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3 years ago

1. Solve each equation. a. 3x = 12 b. -3x = 9 c. 3x = -1 d. 1/2x= 12

Mathematics

1 answer:

adell [148]3 years ago

7 0

Answer:

A. X = 4

B. X = -3

C. X = -1/3

D. X = 1/24

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Solve by quadratic equation

Ymorist [56]

<h2>Question :</h2>

$\tt \dfrac{x+2}{x-2} + \dfrac{x-2}{x+2} = \dfrac{5}{6}$

<h2>Answer :</h2>

$\large \underline{\boxed{\bf{x = \dfrac{\pm 2\sqrt{119}}{7}}}}$

<h2>Explanation :</h2>

$\tt : \implies \dfrac{x+2}{x-2} + \dfrac{x-2}{x+2} = \dfrac{5}{6}$

$\tt : \implies \dfrac{(x+2)(x+2) + (x-2)(x-2)}{(x-2)(x+2)} = \dfrac{5}{6}$

$\tt : \implies \dfrac{(x+2)^{2} + (x-2)^{2}}{(x-2)(x+2)} = \dfrac{5}{6}$

<u>Now, we know that</u> :

$\large \underline{\boxed{\bf{(a+b)^{2} = a^{2} + b^{2}+ 2ab}}}$
$\large \underline{\boxed{\bf{(a-b)^{2} = a^{2} + b^{2} - 2ab}}}$
$\large \underline{\boxed{\bf{(a+b)(a-b) = a^{2} - b^{2}}}}$

$\tt : \implies \dfrac{x^{2}+2^{2}+ 2 \times x \times 2 + x^{2}+2^{2} - 2 \times x \times 2 }{x^{2}-2^{2}} = \dfrac{5}{6}$

$\tt : \implies \dfrac{x^{2}+ 4 + \cancel{4x} + x^{2}+ 4 - \cancel{4x}}{x^{2}-4} = \dfrac{5}{6}$

$\tt : \implies \dfrac{x^{2} + x^{2} + 4 + 4}{x^{2}-4} = \dfrac{5}{6}$

$\tt : \implies \dfrac{2x^{2} + 8}{x^{2}-4} = \dfrac{5}{6}$

<u>By cross multiply</u> :

$\tt : \implies (2x^{2} + 8)6= 5(x^{2}-4)$

$\tt : \implies 12x^{2} + 48 = 5x^{2}-20$

$\tt : \implies 12x^{2} + 48 - 5x^{2} + 20 = 0$

$\tt : \implies 7x^{2} + 68 = 0$

$\tt : \implies 7x^{2} + 0x + 68 = 0$

<u>Now, by comparing with ax² + bx + c = 0, we have</u> :

a = 7
b = 0
c = 68

<u>By using quadratic formula</u> :

$\large \underline{\boxed{\bf{x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}}}}$

$\tt : \implies x = \dfrac{-(0) \pm \sqrt{(0)^{2} - 4(7)(68)}}{2(7)}$

$\tt : \implies x = \dfrac{0 \pm \sqrt{0 - 1904}}{14}$

$\tt : \implies x = \dfrac{\pm \sqrt{- 1904}}{14}$

$\tt : \implies x = \dfrac{\pm \sqrt{2\times 2\times 2\times 2\times 7\times 17}}{14}$

$\tt : \implies x = \dfrac{\pm \cancel{2} \times 2\sqrt{7\times 17}}{\cancel{14}}$

$\tt : \implies x = \dfrac{\pm2\sqrt{119}}{7}$

$\large \underline{\boxed{\bf{x = \dfrac{\pm 2\sqrt{119}}{7}}}}$

Hence value of $\bf x =\dfrac{\pm 2\sqrt{119}}{7}$

5 0

3 years ago

Read 2 more answers

What is the formula for a Arithmetic series and how can you use it in a practical situation? Show explanation!

SVETLANKA909090 [29]

A finite geometric series is that where the consecutive terms have a fix ratio.

Call r the ratio, An the nth term and An+1 the next term to n, then:

An+1 / An = r

For example, the geometric series, 1, 3, 9, 27, 81, ..

You can verify that

3 = 1* 3

9 = 3 * 3

27 = 9 * 3

81 = 27 * 3

So, the formula is An+1 = An * r, so if you know the first term you can find any other term.

For example, Find the fifth term of a geometric series where the first term is 5 and the second term is 25.

r = second term / first term = 25 / 5 = 5

=> Fifth term = First term * r * r * r * r = First term * r^4 = 25 * 5^4 = 15,625

From this you can also see this valid formula:

An = A1 * r^ (n-1).

So now you have two equivalent formulas:

An+1 = An * r, which is called recursive formula, and

An = A1 * r ^ (n-1), which is called explicit formula

hope this helps :)

3 0

3 years ago

After kicking, one coach likes to play practice games with 6 players on each

Nezavi [6.7K]

There are many possible numbers. First, lets begin with the data there giving us. They are saying she wants to play a practice game so there at least needs to be 2 teams. It also says, that she wants 6 players on each team, nothing more and nothing less. So, for this we are going to use the 6 timetables.

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

There are also more numbers, but I am not doing those. But, for your first five, there can be 12, 18, 24, 30, and 36 students to be on the teams for the practice game.

4 0

3 years ago

-1+21y^4-16y^2+17^2+17y^4+19

quester [9]

Answer:

If you simplify the equation, you will get, $38y^{4} -16y^{2} + 307$