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EastWind [94]
1 year 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]1 year 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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15. An irregular pentagon has side lengths of (x + 3), (2x - 4), (4x + 5),
Kobotan [32]

Answer:

A. 11x-3

Step-by-step explanation:

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3 0
2 years ago
A Mexican restaurant sells quesadillas in two sizes: a "large" 10 inch-round quesadilla and a "small" 5 inch-
elena-14-01-66 [18.8K]

Answer:

Half of the 10-inch quesadilla is greater than the entire 5-inch quesadilla

Step-by-step explanation:

we know that

The area of a circle is equal to

A=\pi r^2

where

r is the radius

step 1

Find the area of the 10 inch-round quesadilla

we have

D=10\ in

r=10/2=5\ in

substitute

A=\pi (5)^2

A=25\pi\ in^2

step 2

Find the area of the 5 inch-round quesadilla

we have

D=5\ in

r=5/2=2.5\ in

substitute

A=\pi (2.5)^2

A=6.25\pi\ in^2

step 3

Which is larger, half of the 10-inch quesadilla or the entire 5-inch quesadilla?

Compare

half of the 10-inch quesadilla is equal to ----> \frac{1}{2}(25\pi)=12.5\pi\ in^2

the entire 5-inch quesadilla ---->6.25\pi\ in^2

therefore

Half of the 10-inch quesadilla is greater than the entire 5-inch quesadilla

3 0
2 years ago
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