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avanturin [10]
3 years ago
5

Help with these questions immediately

Mathematics
1 answer:
alisha [4.7K]3 years ago
3 0

Problem 1

<h3>Answer: Choice C)  1/2</h3>

--------------------

Explanation:

Let's plug 8 into f(x)

f(x) = \frac{x+3}{x^2-4x-21}\\\\f(8) = \frac{8+3}{8^2-4(8)-21}\\\\f(8) = \frac{8+3}{64-32-21}\\\\f(8) = \frac{11}{11}\\\\f(8) = 1\\\\

Repeat for g(x)

g(x) = \log_{4}(x)\\\\g(8) = \log_{4}(8)\\\\g(8) = \frac{\log(8)}{\log(4)}\\\\g(8) = \frac{\log(2^3)}{\log(2^2)}\\\\g(8) = \frac{3*\log(2)}{2*\log(2)}\\\\g(8) = \frac{3}{2}\\\\

I used the change of base formula in the third step.

Lastly, we subtract the results like so

(g-f)(x) = g(x) - f(x)\\\\(g-f)(8) = g(8) - f(8)\\\\(g-f)(8) = \frac{3}{2} - 1\\\\(g-f)(8) = \frac{3}{2} - \frac{2}{2}\\\\(g-f)(8) = \frac{3-2}{2}\\\\(g-f)(8) = \frac{1}{2}\\\\

========================================================

Problem 2

<h3>Answer: Choice A)  8</h3>

--------------------

Explanation:

Through trial and error (I recommend the rational root theorem), you should find that the roots of R(x) are:  -1, 3, and 8

We'll only focus on positive x values. So we focus on the roots 3 and 8.

It turns out that the R(x) curve dips below the x axis when x is between 3 and 8. When x > 8 is when R(x) is positive and goes upward forever. This represents when the company is making money.

The company does make money when x is between 0 and 3; however, this is a short timespan compared to the other interval. So it's much more effective and realistic to say that the company makes money after 8 days.

In other words, yes the company makes money between day 0 and day 3, but from day 3 to day 8 is when the company loses money. Ultimately the company is profitable again when it's beyond day 8.

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Oliga [24]

Answer:

30

Step-by-step explanation:

if im reading the qestuion right

so she had 80 bucks she spend 20 on a ticked so she has 60 left so if im reading it right she spent all of her money so 60 divde by 2 is 30.  

hoped this helped!

3 0
2 years ago
The solution set to 6 + 2n &gt; 12 is n &gt; 3. Which are the correct representations of this solution? Select two options.
Alina [70]

The correct representation of 6 + 2n > 12 (n > 3) is  (3, ∞) and a number line with an open circle at +3 and being shaded from +3 to +5.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation::

6 + 2n > 12

Subtracting 6 from both sides:

6 + 2n - 6 > 12 - 6

2n > 6

Dividing by 2:

n > 3

The correct representation of 6 + 2n > 12 (n > 3) is  (3, ∞) and a number line with an open circle at +3 and being shaded from +3 to +5.

Find out more on equation at: brainly.com/question/2972832

#SPJ1

3 0
1 year ago
The data were collected from a statistics class. The column head gives the​ variable, and each of the other rows represents a st
Basile [38]

Answer:

Gender is a categorical variable. The sum gives the total number of students in class.

Step-by-step explanation:

We are given the following in the question:

The variable​ Male, is​ categorical, even though its values are numbers.​

Categorical variable:

  • These variable are the non parametric variable.
  • They do not need values to express the data.
  • They only use number and numerical to express the data or represent the data.
  • There is no relation with true value of numerical.

Thus, gender is a categorical variable. Numbers are only used to represent the data.

Numbers are just a representation.

The sum of these represent the total male and female students in class. Thus, the sum gives the total number of students in class.

8 0
3 years ago
PLZ NEED HELP Reduce this algebraic fraction.36x^5 y^8 z^10/15x^5 y^7 z^2
kvasek [131]
36/15  = 12/5
x^5 / x^5 = 1
y^8 / y^7 = y
z^10 / z^2 = z^8

Answer is 12yz^8/5
7 0
2 years ago
Read 2 more answers
Factor the polynomial 3m^2 + 14m - 5​
Kipish [7]

Answer:

(3m-1)(m+5)

Step-by-step explanation:

7 0
2 years ago
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