1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stira [4]
3 years ago
15

If x, y, and z are positive integers such that xyz+30xy+21xz+2yz+105x+10y+7z=812, find x+y+z.

Mathematics
1 answer:
Ket [755]3 years ago
6 0

Answer:

x= 2, y= 2, and z= 6

Step-by-step explanation:

If this is a Diophantine equation, add 35 to both sides and factor the left:

(3x+1)(2y+7)(z+5) = 847 = 7 times 112

Each integer factorization of 847 into 3 factors leads to a different number/value of x, y, and z. If the first factor, (3x+1), is 1 more than a multiple of 3, and the second factor, (2y+7), is odd, then x, y, and z will be integers.

For example:

847 = 121 times -7 times -1 gives (x, y, z) = (40, -7, -6) because 121 times -7 times -1 is 847 as well, it checks out.

If x, y, and z need to be positive, then the three numbers/factors need to be greater than 1, 7, and 5. The only combination that works is 7 times 11 times 11, which gives (x, y, z) = (2, 2, 6).

:)

You might be interested in
While riding her bike to the ocean and back home 55 times, kimberly timed herself at 48min48⁢min, 48min48⁢min, 49min49⁢min, 46mi
Vsevolod [243]
Total of 5 times = 48 + 48 + 49 + 46 + 64 = 255 mins

Goal:
Average = 53 mins
Total = 53 x 6 = 318 mins

6th ride = 318 - 255 = 63 mins

Answer: She needs to attain 63 mins for her 6th ride.




3 0
2 years ago
Please Help!<br><br> Car X travels 174 miles in 3 hours.
DiKsa [7]

Answer:

The graph =

<h3>y = 58x</h3>

Step-by-step explanation:

(a)

distance covered (y) = 174 miles

time taken (x) = 3 hours

Therefore the points = (3, 174) and (0, 0) = stationary position

Find the gradient (m)

m = 174-0 / 3-0

m = 58

Therefore the equation =

<h3>y = 58x</h3>

(distance = 58 × time)

For the distance = 174 and time = 3 hours, the equation to find either distance or time = y = 58x

(b) the graph is constant, because the time and distance are also contant when the speed used is the same.

____________________

#IndonesianPride - kexcvi

5 0
2 years ago
Angeles weather is making her a sandwich to take to school for lunch she is a loud to have two things on her sandwich and she ca
FinnZ [79.3K]
SHe has 4 choices chhese,tomato,lettuce,ham
3 0
2 years ago
Read 2 more answers
Which expression represents the word phrase six decreased by one third of a number?
sergij07 [2.7K]

Answer: 6-1/3n

Step-by-step explanation:

4 0
2 years ago
What is the value of -2xy if x = -1 and y= 6?<br> A. 12<br> B. -12<br> C. 26<br> D. 8
almond37 [142]

Answer:

A. 12

Step-by-step explanation:

-2*-1=2*6=12

plz mark brainliest

6 0
3 years ago
Other questions:
  • I'm really confused on point-slope form, and slope-intercept form. Can anyone help?
    10·1 answer
  • Find the solution set of 5b-13=22 if the replacement set is (5,6,7,8,9)
    15·1 answer
  • the new dolphin tank at the aquarium has a radius of 75 feet and a height of 20 feet. what is the volume of the dolphin tank? ro
    5·2 answers
  • List the correlation coefficients in order from least to greatest: 0.79,-0.43,-0.4,0.82,0.08
    5·2 answers
  • Ameekah is working with consecutive integers
    9·2 answers
  • Which type of probability was used in the following example? The probability that you will complete your college education (that
    9·1 answer
  • Help please!! What is the answer?
    6·1 answer
  • HELP I NEED HELP ASAP
    10·1 answer
  • Hello, please help me!!​
    6·1 answer
  • Someone please help me.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!