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

What is the value of x?







2

5

3

4

Answers

The Answer is: x = 3

Un comerciante tiene en cartera una letra de 14000 con vencimiento a 2 años y le somete a un descuento bancario 1 año y 8 meses antes de su vencimiento a una taza de 14%anual con capitalización trimestral ¿cuanto recibira el propetario de la letra ?

Answers

Answer:

dud

Step-by-step explanation:

fjfn

kgoipyx

vbjjkkkkkkjjjjhcblxkcjl

Robert accepted a new job at a company with a contract guaranteeing annual raises.
Robert's salary after working for n years can be determined using the equation
S = 5000n + 60000. What is the slope of the equation and what is its
interpretation in the context of the problem?

Answers

Answer:

The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.

Step-by-step explanation:

The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.

What is slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Here, given that,

Robert's salary after working for n years can be determined using the equation

S = 5000n + 60000.

Hence, The slope is 5000,

this means that for each additional year Robert works at the company, he earns 5000 more dollars.

To learn more on slope click:

brainly.com/question/3605446

#SPJ2

Select three ratios that are equivalent to 11:1.
Choose 3 answers:
1:11
22:2
55:5
9:99

Answers

Answer:

22:2, 55:5, 1:11

Step-by-step explanation:

Answer:

22:2 55:5 and no others

Step-by-step explanation:

Siobhan earned $45 babysitting on Friday. On Saturday, she babysat for 5 hours at $4 per hour. On Sunday she bought a DVD for $32. How
much money did she have left after buying the DVD?

Answers

$30

Work: 45+20=65

          65-35=30

Determine the midpoint of the segment with endpoints of (-3, 8) and (-3,
-2).

Answers

Answer:

(-3,3)

Step-by-step explanation:

Sharon buys a 60" tv for $1,450 plus the sales tax rate, which is 8.25%. what is the total cost of what she paid after taxes. round to two decimal place ​

Answers

Answer:

1,569.625

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total cost of the 60" TV is $1,569.63.

How many hundredths are in one tenth how many thousandths are in one hundredth

Answers

Answer:

10 hundredths

Step-by-step explanation:

One-tenth equals 0.1 and one-hundredth equals 0.01, which means that hundredth equals 10 hundredths.

1. FRUITS Find the ratio of bananas to oranges in the graphic at the right. Write the
ratio in simplest form. Then explain its meaning.
Ratio:
Simplified Ratio:
Explanation:
so what is the answer?​

Answers

Answer:

999kkk b8llion

Step-by-step explanation:

iiuugghhgvvjhhffffffffffffffggttgggg

Jesse is driving to a town that is 210 miles away with a speed of 60 miles per hour. If he makes no stops, how long will the trip take?

Answers

Answer: The trip should take 3.5 hours.

Step-by-step explanation: To find the time, divide the distance by the rate. In this case, 210/60 = 3.5.

Answer:

3.5 hours or specifically, 3 hours and 30 minutes

Step-by-step explanation:

We know that the car can be driven 60 miles per hour. The goal is 210 miles. If you divide 210 miles by 60, the result is 3.5. The whole number 3 in 3.5 will represent the hours taken which means 3 hours. The 0.5 will also represent the minutes. 0.5 = 1/2, 1/2 of an hour = 30 minutes.

g Regression is a functional relationship between two or more correlated variables, where one or more variables are used to predict a single variable of interest. Group of answer choices True False

Answers

Answer:

True

Step-by-step explanation:

In regression analysis, it tries to infer that there is a supposed relationship between two or more variables.

Now it has a couple of functions such as;

It allows us to directly estimate the parameters in linear functions only, although there are some other ways in which it would allow many non - linear functional forms to get estimated indirectly.

Regression also allows us to test and find out if there is a functional relationship between two or more variables. This is done by testing the hypothesis whether each of the slopes have a value of zero.

Thus, from the definitions given, we can see that regression is a basically a functional relationship between two or more variables, where one or more variables are used to predict a single variable of interest.

Thus, the given statement is true.

need quick aaaaaaaaaaaaa

Answers


5.0 x 10^4 < answer

Answer:

5.0 x 10^4

did the thing this is right

5 + 5 + 5 + 5 + 220+ 30004

Answers

Answer:

30244

Step-by-step explanation:

Assemble the proof by dragging tiles to the statements and reasons columns

Answers

Answer:

Here, I did the assignment. I wish you good luck!

the ray XZ is the angle bisector of WXY and m WXY = 125°. Enter m WXZ

Answers

145 degrees it is thank you have a wonderful day

The base of a triangle exceeds the height by 5 yards. If the area is 250 square yards, find the length of the base and the height of the triangle

Answers

Answer:

height = 20 yards and base = 25 yards.

Step-by-step explanation:

let the height = x yards.

base = (5 + x) yards.

area = 250 square yards

Area = 1/2 bh

250 = 1/2 × (x)(5+x)

250 × 2 = 5x + x2

500 = x2 + 5x

x2 + 5x - 500 = 0

factorizing:

(x + 25)(x - 20) = 0

x = -25 or 20

but length cannot be negative,

hence x = 20 yards.

height = 20 yards

base = (5 + 20) = 25 yards.

please help!! The picture has the question.

Answers

Answer:

B.

Step-by-step explanation:

They are used to the climate and they are harder the the rest.

Answer:

dry climate or

Step-by-step explanation:

they are in wet climate

Wilbur has a bag of coins. The bag contains 10 dimes, 5 nickels, and 1 penny. He will randomly select 2 coins from the bag, one at a time, without replacement. What is the probability that Wilbur will select a dime first and then a penny? A) 0.1 B) 0.04167 C) 0.03906 D 0.04444 ​

Answers

b. you would multiple the odds of drawing a dime from the 16 coins (10/16) times getting a penny from the remainder of coins (1/15) and get .04167.

The two lines graphed below are not parallel. How many solutions are there to
the system of equations?

Answers

Answer:

I think it might be zero

Step-by-step explanation:

you might want to look into this all the way beforyou trust put it into*

choose the equation below that represents the line passing through the point (-3, -1) with a slope of 4​

y = 4x - 11
y = 4x + 11
y = 4x + 7
y = 4x - 7

Answers

Answer:

y = 4x +11

Step-by-step explanation:

[tex](-3,-1) = (x_1, y_1) \\ m = 4[/tex]

Substitute values into point slope form

[tex]y-y_1 = m(x-x_1) \\ y - ( - 1) = 4(x - ( - 3)) \\ y + 1 = 4(x + 3) \\ y + 1 = 4x + 12[/tex]

Collect like terms and simplify

[tex]y = 4x + 12 - 1 \\ y = 4x + 11[/tex]

Answer:

y=4x + 11

Step-by-step explanation:

y = mx + b

y = 4x + b

-1= 4(-3) + b

b= 11

y= 4x + 11

SOMEONE HELP PLZ BRAINLIEST

Answers

Answer:

f = 3n = -16h = -10z = 7.5x = 54v = -12[tex]d = -\frac{417}{25}[/tex]  w = -27.6t = -5w = 43

I hope this helps!

Answer:

F=3

n= -16

h= -10

z =7.5

x=54

v= -12

d= -416÷25

w= -27.6

t= -5

w= 43

Jackson spent $3,472 on a new TV. If he paid it off in 16 equal payments, how much was each payment?

A $217
B $237
C $207
D $227

Answers

Answer:

A. 217

Step-by-step explanation:

3,472/16 = 217

a is the answer hope this helped a lot man have a good day

60 POINTS BRAINLIES
PLEASE WORKOUT QUESTIONS a b & c
PHOTO OF GRAPH ATTACHED BELOW

a) Calculate the median number of medals for each medal type, stating the formula you would use for determining the median for the gold medals.


b) Calculate the mean number of medals for each of the 3 medal types, stating the formula you would use for determining the mean for the bronze medals.


c) Calculate the standard deviation of the total medals awarded to each country
(column F) using the formula below.
Show all the steps ( show your work ).

USE the STDEV.P function to cross-check your final answer.

Answers

Answer:

see below

Step-by-step explanation:

a)  median : re-arranged the numbers in order. i.e. min to max

gold:          147 , 147 , 175 , 206 , 212 , 227 , 263 , 275 , 440 , 1022

                 212  + 227    =  219.50

                        2

silver:       147 , 163 , 165 , 170 , 178 , 241 , 295 , 313 , 357 , 794

                178 + 241     =  209.50

                       2

bronze:    151 , 169 , 179 , 187 , 193 , 260 , 289 , 325 , 349 , 704

                193  +  260  =  226.50

                        2

b)  mean : sum of all numbers divide by n, where n=10  

gold:        =   (147 , 147 , 175 , 206 , 212 , 227 , 263 , 275 , 440 , 1022 ) / 10

               =  311.40

silver:      =   (147 , 163 , 165 , 170 , 178 , 241 , 295 , 313 , 357 , 794 ) / 10

              =  282.30

bronze:   =  (151 , 169 , 179 , 187 , 193 , 260 , 289 , 325 , 349 , 704 ) / 10

               =  280.60

c) standard deviation on population (STDEV.P)

Australia          = 16.44

china               = 33.03

france              = 19.74

germany          = 30.21

great britain    = 13.89

hungary           = 12.04

italy                  = 11.44

soviet union    = 48.46

sweden           = 13.47

united states   = 133.84

Help!!! ASAP!!!
The sum of the areas of a polyhedron’s face is

A: Its perimeter divide by two.
B: its surface area.
C: its volume
D: non of these

Answers

Answer: The sum of the area of it's faces

Step-by-step explanation: its the surafce area.

What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid?

Answers

ANSWER: 17

The distance horizontally is 15 units because 7-(-8) = 15

The distance vertically is 8 units because 8-0 = 0

Pythagorean theorem
a2 + b2 = c2
(225) + (64) = (289)

Square root 289 = 17 is the distance

Find the measure of an angle such that the sum of its supplement and four times its
complement is 13° less than twice the angle.
Show work

Answers

Answer:

Angle=79°

Step-by-step explanation:

Hope it helps!

Maggie claims that there are transformations that preserve the length of the rectangle's sides. Which of the following transformations could be used to support Maggle's claim? Select all that apply.
reflection over the side RS
a translation of 10 units to the right
a rotation of 90' clockwise about vortex Q
a vertical stretch of scale factor 2 through contor C
a dilation of scale factor 1 through conter

Answers

Answer: B,D,E. Step-by-Step explanation

Transformation that preserve lengths are rigid transformation.

The options that support Maggie's claim are:

reflection over the side RS a translation of 10 units to the right a rotation of 90' clockwise about vortex Q  

All transformations are rigid transformation, except dilation.

Dilation are of two types

StretchCompress

Either of the two above, do not preserve length

This means that:

Options (d) and (e) will not preserve the lengths of the rectangle, because they represent dilation

Hence, the correct options that will preserve the length of the rectangle are: (a), (b) and (c)

Read more about transformation at:

https://brainly.com/question/13801312

please help my geometry assginment, brainly if answer properly

Answers

Answer:

Please mark me brainliest     :)   Hope it helps

Step-by-step explanation:

So basically, since CD and AB are parallel, that means that angle2 and angle3 are similar, due to the corresponding angle postulate. Furthermore, it is given that AG and CE are similar, so angle1 and angle2 are similar on the same principle.

This means that angle3 and angle4 are similar, since it is given that angle1 and angle4 are similar. A bisecting line divides a whole angle into two, equal value angles, and since ECF is composed of angle3 and angle4, and angle3 and angle4 are the same value, that means the line that forms angle3 and angle4 is bisecting the ECF, therefore CD bisects ECF.

Line e has a slope of -6/5. Line f has a slope of 6/5. Are line e and line f parallel or perpendicular

Answers

Answer:

none of those

Step-by-step explanation:

to be parallel it needs to be the exact slope

to be perpendicular it would f would look like this [tex]\frac{5}{6}[/tex]

You measure the mass of a book and it’s 420.0890g how many significant digits are in the measurement

Answers

9514 1404 393

Answer:

  7

Step-by-step explanation:

All of the digits in the given number are significant. There are 7 significant digits.

__

Comment on other cases

When there are non-zero digits to the left of the decimal point in a number with a decimal point, all of the digits are significant.

When there are no non-zero digits to the left of the decimal point, leading zeros are not significant. All digits following the leading zeros are significant.

In a number with no decimal point, the leading and trailing zeros are not significant.

If the number is written in scientific notation, all digits of the mantissa are significant. (This can be a way to ensure the correct number of significant digits is known in a number with trailing zeros.)

Other Questions
Solve and prove the solution for the equation -2(1-4x)=3x+8. how are earthquakes related to tectonic activities Evaluate 22/(2-3) What was an effect of the abolitionist movement?A. Greater cooperation between people of different areas andbackgroundsB. Social and political activismC. Greater understanding between whites and African AmericansO D. All of the aboveNBMIT 15 men can dig a ditch in 10 days, how many dayWill 10men take working at the same rate 4x + y =1x + 2y = 9 What algebraic expression could represent the average of 2x, x + 3, and 6x? 3. Explain the term mathaphobia, then explain how that term might apply to you as a STEM student. Also, does itonly apply to math? Select the correct answer.Which of the following is an example of a long-term goal:OA.Go running todayOB.Finish this week's homework on time.O C.Become a medical doctorOD.Eat 5 fruits and vegetables every day this month How is someone death the sead of a nation witch of the following best describes the slope of the line below Vladimir buys 1.20 pounds of Skittles, 3 1/2 pounds of M&Ms, and 5.2 pounds of pretzels. If the candy cost $1.20 a pound and the pretzels cost $1.10 a pound, how much did Vladimir spend? 3x(2x+1) for x=7 5/13 Is he Govoner of New York aloud to invade Canada A local supermarket sells shrimp $9.49/lb and beef for $5.99/lb Todd buys s pounds of shrimp and b pounds of beef. Which of the following inequalities represents that Sandy only has $65 to spend? Taiga includes the largest contiguous forests on the planet and make up about _____ percent of all of Earth's forests. make a list of the 10 highest mountains in the world, and indicate what kind of mountain's they are what is one way in which the mongal political structure changed when they ruled china Write your answer as a whole number and remainder.73 : 8= R Mindy Novak is writing a paper and he must determine which of Porter's three generic strategies Beulahs Boutiques has implemented. Mindy finds out that Beulahs Boutiques offers specialty products found only in boutiques around the world to affluent customers. What would Mindy determine Beulahs Boutiques is using as its generic strategy?