Answer:

Step-by-step explanation:
If
, then
. 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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5C%5C%5Cfrac%7Bg%28x%2Bh%29-g%28x%29%7D%7Bh%7D%20%26%3D%20%5Cfrac%7B1%7D%7Bh%7D%20%5Ccdot%20%5Bg%28x%2Bh%29%20-%20g%28x%29%5D%20%5C%5C%26%3D%20%5Cfrac%7B1%7D%7Bh%7D%20%5Cleft%28%20%5Cfrac%7B1%7D%7Bx%2Bh%7D%20-%20%5Cfrac%7B1%7D%7Bx%7D%20%5Cright%29%5Cend%7Baligned%7D)
Technically we are done, but some more simplification can be made. We can get a common denominator between 1/(x+h) and 1/x.

Now we can cancel the h in the numerator and denominator under the assumption that h is not 0.

Answer:
Mauricio nació en el año 2000.
Step-by-step explanation:
Supóngase que el cumpleaños se celebra en el año 2020, si
es la edad actual de Mauricio, entonces la expresión matemática que traduce el enunciado del problema es:

Ahora, se desarrolla y se simplifica la ecuación:

Se despeja
:


Mauricio tiene 20 años.
Ahora, el año de nacimiento de Mauricio es la sustracción de la edad de Mauricio del año actual:


Mauricio nació en el año 2000.
The GCF of the three terms (9a, -18b and 21c) is 3
Rewrite each of the terms so 3 is a factor
9a = 3*3a
-18b = -3*6b
21c = 3*7c
So we can say...
9a - 18b + 21c = 3*3a - 3*6b + 3*7c
9a - 18b + 21c = 3(3a - 6b + 7c)
Answer: 3(3a - 6b + 7c)
If you distribute outer 3 to each of the inner terms and multiply, you'll get the original expression again.
Answer:
1 : 3000
Step-by-step explanation:
Given that:
Scale measurement as following:
4 centimeters are equal to 120 meters.
To find:
The scale factor = ?
Solution:
First of all, let us learn about the definition of scale factor.
Scale factor means 1 unit on scale is equal to what length of actual measurement.
We are given that 4 cm on scale is equal to 120 meters of actual length.
We need to find nothing but how much 1 cm of scale is equal to actual length.
4 cm of scale = 120 meters or 12000 cm of actual length
Dividing by 4 on both sides, we get:
= 1 cm of scale =
= 3000 cm of actual length
Therefore, the scale factor is <em>1 : 3000</em>
Answer:
4.58
Step-by-step explanation:
21 is not a perfect square, but lies between the perfect squares 16 and 25. Thus, √21 lies between √16 and √25, that is, between 4 and 5. Since 21 is closer to 25 than to 16, √21 is closer to 5 than to 4. A rough estimate of √21 would be 4.7.
√21 done on a calculator comes out to 4.58.