Answer:
4+(-6)+8+(-1)
Step-by-step explanation:
if she starts off at 4 points and her first turn she cuts 6 trees then you can add a negative 6 which is the same as subtracting that 6 when she plants 8 add those points then for her last turn add a negative 1 which is the same as subtracting 1 and she should end up with 5 points.
Answer:
18 : 3
Step-by-step explanation:
Basic proportionality question. All we need to here is to expression the given fractions (
, and
) as a fraction itself, and hence expressing the ratio we need to get, in fraction form.
- So, we have expressed this in a fraction, which we want to reduce
- The fractions have been taken as improper fractions
- Now we took the inverse fraction, through multiplication
- 35 and 35 cancel out, leaving us with the simplified fraction 18 / 3
_____
So now we have 18 / 3, the ratio in fraction form. The scale is thus 18 to 3, or in other words 18 : 3.
Hope that helps!
Answer:
See explanation
Step-by-step explanation:
Given
![A = (-1,1)](https://tex.z-dn.net/?f=A%20%3D%20%28-1%2C1%29)
![B = (3,3)](https://tex.z-dn.net/?f=B%20%20%3D%20%283%2C3%29)
![C =(4,-2)](https://tex.z-dn.net/?f=C%20%3D%284%2C-2%29)
Solving (a): ![P(0,0) \to Q(1,3)](https://tex.z-dn.net/?f=P%280%2C0%29%20%5Cto%20Q%281%2C3%29)
This means that:
![(x,y) \to (x+1,y+2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2B1%2Cy%2B2%29)
So, we have:
![A = (-1,1)](https://tex.z-dn.net/?f=A%20%3D%20%28-1%2C1%29)
![A' = (-1 + 1,1+2)](https://tex.z-dn.net/?f=A%27%20%3D%20%28-1%20%2B%201%2C1%2B2%29)
![A' = (0,3)](https://tex.z-dn.net/?f=A%27%20%3D%20%280%2C3%29)
![B = (3,3)](https://tex.z-dn.net/?f=B%20%20%3D%20%283%2C3%29)
![B'= (3 + 1,3+2)](https://tex.z-dn.net/?f=B%27%3D%20%283%20%2B%201%2C3%2B2%29)
![B'= (4,5)](https://tex.z-dn.net/?f=B%27%3D%20%284%2C5%29)
![C =(4,-2)](https://tex.z-dn.net/?f=C%20%3D%284%2C-2%29)
![C' = (4+1,-2+1)](https://tex.z-dn.net/?f=C%27%20%3D%20%284%2B1%2C-2%2B1%29)
![C' = (5,-1)](https://tex.z-dn.net/?f=C%27%20%3D%20%285%2C-1%29)
Solving (b): ![P(0,-1) \to Q(4,-2)](https://tex.z-dn.net/?f=P%280%2C-1%29%20%5Cto%20Q%284%2C-2%29)
This means that:
![(x,y) \to (x+4,y-1)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2B4%2Cy-1%29)
So, we have:
![A = (-1,1)](https://tex.z-dn.net/?f=A%20%3D%20%28-1%2C1%29)
![A' = (-1+4,1-1)](https://tex.z-dn.net/?f=A%27%20%3D%20%28-1%2B4%2C1-1%29)
![A' = (3,0)](https://tex.z-dn.net/?f=A%27%20%3D%20%283%2C0%29)
![B = (3,3)](https://tex.z-dn.net/?f=B%20%20%3D%20%283%2C3%29)
![B'= (3+4,3-1)](https://tex.z-dn.net/?f=B%27%3D%20%283%2B4%2C3-1%29)
![B'= (7,2)](https://tex.z-dn.net/?f=B%27%3D%20%287%2C2%29)
![C =(4,-2)](https://tex.z-dn.net/?f=C%20%3D%284%2C-2%29)
![C' = (4+4,-2-1)](https://tex.z-dn.net/?f=C%27%20%3D%20%284%2B4%2C-2-1%29)
![C' = (8,-3)](https://tex.z-dn.net/?f=C%27%20%3D%20%288%2C-3%29)
Solving (c): ![P(-1,-2) \to Q(-2,-2)](https://tex.z-dn.net/?f=P%28-1%2C-2%29%20%5Cto%20Q%28-2%2C-2%29)
This means that:
![(x,y) \to (x-1,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x-1%2Cy%29)
So, we have:
![A = (-1,1)](https://tex.z-dn.net/?f=A%20%3D%20%28-1%2C1%29)
![A' = (-1-1,1)](https://tex.z-dn.net/?f=A%27%20%3D%20%28-1-1%2C1%29)
![A' = (-2,1)](https://tex.z-dn.net/?f=A%27%20%3D%20%28-2%2C1%29)
![B = (3,3)](https://tex.z-dn.net/?f=B%20%20%3D%20%283%2C3%29)
![B'= (3-1,3)](https://tex.z-dn.net/?f=B%27%3D%20%283-1%2C3%29)
![B'= (2,3)](https://tex.z-dn.net/?f=B%27%3D%20%282%2C3%29)
![C =(4,-2)](https://tex.z-dn.net/?f=C%20%3D%284%2C-2%29)
![C'= (4-1,-2)](https://tex.z-dn.net/?f=C%27%3D%20%284-1%2C-2%29)
![C'= (3,-2)](https://tex.z-dn.net/?f=C%27%3D%20%283%2C-2%29)
![x = 47](https://tex.z-dn.net/?f=x%20%3D%2047)
Step-by-step explanation:
The 3rd interior angle of the triangle can be written as
![\angle{3} = 180 - 45 - x = 135 - x](https://tex.z-dn.net/?f=%5Cangle%7B3%7D%20%3D%20180%20-%2045%20-%20x%20%3D%20135%20-%20x)
The angle above is supplementary to the angle (2x - 2), therefore
![(135 - x) + (2x - 2) = 180 \Rightarrow 133 + x = 180](https://tex.z-dn.net/?f=%28135%20-%20x%29%20%2B%20%282x%20-%202%29%20%3D%20180%20%5CRightarrow%20133%20%2B%20x%20%3D%20180)
Solving for x, we get
![x = 47](https://tex.z-dn.net/?f=x%20%3D%2047)
Answer:
D ) 11 x² + 11 x - 6 .. .. ... ... ... .
. . . . . . . . .