Answer:
9.45
Step-by-step explanation:
2.70*3 = 8.10
8.10 + 1.35= 9.45
<span>1)A ray has one endpoint and extends indefinitely in one direction.
2)A pair of opposite rays are two rays that have the same endpoint and extend in opposite directions.
<span>3)Rays are always named with two points and the first point in the name must be the endpoint.</span></span>
A) sum 3 + 7 =10
b) divide <span> £</span>300 ÷ 10 = <span> £</span>30
c) multiply:
3 x 30 = <span> £</span>90
7 x 30 = <span> £</span>210
Values are: £90 and <span> £210</span>
<h3>Answer:</h3>
The Slope is ![2](https://tex.z-dn.net/?f=2)
<h2>Explanation:</h2>
Notice that both the points,
and
, are on the line. So we can use those points to calculate the slope. Recall that that slope of the line
can be calculated by
if we have the points,
and
.
<h3>Calculating for the slope of the line:</h3>
Given:
![(60,0)](https://tex.z-dn.net/?f=%2860%2C0%29)
![(70,20)](https://tex.z-dn.net/?f=%2870%2C20%29)
![m = \frac{20 -0}{70 -60} \\ m = \frac{20}{10} \\ m = 2](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B20%20-0%7D%7B70%20-60%7D%20%5C%5C%20m%20%3D%20%5Cfrac%7B20%7D%7B10%7D%20%5C%5C%20m%20%3D%202)
The slope of the tangent line to
at
is given by the derivative of
at that point:
![f'(-1)=\displaystyle\lim_{x\to-1}\frac{f(x)-f(-1)}{x-(-1)}=\lim_{x\to-1}\frac{2x^2-2}{x+1}](https://tex.z-dn.net/?f=f%27%28-1%29%3D%5Cdisplaystyle%5Clim_%7Bx%5Cto-1%7D%5Cfrac%7Bf%28x%29-f%28-1%29%7D%7Bx-%28-1%29%7D%3D%5Clim_%7Bx%5Cto-1%7D%5Cfrac%7B2x%5E2-2%7D%7Bx%2B1%7D)
Factorize the numerator:
![2x^2-2=2(x^2-1)=2(x-1)(x+1)](https://tex.z-dn.net/?f=2x%5E2-2%3D2%28x%5E2-1%29%3D2%28x-1%29%28x%2B1%29)
We have
approaching -1; in particular, this means
, so that
![\dfrac{2x^2-2}{x+1}=\dfrac{2(x-1)(x+1)}{x+1}=2(x-1)](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%5E2-2%7D%7Bx%2B1%7D%3D%5Cdfrac%7B2%28x-1%29%28x%2B1%29%7D%7Bx%2B1%7D%3D2%28x-1%29)
Then
![f'(-1)=\displaystyle\lim_{x\to-1}\frac{2x^2-2}{x+1}=\lim_{x\to-1}2(x-1)=2(-1-1)=-4](https://tex.z-dn.net/?f=f%27%28-1%29%3D%5Cdisplaystyle%5Clim_%7Bx%5Cto-1%7D%5Cfrac%7B2x%5E2-2%7D%7Bx%2B1%7D%3D%5Clim_%7Bx%5Cto-1%7D2%28x-1%29%3D2%28-1-1%29%3D-4)
and the tangent line's equation is
![y-f(-1)=f'(-1)(x-(-1))\implies y-4x-2](https://tex.z-dn.net/?f=y-f%28-1%29%3Df%27%28-1%29%28x-%28-1%29%29%5Cimplies%20y-4x-2)