Mathematics, 23.09.2019 01:30 abbz13

Q4.) solve the equation by the method of your choice.

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Hey there!

First, you must find the common denominator of the equation.

To find the common denominator, first take a look at all the factors of each denominator:

x: x
x+4: x+4
6: 2*3

Next, because you do not have a common multiple in the denominators, you would multiply the denominators together to create one common multiple:
6(x)(x+4). This would be used to remove the fractions from the equation to make it easier to solve.

Now, multiply the common multiple 6(x)(x+4) to the entire equation:
(6(x)(x+4)) × ( $\frac{1}{x}$ + $\frac{1}{x+4}$ = $\frac{1}{6}$ )

When you multiply the factor to the equation, the x in the common factor would cancel out the x in $\frac{1}{x}$ resulting in just 6(x+4).

The x+4 would cancel out the x+4 factor in $\frac{1}{x+4}$ resulting in just 6x.

The 6 would cancel out the 6 in $\frac{1}{6}$ resulting in just x(x+4).

As a result, when you multiply the common factor 6(x)(x+4) to $\frac{1}{x}$ + $\frac{1}{x+4}$ = $\frac{1}{6}$ , you will get
(6(x+4))+ 6x = x(x+4)

Now, simplify the equation further:
(6(x+4))+ 6x = x(x+4)
6x+24+6x=x^2+4x (I have distributed the values in the parentheses)
12x+24=x^2 + 4x (I combined like terms on both sides)
0=x^2-8x-24 (I have moved all terms to one side so that the x values can be solved for using the quadratic formula)

Because this quadratic does not factor evenly, we must use the quadratic formula in order to find the exact x values:
x= $\frac{-b±\sqrt{b^2-4ac} }{2a}$

Your a value is 1, your b value is -8, and your c value is -24:
x= $\frac{-(-8) ±\sqrt{(-8)^2-4(1)(-24)} }{2(1)}$
x= $\frac{8 ±\sqrt{64+96} }{2}$
x= $\frac{8 ±\sqrt{160} }{2}$
x= $\frac{8 ±4\sqrt{10} }{2}$
x=4±2 $\sqrt{10}$

Therefore, your x values are 4+2 $\sqrt{10}$ and 4-2 $\sqrt{10}$

Answer from: Quest

The answer would be the second choice : )

Answer from: Quest

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1 1

1 2

1 3

1 4

2 1

2 2

2 3