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1 year ago

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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Answer:

<h2>SEE BELOW</h2>

Step-by-step explanation:

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vertex form of quadratic equation:

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therefore

y=a(x-(-1))²+4
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the graph crosses y-asix at (0,3) coordinates

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simplify exponent:

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therefore

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y=-(x+1)²+4

let's simplify it to standard form

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simplify parentheses:

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simplify addition:

$y = - {x}^{2} - 2x + 3$

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the domain of the function

$x\in \mathbb{R}$

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$y\leqslant 4$

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$\sf \implies \: x(x + 3) - 1(x + 3 )= 0$

group:

$\implies \: (x - 1)(x + 3) = 0$

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4 0

2 years ago

Which shows the image of quadrilateral ABCD after the transformation R0, 90°?

avanturin [10]

Answer:

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Therefore the image rectangle has coordinates:

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The first choice is correct.

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muminat

I am rocking with C. Jasmine left class for head.

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2 years ago

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Answer:

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where

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