What equation is equivalent to 2+3(2x+4)=13

Mathematics

1 answer:

svlad2 [7]2 years ago

6 0

Answer:

14+6x=13, or further 1+6x=0

Step-by-step explanation:

2+3(2x+4)=13,

Distribute the 3 into the parenthesis:

2+6x+12=13

Now combine like terms: 14+6x=13.

You can also write this as 1+6x=0 by subtracting 13 to the left, though it might not be necessary.

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An 8-sided die is rolled. Find the probability of rolling a 1 or even number

leonid [27]

The probability of rolling a 1 or an even number is 5/8.

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If g (x) = 1/x then [g (x+h) - g (x)] /h

lys-0071 [83]

Answer:

$\dfrac{-1}{x(x+h)}, h\ne 0$

Step-by-step explanation:

If $g(x) = \dfrac{1}{x}$ , then $g(x+h) = \dfrac{1}{x+h}$ . It follows that

$\begin{aligned} \\\frac{g(x+h)-g(x)}{h} &= \frac{1}{h} \cdot [g(x+h) - g(x)] \\&= \frac{1}{h} \left( \frac{1}{x+h} - \frac{1}{x} \right)\end{aligned}$

Technically we are done, but some more simplification can be made. We can get a common denominator between 1/(x+h) and 1/x.

$\begin{aligned} \\\frac{g(x+h)-g(x)}{h} &= \frac{1}{h} \left( \frac{1}{x+h} - \frac{1}{x} \right)\\&=\frac{1}{h} \left(\frac{x}{x(x+h)} - \frac{x+h}{x(x+h)} \right) \\ &=\frac{1}{h} \left(\frac{x-(x+h)}{x(x+h)}\right) \\ &=\frac{1}{h} \left(\frac{x-x-h}{x(x+h)}\right) \\ &=\frac{1}{h} \left(\frac{-h}{x(x+h)}\right) \end{aligned}$