Write an equation in point-slope form of the line that passes through (-1,-4) with slope -2.
1 answer:
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You can use the definition of logarithm and the fact that a positive number raised to any power will always stay bigger than 0.
The domain of the given function is {x | x > 1 and a real number }
The range of the given function is (set of real numbers)
If a is raised to power b is resulted as c, then we can rewrite it that b equals to the logarithm of c with base a.
Or, symbolically:
Since c was the result of a raised to power b, thus, if a was a positive number, then a raised to any power won't go less or equal to zero, thus making c > 0
<h3>How to use this definition to find the domain and range of given function?</h3>Since log(x-1) is with base 10 (when base of log isn't specified, it is assumed to be with base 10) (when log is written ln, it is log with base e =2.71828.... ) thus, we have a = 10 > 0 thus the input x-1 > 0 too.
Or we have:
x > 1 as the restriction.
Thus domain of the given function is {x | x > 1 and a real number }
Now from domain, we have:
(log(x-1) > -infinity since log(0) on right side have arbitrary negatively large value which is denoted by -infinity)
Thus, range of given function is whole real number set (since all finite real numbers are bigger than negative infinity)
Thus, the domain of the given function is {x | x > 1 and a real number }
The range of the given function is (set of real numbers
Learn more about domain and range here:
Answer:
$ <em>is the total price.</em>
Step-by-step explanation:
<em>Mulitply the total by the percentage.</em>
<em />
<em>Add those together. </em>
<em />
<em>Total price of mangoes: $</em><em> </em>
The number of calories per ounce of soda is 10
<h3>Part A: Represent the relationship between the number of calories and the number of ounces</h3>The given parameters are:
Calories = 50
Ounces = 5
Let the number of calories be y and the ounces be x.
So, we have:
y = kx
Substitute y = 50 and x = 5
50 = 5k
Divide by 5
k = 10
Substitute k = 10 in y = kx
y = 10x
See attachment for the graph of the relationship between the number of calories and the number of ounces
<h3>Part B: What is the number of calories per ounce of soda?</h3>In (a), we have:
k = 10
This means that the number of calories per ounce of soda is 10
<h3>Part C: How does the unit rate relate to the slope of the line in the graph above? </h3>The unit rate and the slope represent the same and they have the same value
Read more about linear graphs at:
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