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
What is the value of x?​
ANTONII [103]

Answer:

its x=2

Step-by-step explanation:

5 0
3 years ago
In a standard normal curve, what percentile corresponds to a z-score of 2.0?
Alja [10]
The percentile that corresponds to Z=2 is about 97.7.

4 0
2 years ago
Find the scale factor abc def
Vesna [10]

Answer:

The scale factor is 1.2.

Step-by-step explanation:

18/15 = 1.2

30/25 = 1.2

24/20 = 1.2

Hope that helps!

8 0
3 years ago
State the domain of the rational function. f(x)= 7/14-x
34kurt
The denominator is 14-x.
Since the denominator cannot be equal to zero, you take the denominator, set it equal to zero, and solve.
This ill give you the value or values that must be eliminated (cannot be in the domain).

14 - x = 0
add x to both sides
14 = x
The domain is x ≠ 14
OR
(- ∞, 14) ∪ (14, ∞)
OR
All real numbers except 14
4 0
3 years ago
Are negative numbers prime or composite?
user100 [1]

Negative numbers aren't considered in any of those categories.

3 0
2 years ago
Read 2 more answers
Other questions:
  • 78 = -2 (m + 3) + m <br><br> Solve for m
    10·2 answers
  • Y=1/2x<br><br> Y= 4x<br><br> Y= 1/4 x<br><br> Y= 2 x
    7·1 answer
  • Which could be the measures of angle POS and angle POQ
    14·2 answers
  • Billy collects marbles. Each marble in his collection weighs about 4 ounces. His collection weighs about 20 pounds in all. About
    6·1 answer
  • The strip below is divided into 10 equal parts. Fill in the missing fractions and percentages.Note that your fractions don't nee
    13·1 answer
  • 261, 256,251,... what would be the 46th term
    8·1 answer
  • This is the second one pic of the problem
    6·1 answer
  • Plz help asappppp I’ll give brainliest
    6·1 answer
  • This pattern follows the "divide by 2" rule. What is the next number in the pattern?
    7·2 answers
  • 50 points!!!!!! and brainliest if answered correctly 6-10 please show work
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!