Answer:
a. p(x) and q(x) have the same domain and the same range.
Step-by-step explanation:
Which statement best describes the domain and range of p(x) = 6–x and q(x) = 6x? a. p(x) and q(x) have the same domain and the same range. b. p(x) and q(x) have the same domain but different ranges. c. p(x) and q(x) have different domains but the same range. d. p(x) and q(x) have different domains and different ranges.
Answer: The domain of a function is the set of all values for the independent variable (i.e the input values, x values).
The range of a function is the set of all values for the dependent variable (i.e the output values, y values).
Both p(x) = 6–x and q(x) = 6x are linear functions, the domain and range of a linear function is the set of all real numbers i.e for a linear function:
Domain = (-∞, ∞)
Range = (-∞, ∞)
Therefore p(x) and q(x) have the same domain and the same range.
Answer:
![d=5](https://tex.z-dn.net/?f=d%3D5)
Step-by-step explanation:
Distance Formula: ![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Simply plug in the 2 coordinates into the formula to find distance <em>d</em>:
![d=\sqrt{(4-1)^2+(-1-3)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%284-1%29%5E2%2B%28-1-3%29%5E2%7D)
![d=\sqrt{(3)^2+(-4)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%283%29%5E2%2B%28-4%29%5E2%7D)
![d=\sqrt{9+16}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B9%2B16%7D)
![d=\sqrt{25}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B25%7D)
![d=5](https://tex.z-dn.net/?f=d%3D5)
Answer: The MAD describes the average distance from a data point to the mean. It measures variability. For this data, it shows that Evelyn’s scores varied slightly more than Robin’s.
Step-by-step explanation: Add 8+1+5+0+12 and divide it by 5 and get 5.2
Let's find at first
![\sqrt((a+b)/(a-b))](https://tex.z-dn.net/?f=%5Csqrt%28%28a%2Bb%29%2F%28a-b%29%29)
Let's find (a+b)(a-b)....
we should divide both side of fraction by b and we will get the following:
![\frac{ \frac{a+b}{b} }{ \frac{a-b}{b} } \\ \frac{ \frac{a}{b} + 1 }{ \frac{a}{b} - 1 } \\ \frac{ tanx + 1 }{ tanx - 1 }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cfrac%7Ba%2Bb%7D%7Bb%7D%20%7D%7B%20%5Cfrac%7Ba-b%7D%7Bb%7D%20%7D%20%20%5C%5C%20%20%5Cfrac%7B%20%5Cfrac%7Ba%7D%7Bb%7D%20%2B%201%20%7D%7B%20%5Cfrac%7Ba%7D%7Bb%7D%20-%201%20%7D%20%20%5C%5C%20%0A%5Cfrac%7B%20tanx%20%2B%201%20%7D%7B%20tanx%20-%201%20%7D)
and (a-b)/(a+b) is same as (1/[(a+b)/(a-b)]) so we can use previous answer and finally we will have (a-b)/(a+b) = 1/[ (tanx + 1) / (tanx - 1)] = (tanx - 1)/(tanx + 1) and final answer will be this:
The answer to this is 4 4/9