Answer:
The number 6.25 would be located on a number line between 6 and 7.
To be more precise in between 6.1 and 6.3.
To take it a step farther in between 6.25 and 6.27
Answer:
y= x -1.25
Step-by-step explanation:
Use slope= y2-y1/x2-x1
(13.75, 12.50), (3.25 , 2.00)
12.50 -2.00/ 13.75 -3.25
10.50/ 10.50
slope= 1
Substitute into y=mx+b
12.50= 1(13.75) +b
b= -1.25
y= x -1.25
Step-by-step explanation:
169 = (13)²
169 is the square of 13.
An exponential function is given by
![y=a(b)^x](https://tex.z-dn.net/?f=y%3Da%28b%29%5Ex)
Given two points, (m, n) and (p, q), we find the equation of the exponential function as follows:
![n=a(b)^m \ .\ .\ .\ (1) \\ \\ q=a(b)^p \ .\ .\ .\ (2) \\ \\ \frac{(1)}{(2)} \Rightarrow \frac{n}{q} = \frac{b^m}{b^p} =b^{m-p} \\ \\ \Rightarrow \ln\left( \frac{n}{q} \right)=(m-p)\ln(b) \\ \\ \Rightarrow \ln(b)= \frac{\ln\left( \frac{n}{q} \right)}{m-p} \\ \\ \Rightarrow b=e^{\frac{\ln\left( \frac{n}{q} \right)}{m-p}](https://tex.z-dn.net/?f=n%3Da%28b%29%5Em%20%5C%20.%5C%20.%5C%20.%5C%20%281%29%20%5C%5C%20%20%5C%5C%20q%3Da%28b%29%5Ep%20%5C%20.%5C%20.%5C%20.%5C%20%282%29%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B%281%29%7D%7B%282%29%7D%20%5CRightarrow%20%5Cfrac%7Bn%7D%7Bq%7D%20%3D%20%5Cfrac%7Bb%5Em%7D%7Bb%5Ep%7D%20%3Db%5E%7Bm-p%7D%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%3D%28m-p%29%5Cln%28b%29%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Cln%28b%29%3D%20%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%20%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20b%3De%5E%7B%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D)
From (1), we have:
![n=a\left(e^{m\frac{\ln\left( \frac{n}{q} \right)}{m-p}\right) \\ \\ \Rightarrow a= \frac{n}{\left(e^{m\frac{\ln\left( \frac{n}{q} \right)}{m-p}\right)}}](https://tex.z-dn.net/?f=n%3Da%5Cleft%28e%5E%7Bm%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%5Cright%29%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20a%3D%20%5Cfrac%7Bn%7D%7B%5Cleft%28e%5E%7Bm%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%5Cright%29%7D%7D)
Therefore, the equation of an exponential function given two points (m, n) and (p, q) is given by
![y=\frac{n}{\left(e^{m\frac{\ln\left( \frac{n}{q} \right)}{m-p}\right)}}\left(e^{\frac{\ln\left( \frac{n}{q} \right)}{m-p}\right)^x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bn%7D%7B%5Cleft%28e%5E%7Bm%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%5Cright%29%7D%7D%5Cleft%28e%5E%7B%5Cfrac%7B%5Cln%5Cleft%28%20%5Cfrac%7Bn%7D%7Bq%7D%20%5Cright%29%7D%7Bm-p%7D%5Cright%29%5Ex)
[i.e. you can choose any set of points and substitute the values in the equation above to get the exponential equation]
Answer:
A. (1, 0)
Reason:
When the first equation is graphed: y <u><</u> x + 1, the left side of the line is shaded and when the second equation is graphed: y <u><</u> x^2 -3x, the bottom is shaded.
The green section does not contain solutions. So D is automatically out.
The red section does not contain solutions as well. So C is automatically out.
For choice B, the point goes out of the shaded blue section, so that's out also.
As for choice A its in the blue shaded section, which makes that answer correct.
(when the two equations are within each other and combine a color, then whatever points is within the shaded part is the right answer)