Answer:
Because to get a straight line you need a scale. Otherwise you will not be able to graph a straight line.
Hope this helps:)
Answer:
Step-by-step explanation:
3(4x+5)
12x + 15
Multiply the 3 by numbers inside parentheses.
Answer:
Time - independent variable
Score in test - dependent variable
Step-by-step explanation:
The relationship between Dependent and independent variables lies in the fact that, the outcome (dependent variable) relies on the value of the independent variable. Hence, the independent variable could be explained as a series of different possible values which has an effect on the value of the predicted variable. In an experiment, the dependent variable is predicted based on the input or value of the independent variable entered into the model.
Hence, in the scenario above, the study time could take up series of different possible values which could affect the score obtained in her tests. Hence, the test scores depends on the time dedicated to studying, making score obtained in test the dependent variable and the study time the independent variable.
<h2>
Answer:</h2>
9 inches
<h2>
Step-by-step explanation:</h2>
Let x be the length of the side of the square.
If the base of the triangle is 3 times as long as the side of the square, it is 3 times x, or 3x.
The same can be said for the legs, which is 1 inch more than twice the side of the square, so 2x + 1.
The triangle can therefore be thought to look like the triangle below.
The perimeter is therefore (2x+1) + (2x+1) + 3x, which is 7x + 2.
The sum of perimeters of both the square and triangle is 46.
The perimeter of the square is 4x, so the sum of perimeters is 4x + (7x+2), or 11x + 2.
11x + 2 = 46, so 11x = 44.
x is therefore 4
The leg is 2x + 1, so the leg is 8 + 1, so the length of the leg is 9 inches.
Answer:
The answer is "It must be shown that both 
"
Step-by-step explanation:
Given:
To show that both are equal functions, and show that both
For 
![j(k(x)) = j[(\ln \frac{x}{11.6})]\\\\j[(\ln (\frac{x}{11.6})] = 11.6e^{\ln (\frac{x}{11.6})}\\\\j[(\ln \frac{x}{11.6})] = 11.6(\frac{x}{11.6})\\\\](https://tex.z-dn.net/?f=j%28k%28x%29%29%20%3D%20j%5B%28%5Cln%20%5Cfrac%7Bx%7D%7B11.6%7D%29%5D%5C%5C%5C%5Cj%5B%28%5Cln%20%28%5Cfrac%7Bx%7D%7B11.6%7D%29%5D%20%3D%2011.6e%5E%7B%5Cln%20%28%5Cfrac%7Bx%7D%7B11.6%7D%29%7D%5C%5C%5C%5Cj%5B%28%5Cln%20%5Cfrac%7Bx%7D%7B11.6%7D%29%5D%20%3D%2011.6%28%5Cfrac%7Bx%7D%7B11.6%7D%29%5C%5C%5C%5C)
(The natural logarithm is canceled by exponential function)
![j[(\ln \frac{x}{11.6})] = 11.6 \times\frac{x}{11.6}\\\\j[(\ln \frac{x}{11.6})] = x\\\\j[k(x)] = x\\\\for\ \ k[j(x)]:\\\\k[j(x)] = k[11.6e^x]\\\\k[11.6e^x] = \ln (\frac{11.6e^x}{11.6})\\\\k[11.6e^x] = \ln(e^x)](https://tex.z-dn.net/?f=j%5B%28%5Cln%20%5Cfrac%7Bx%7D%7B11.6%7D%29%5D%20%3D%2011.6%20%5Ctimes%5Cfrac%7Bx%7D%7B11.6%7D%5C%5C%5C%5Cj%5B%28%5Cln%20%5Cfrac%7Bx%7D%7B11.6%7D%29%5D%20%3D%20x%5C%5C%5C%5Cj%5Bk%28x%29%5D%20%3D%20x%5C%5C%5C%5Cfor%5C%20%5C%20k%5Bj%28x%29%5D%3A%5C%5C%5C%5Ck%5Bj%28x%29%5D%20%3D%20k%5B11.6e%5Ex%5D%5C%5C%5C%5Ck%5B11.6e%5Ex%5D%20%3D%20%5Cln%20%28%5Cfrac%7B11.6e%5Ex%7D%7B11.6%7D%29%5C%5C%5C%5Ck%5B11.6e%5Ex%5D%20%20%3D%20%5Cln%28e%5Ex%29)
Its natural logarithm leaving x will nullify expanding universe.
![k[11.6e^x] = x\\\\k[j(x)] = x](https://tex.z-dn.net/?f=k%5B11.6e%5Ex%5D%20%20%3D%20x%5C%5C%5C%5Ck%5Bj%28x%29%5D%20%3D%20x)
In the question, it is seen that![j[k(x)] = k[j(x)] = x](https://tex.z-dn.net/?f=j%5Bk%28x%29%5D%20%3D%20%20k%5Bj%28x%29%5D%20%20%3D%20x)
, shows that the functions 
is inverse functions.
