Use the general solution to solve

Mathematics

1 answer:

Whitepunk [10]3 years ago

5 0

For this case we must solve the following linear equation:

$5-6x = 8x + 17$

Adding $6x$ to both sides of the equation we have:

$5 = 8x + 6x + 17\\5 = 14x + 17$

Subtracting 17 from both sides of the equation:

$5-17 = 14x$

Different signs are subtracted and the major sign is placed:

$-12 = 14x$

We divide by 14 on both sides of the equation:

$x = - \frac {12} {14}\\x = - \frac {6} {7}$

Answer:

$x = - \frac {6} {7}$

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How do I show that this function is one-to-one algebraically?<br> <img src="https://tex.z-dn.net/?f=f%28x%29%3D%20%28x-2%29%5E%7

Gwar [14]

For a one-to-one function, f(x) = f(y).
So, lets find f(x) and f(y).

We know,
f(x) = (x - 2)³ + 8

Now,
f(y) = (y - 2)³ + 8

Now, we said earlier, for a function to be one-to-one, f(x) = f(y).

Therefore,

  f(x) = f(y)
(x - 2)³ + 8 = (y - 2)³ + 8
  (x - 2)³ = (y - 2)³
  x - 2 = y - 2
x = y

Since we got x = y, we know for every x, there is one and only one y. Therefore, the function is one-to-one function.

6 0

4 years ago

Very large or very small numbers are best input with exponential notation. For instance, the number 8,000,000 (eight million) is

Lerok [7]

Answer:

$9*10^{12}km$

Step-by-step explanation:

$9,460,730,472,580.8 km$

First, we can work out 5% of our number, by multiplying it by 0.05

$9,460,730,472,580.8 * 0.05 = 473,036,523,629$

Now, if we add and subtract our 5% calculated from our original number, we can work out the minimum and maximum value that our final answer can be in the range of.

$9,460,730,472,580.8 + 473,036,523,629 = 9.933767*10^{12}\\9,460,730,472,580.8 - 473,036,523,629 =8.98769395*10^{12}$