If a, b and c are positive integers for which (a,b,c) is the only
ordered triple such that 6a +9b + 20c = 61, then what is
a+b+c?

Answers

Answer 1

If a, b, and c are all positive integers and 6a + 9b + 20c = 61, then right away you know c < 3, because if c = 3, then 20c = 60, and there are no solutions for a and b.

So consider two cases:

• If c = 2, then we're left with 6a + 9b = 21.

• If c = 1, then 6a + 9b = 41.

We have gcd(6, 9) = 3, but 41 is prime and 3 does not divide 41. So we throw out the second case.

This leaves us with 6a + 9b = 21. Notice that if a = b = 1, then 6a + 9b = 15. Add 6 to both sides to get 21. So a = 2, b = 1, and c = 2, and hence a + b + c = 5.


Related Questions

Find The Difference.
1)5-15=
2)-13-7=
3)-19-7=
4)36-(-12)=
5)-29-(-11)=
6)-7-(-5)

Answers

Answer:

-10

-20

-26

48

40

-2

Step-by-step explanation:

I used a calculator to make sure

A river has a current of 2km per hour. Find the rate of Fred’s boat in still water if it travels 30 km downstream and the same time it takes to travel 14 km upstream.

Answers

Answer:

32km

Step-by-step explanation:

1. Describe how to show that triangle PMO = triangle PMN using the SSS Congruence Postulate. Then, without using a protractor, find a way to show that the triangles are congruent using the SAS Congruence Postulate.

Answers

Answer:

ayudenle porfa :)

Step-by-step explanation:

porfa

Darnell uses 1 1/4 packages of beads to make 10 bracelets. He wants to make 25 bracelets. How many packages of beads will he use?

Answers

Answer:

I believe the answer is 3 1/8

Step-by-step explanation:

Since he uses 1 1/4 packages just to make 10, we can start with him making the 20. That would mean he uses 2 1/2 packages. Now all we have left is the 5 in 25. 5 is half of 10 and since you use 1 1/4 to make 10 bracelets, use half of it to make 5. Add up all the package use and you get 3 1/8. This was kinda rushed so I'm not 100% sure, but I'm like 95% sure. Hope this helps!

3¹/₈ packages of beads are required to make 25 bracelets

What is proportion ?

A proportion is an equation based on the equality of two ratios.

Here it is given that :

Darnell uses 1 1/4 packages of beads to make 10 bracelets that is :

1 ¹/₄ = 5/4 packages of beads requires to make = 10 bracelets

Now, divide both side by 10 we get :

to make 1 bracelets = 5/40 = 1/8  packages of beads are required

Now, to find the numbers  packages of beads to make 25 bracelets multiply both side by 25 :

to make 25 bracelets =  25/8  = 3¹/₈ packages of beads are required.

Therefore, 3¹/₈ packages of beads are required to make 25 bracelets

Read more about ratio at:

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Write all prime numbers between 10 and 20​

Answers

Answer:

11,13,17,19

Step-by-step explanation:

Answer:

11 , 13 , 17 and 19

Step-by-step explanation:

good luck :)

Set up a system of linear equations, and then solve for the indicated quantities.
Three times the smaller of two numbers plus three times the larger number is – 15.
Six times the smaller number minus three times the larger number is – 21.
Find the numbers.
Let x represent the smaller number. Let y represent the larger number.

Answers

9514 1404 393

Answer:

smaller: -4larger: -1

Step-by-step explanation:

Substituting the given variables into the word problem, we have two equations:

  3x +3y = -15

  6x -3y = -21

Adding these equations eliminates y:

  9x = -36

  x = -4 . . . . divide by 9

Using this in the first equation, we have ...

  3(-4) +3y = -15

  -4 +y = -5 . . . . . divide by 3

  y = -1 . . . . . . . . . add 4

The smaller number is -4; the larger is -1.

The following table shows the annual profits for two small florist shops what shop had the greater total profit? How much greater was its profit?


Plz answer ASAP I will mark u brainlyest this is my 5th time asking please answer

Answers

Answer:

Shop A & $400

Step-by-step explanation:

-4.7 + 27.5 + 122.3 = $145.1 (Shop A)

-0. 2 + 14.5 + 130.4 = $144.7 (Shop B)

Difference = 145.1 - 144.7 = $0.4

0.4 × 1000 = $400

Shop A, $400

Have a nice day / night :)

is |-4| equal to |4|?

Answers

Answer:

Yes

Step-by-step explanation:

Absolute value measures the distance between the number and 0. The distance between -4 and 0 is 4, and the distance between 0 and 4 is 4. Therefore, they are equal.

Answer:

yes

Step-by-step explanation:

the l l symbol is the absolute value symbol, it counts how far the number is from zero meaning that the outcome is always positive.

Solve for f:
f divided by -2/3 = -1/3

Answers

-f (3/2) = -1/3
-3/2f = -1/3
f= 2/9 or 0.2

Answer:

2/9

Step-by-step explanation:

Ik y’all good at math, help me out yall!

Answers

Answer:

i think the answer be 150 feet per minute

hope this is right

Answer:

150

Step-by-step explanation:

use points on the line i'll use (2,300) and (1,150)

m=y2-y1/x2-x1

300-150=150

2-1=1

150/1=150

hope this helps :3

sorry if im wrong

I mark as brainliest ​

Answers

B i think- jsjdjdndnjdddkjskskdjdjdbsbsbdnd
Answer:
The second answer
Explain:
if you count the grid, it's 8 right and 5 up from the dentist to his house

Write the ratio in fractional notation in lowest terms.
5 megabytes to 22 megabytes
The ratio is (Type the ratio as a simplified fraction.)

Answers

Answer:

99999k

Step-by-step explanation:

kjjuhhhhhhhhhuurdghsex

On Joe's bookshelf are: • 8 fiction books 3 non-fiction books • 4 historical drama books Joe will randomly choose 1 book to read from the shelf. What is the probability that he will choose a non-fiction book? A)0.267 B)0.8 C)0.2 D)0.533​

Answers

Answer:

There is a 0.2 chance or 20% change that he will choose a nonfiction book. PLease mark as helpful if it is! thanks

|
1.64 divided by what equals 0.04?

Answers

Answer:

41

Step-by-step explanation:

1.64 : x = 0.04 ⇒ x = 1.64 : 0.04

1.64 : 0.04 → 164 : 4 = 41

Check:

1.64 : 41 = 0.04

1.64 divided by the number 41 equals 0.04.

What is the division?

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

The given numbers are 1.64 and 0.04.

Let the unknown number be x.

1.64 divided by x equals 0.04, that is

1.64/x =0.04

0.04x=1.64

x=1.64/0.04

x=41

Therefore, 1.64 divided by 41 equals 0.04.

To learn more about the division visit:

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HELP ME PLEASE 9 3/5 + 8 3/5

Answers

Answer:

18 1/5

Step-by-step explanation:

9 3/5 + 8 3/5

We have a common denominator, so add the whole numbers

9+8 = 17

Add the fractions

3/5+ 3/5 = 6/5

17 6/5

We can simplify since we have an improper fraction

17 + 5/5 + 1/5

17+1+1/5

18 1/5

Answer:

18 1/5

Step-by-step explanation:

9 3/5 + 8 3/5=

First we do 9+8 which is 17

3/5+3/5= 6/5

17 6/5

Simplify:

18 1/5

Alice drops a rubber ball from a height of 4 feet. The equation t2=4/16 represents the amount of time, in seconds, it takes for the ball to reach the ground. How long will it take the ball to reach the ground?

A 1/4 second
B 1/2 second
C 2 seconds
D 4 seconds

Answers

Answer:

Letter B

Step-by-step explanation:

Answer:

I belive the answer is B

Step-by-step explanation:

In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third is 92° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle.

The measure of the first angle is ______
The measure of the second angle is _____
The measure of the third angle is _______

Answers

Answer:

The measure of first angle is 44°.

The measure of second angle is 22°.

The measure of third angle is 114°.

Step-by-step explanation:

First, you have to form expressions for the 3 angles. Let second angle be x :

First angle = (2x)°

Second angle = x°

Third angle = (92 + x)°

Next, you have to add up altogether as the total angles in a triangle is 180° :

2x + x + 92 + x = 180

4x + 92 = 180

4x = 180 - 92

4x = 88

x = 88 ÷ 4

x = 22°

Lastly, you have to substitute the x-value into the expressions :

First angle = 2(22) = 44°

Second angle = 22°

Third angle = 92 + 22 = 114°

15. To receive a B in his English class, Nicolas must have an average score of at least 84 on five
tests. He scored 90,91, 79, and 81 on his first four tests. What is the score range he can receive
on his last test and still receive a B in the class?

Answers

Answer:

(90+91+79+81+x)/5=84and 341+x=84*5and341+x=420and x=420-341 finally x=79

Please help!!!- Find the measure of the angle in bold.
Need help to figure out to solve this.

Answers

Answer:

11x-6+(19x+6)=180°

11x+19x-6+6=180°

30x=180

x=180/30

x=6

it means that

19x+6=19*6+6=114+6=120°

Question 4
5 pts
4. Cassie has 45 marbles. Abdul has m If Cassie has 9 times as many
marbles as Abdul. Choose the equation that correctly represents the
number of marbles Abdul has.
O 9 x m = 45
O 45 - 9 = m
O C. 9+ m = 45
O D. 9 x 45 = m

Answers

Answer:

8 x m = 45

Step-by-step explanation:

cassie has 9 times which means multiplcation so its the first one

What is the ratio of daises to all the flowers in the vase?

Answers

Answer: Do you have the original ration so we can simplify it then??

Step-by-step explanation:

An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a:

Answers

Answer:

the speed value that the radar equipment outputs.

Step-by-step explanation:

A random variable in an experiment is also (and most times the case) called a dependent variable. In this scenario, the random variable would be the speed value that the radar equipment outputs. This is because this value depends on the actual velocity of the cars that pass by the equipment. The faster the car is moving when it passes the radar the higher value will be displayed on the equipment. Therefore, depending completely on the vehicles.

what number is 1/10 of 8000000

Answers

Answer:

800000

Step-by-step explanation:

bernie spends three hours a day on homework. if the spends 3/4 of an hour on science, 3/4 of an hour on social studies, and 1/4 of an hour on english, how much time does bernie spend on math

Answers

3/4 of an hour is 45 minutes
1/4 of an hour is 15 minutes
3 hours is 180 minutes

3/4 + 3/4 = 90 minutes ( 45 + 44 )
90 + 15 = 105

180 - 105 = 75 minutes

Bernie will spend 75 minutes on math

Answer:

Step-by-step explanation:

Math = 3 - Science - social studies - english

Math = 3 - 3/4 - 3/4 - 1/4

Math = 3 - 1 3/4

Math = 3 - 1.75

Math = 1.25 or 1 1/4

Find the LCD of the given rational equation:

Answers

Answer:

The correct answer is: D

Step-by-step explanation:

Consider the domain, which in this case x cannot be equal to -4 and -2.

The LCD of the rational equation is (a) (x + 4)(x + 2)(x - 2)

How to determine the LCD?

The rational equation is given as:

[tex]\frac{x}{x + 4} + \frac{x - 1}{x + 2} = \frac{3}{x^2 + 2x - 8}[/tex]

Factorize the denominator of the fraction on the right hand side

[tex]\frac{x}{x + 4} + \frac{x - 1}{x + 2} = \frac{3}{(x - 2)(x + 4)}[/tex]

Write out the common factors in the denominator

LCD = (x + 4)(x + 2)(x - 2)

Hence, the LCD of the rational equation is (a) (x + 4)(x + 2)(x - 2)

Read more about rational equation at:

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Emilia made fewer than 27 bracelets last week. The variable b represents the number of bracelets. The inequality b less-than 27 describes the number of bracelets that Emilia made. Which could be a solution to the inequality?
26
29
33
40

Answers

Answer:

26

Step-by-step explanation:

26 is the only thing less than 27

Answer:

26

Step-by-step explanation:

Give a counterexample that disproves each conjecture below.
1) No triangles have two sides of the same length.

2) No women have been elected U.S. senators.

3) All~basketball players are more than 6 feet tall.

4) If you live in Texas, then youlive in Houston.

5} If it is a cell phone, then it has a touch screen.

6) If x is any number, then x2> 2.

8) If x >_ 0, then x + 2 = 7.

9) If x2 =16 , then x = 4.

10) All figures with four sides of equal length are squares.

11) The square of a number rs largex than the number.

12) If a numbex is prime, then it zs an. odd number.

Answers

Answer:

1) No triangles have two sides of the same length.

An isosceles triangle is a triangle that has 2 sides that have a same length.

2) No women have been elected U.S. senators.

Dianne Feinstein, a woman-elected senator of California.

3) All basketball players are more than 6 feet tall.

Isaiah Thomas is a prime example of a basketball player who has the height of 5'9.

4) If you live in Texas, then you live in Houston.

Matthew McConaughey, a born-and-raised Texan star lives in Austin near his mom and other family members.

5) If it is a cell phone, then it has a touch screen.

Before smart phones, there were flip phones where the user would have to dial everything to able to use it.

6) If x is any number, then x2> 2.

Not sure what you meant.

8) If x >_ 0, then x + 2 = 7.

Not sure what you meant.

9) If x2 =16 , then x = 4.

Not sure what you meant.

10) All figures with four sides of equal length are squares.

Rectangles have longer sides equal in length and their shorter sides equal in length with each other, but is not considered a square.

11) The square of a number rs largex than the number.

Not sure what you meant.

12) If a number x is prime, then it zs an. odd number.

Not sure what you meant

Hoped this help!

You should rephrase some of your questions because I have no idea what it's saying.

-Bob Ross

PLEASE HELP!!!!


Drag each tile to the correct box.
Match each savings plan to its description.

401(k)
Roth IRA
403(b)
529 plan
health FSA

a tax-deferred retirement savings plan available to employees of some nonprofit
organizations and educational Institutions

a tax-advantaged college savings plan

an employer-offered retirement account that accepts contributions from
employees and employers

a tax-advantaged savings account available through employers to pay for
qualified medical expenses

a retirement Investment account managed by individuals, deposits are taxable,
but funds are tax exempt when withdrawn at retirement

Answers

Answer:

403(b)

529 plan

401(k)

health FSA

Roth IRA

Step-by-step explanation:

I looked it up. Good luck :)

Answer:

401(b)

529 plan

401(k)

health FSA

Roth IRA

Step-by-step explanation:

the set
of whole number less than 20

Answers

Answer:

maybe 3, 6, 9, 12, 15, 18?

Step-by-step explanation:

sorry if this doesn't help but I hope someone else can help you! good luck

Whole numbers less than 20 are 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1. How to know if they are divisible by 3? Add the numbers, and if the sum is divisible by 3.

the product of -4 and a number is 36 find the number?​

Answers

Answer:

32

Step-by-step explanation:

if you add 4- + 36 it's exactly the same as saying 4 - 36 = 32

pls mark brainlest for real :,,(

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