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jeka94
3 years ago
11

What can a set of points tell you about a linear relationship?

Mathematics
1 answer:
hodyreva [135]3 years ago
3 0

Answer:

A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between two variables. Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.

Step-by-step explanation:

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For what values of x is log base 0.8 (x+4)&gt;log base 0.4 (x+4)<br>Thank you!
Radda [10]
We are seeking the solution of the inequality:

\displaystyle{ \log_{0.8}(x+4)\ \textgreater \ \log_{0.4}(x+4).


We recall that a log function f(x)=\log_b(x) is either increasing or decreasing:

i) it is increasing if b>1, 

ii) it is decreasing if 0<b<1.

Consider the functions \displaystyle{ \log_{0.8}(x) and \displaystyle{ \log_{0.4}(x).

The graphs of these functions both meet at x=1 (clearly), and after 1 they are both negative. So from 0 to 1 one of them is larger for all x, and from 1 to infinity the other is larger. (Being strictly decreasing, their graphs can only intersect once.)


We can check for a certain convenient point, for example x=0.8:

\displaystyle{ \log_{0.8}(0.8)=1 and

\displaystyle{ \log_{0.4}(0.8)=\log_{0.4}(0.4\cdot 2)=\log_{0.4}(0.4)+\log_{0.4}(\cdot 2)=1+\log_{0.4}(2).

Now, \displaystyle{ \log_{0.4}(2) is negative since we already explained that for x>1 both functions were negative. This means that 

\displaystyle{ \log_{0.8}(0.8)\ \textgreater \ \log_{0.4}(0.8), and since 0.8\in (0, 1), then this is the interval where \displaystyle{ \log_{0.8}(x)\ \textgreater \ \log_{0.4}(x).


So, now considering the functions \displaystyle{ \log_{0.8}(x+4) and \displaystyle{ \log_{0.4}(x+4), we see that 

x+4 must be in the interval (0,1), so we solve:

0<x+4<1, which yields -4<x<-3 after we subtract by 4.


Answer: (-4, -3). Attached is the graph generated using Desmos.

7 0
2 years ago
In the year 2000, there were 200,000 cell phone subscribers in a city in new york. the number of subscribers increased by 60 per
Semmy [17]

The equation can be used to model the number of subscribers, y, in the city t years after 2000 is  y = 200,000(1+60)t.

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

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

The first step is to calculate the percentage increase for each year.

If the subscribers increase by 60%, it means that the subscribers will be (100+60)% of the previous year.

(100+60)% = (100/100 + 60/100)

                 =  (1 + 0.6)

After 2,000, the subscribers will be 200,000×(1+0.6).

For the following years the 200,000×(1+0.6)t

So, the value of y will be given by,

Y=200,000(1+0.6)t

Hence,The equation Y=200,000(1+0.6)t .

To learn more about equation from the given link:

brainly.com/question/10270435

#SPJ4

6 0
2 years ago
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