had 37 people, and they added 4 people between consecutive rows. How many rows tall is their pyramid? e.What is the total number of people in the Simpson’s pyramid described in part d?

A. It's a trick question, if there is two people per row excluding the very top, then there should only be two in the seventh row.

B. there would be 15 total people in the seventh row.

If it's 1 person on top and 2 people each row, that would be 1+2(x)

1+2(x)
1+2(7)
1+14
=15

C. If it's the same way then we would just use the same equation.

1+2(x)
1+2(10)
1+20
=21

There would be a total of 21 people in the pyramid.

D. We would just need to subtract 4 from 37 repeatedly to find how many rows. 

I did the math and it is 10 people since we can't have half a person.

E. If the bottom row has 37 and we know that it is 4 people up each time, and there are a total of 10 rows roughly, then we can safely assume there are 40 people + the bottom row 37 which is 77 people total.

I know I may not be right, but I hope this helps.

- Kathryn Irene

ANSWERED AT 17/10/2019 - 01:31 AM


QUESTION POSTED AT 17/10/2019 - 01:31 AM

The sum of the squares of two consecutive negative even integers is 52. Find the integers. show all work!!!

The two numbers are -4 and -6.

- two negatives make a positive. in this case -4×-4 equals 16 and -6×-6 equals 36. these are the squares

- 16+36 equals 52

please vote my answer branliest. Thanks!

ANSWERED AT 17/10/2019 - 01:22 AM


QUESTION POSTED AT 17/10/2019 - 01:22 AM

What integer can be represented by 13 positive tiles and 26 negative tiles?

What integer can represent 13 positive tiles?
+ 13
What integer can represent 26 negative tiles?
- 26

ANSWERED AT 17/10/2019 - 01:17 AM


QUESTION POSTED AT 17/10/2019 - 01:17 AM

Name a positive or negative integer to represent the following situation. "Jon lost 12 yards on the play"

An integer is a number. He lost twelve yards, not gained, so it would be negative, not positive. Thus, the integer would be -12 yards.

ANSWERED AT 17/10/2019 - 01:16 AM


QUESTION POSTED AT 17/10/2019 - 01:16 AM

You think of a number from the first 20 negative integers what is the probability that the integers chosen will be divisible by 4

The probability is 1/4 because there are 20 numbers (?/20) and 5 are divisible by four (-4,-8,-12,-16,-20) which makes 5/20 which simplified = 1/4.

ANSWERED AT 17/10/2019 - 01:05 AM


QUESTION POSTED AT 17/10/2019 - 01:05 AM

Precal on plato help please A plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour. If the plane's resultant speed due to the wind is 180 miles/hour, what is the plane's actual speed, rounded to the nearest integer? 120 miles/hour 130 miles/hour 135 miles/hour 140 miles/hour

We can use the Cosine Law:
c² = a² + b² - 2 ac cos C
180² = 50² + x² - 2 · 50 · x · cos 150°
32,400 = 2,500 + x ² - 100 x · ( - √3/2 )
32,400 - 2.500 - x² = 100 x · 0.866
29,900 - x² = 86.6 x
- x² - 86.6 x + 29,900 = 0  / · ( - 1 )
x² + 86.6 x - 29,900 = 0
x 1/2 = ( - 86.6 +/- √(86.6² + 4 · 1 · (-29,900) )) / 2
x = ( - 86.6 + 356.6 )/ 2  ( other solution is negative )
x = 135
Answer: C ) 135 miles/hour

ANSWERED AT 16/10/2019 - 10:59 PM


QUESTION POSTED AT 16/10/2019 - 10:59 PM

What 3 consecutive even numbers added together equal 42? Use the equation n + (n + 2) + (n + 4) = 42 to help you solve.

Solve for n by simplifying both sides of the equation, then isolating the variable:
N + (n + 2) + (n + 4) = 42
N = 12

ANSWERED AT 16/10/2019 - 10:18 PM


QUESTION POSTED AT 16/10/2019 - 10:18 PM

What 3 consecutive even numbers added together equal 42? Use the equation n + (n + 2) + (n + 4) = 42 to help you solve.

N+(n+2)+(n+4)=42
isolate n
n+(n+2)+(n+4)-(n+2)=42-(n+2)      n+(n+4)=42-n-2     n+(n+4)=40-n
n+(n+4)-(n+4)=40-n-(n+4)    n=40-n-n-4   n=36-2n 
n+2n=40-2n+2n
3n/3=40/3
n=12

ANSWERED AT 16/10/2019 - 10:18 PM


QUESTION POSTED AT 16/10/2019 - 10:18 PM