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3 years ago

7n^2+16n+15=2n^2+3 solve using Quadratic

Mathematics

1 answer:

Harrizon [31]3 years ago

3 0

Answer:

n=6/5 or n=-2

Step-by-step explanation:

7n^2+16n+15=2n^2+3

collect like terms

7n^2-2n^2 +16n=3-15

5n^2 + 16n= -12

5n^2 +16n + 12

(5n^2+10n)+(6n+12)

5n(n+2)+6(n+2)

(5n+6)(n+2)

n=6/5 or n=-2

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Answer:

$E\ n\ F = \{1, 5, 6,7\}$

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Step-by-step explanation:

Given

$S = \{1,2,3,4, 5,6,7,8, 9, 10, 11, 12\}$

$E = \{1,2, 3, 4, 5, 6,7\}$

$F =\{1,5,6, 7, 8,9\}$

$G = \{9,10, 11, 12\}$

$H = \{2, 3, 4\}$

Solving (5): E and F

Sets of E and F = E n F

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List out common elements

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They are not mutually exclusive because $n(E\ n\ F) \neq 0$

Solving (6): F and G

Sets of F and G = F n G

$F\ n\ G =\{1,5,6, 7, 8,9\}\ n\ \{9,10, 11, 12\}$

List out common elements

$F\ n\ G =\{9\}$

They are not mutually exclusive because $n(F\ n\ G) \neq 0$

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Sets of F or G = F U G

$F\ U\ G =\{1,5,6, 7, 8,9\}\ U\ \{9,10, 11, 12\}$

List all elements without repetition

$F\ U\ G =\{1,5,6, 7, 8,9,10, 11, 12\}$

Solving P(F U G)

$P(F\ U\ G) = \frac{n(F\ U\ G)}{n(S)}$

$n(F\ U\ G) = 9$

$n(S) = 12$

Hence;

$P(F\ U\ G) = \frac{9}{12}$

Divide by 3

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