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EastWind [94]
2 years ago
12

Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and z ≥ 3.

Mathematics
1 answer:
SashulF [63]2 years ago
5 0

There are 59 integer solutions

Such questions are best solved by writing cases and calculating the total number of cases. So beginning with

1)  x = -3. The possible combinations are as follows:-

-3 2 13

-3 3 12

-3 4 11

-3 5 10

-3 6 9

-3 7 8

-3 8 7

-3 9 6

-3 10 5

-3 11 4

10 combinations

2) x = -2

-2 2 12

through

-2 11 3

10 combinations

3) x = -1

-1 2 11

through

-1 10 3

9 combinations

4) x = 0

0 2 10

through

0 9 3

8 combinations

as we can see from the pattern at x =1  we get 7 combinations, at x =2  we get 6 combinations, at x=3 we get 5 combinations and at x =4  we get 5 combinations.

Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.

Learn more about combinations here :

brainly.com/question/13387529

#SPJ1

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Answer:

NO

Step-by-step explanation:

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first, check the directions to make sure they are opposite,

then read the digits, or count the tick marks or compare lengths with dividers or ruler or marks on a piece of paper to see if the distances are the same.

3 is not the opposite of -6

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3 years ago
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For each situation below, write the equation of the line and explain how you can tell.
sveticcg [70]

Answer:

see below

Step-by-step explanation:

a. Has a slope of 2 and passes through (10,17)

Using the slope intercept form

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Substitute the point into the equation

17 = 2(10)+b

17 = 20+b

Subtract 20 from each side

17-20 =b

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b. passes through (1,-4) and (2,-5)

First find the slope

m= (y2-y1)/(x2-x1)

   = (-5- -4)/(2-1)

  = (-5+4)/(2-1)

  = -1/1

  = -1

Using the slope intercept form

y = -x+b

Substitute a point into the equation

-4 = -1(1) +b

-4 = -1+b

Add 1 to each side

-3 = b

y = -x+3

   

6 0
3 years ago
Please help .......You are guaranteed a minimum salary of $2000 per month PLUS 5.75% 5 points
RUDIKE [14]

Answer:

6600

Step-by-step explanation:

0.0575*80000=4600

4600+minimum salary which is 2000=6600

(can I get brainliest please)

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Step-by-step explanation:

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