Answer:
![-37\leq x\:](https://tex.z-dn.net/?f=-37%5Cleq%20x%5C%3A%3C19)
Step-by-step explanation:
To find the values of
for which, the value of
belongs to
,we solve the inequality;
![-2\:](https://tex.z-dn.net/?f=-2%5C%3A%3C%5Cfrac%7B3-x%7D%7B8%7D%5Cleq%205)
We multiply through by 8 to obtain;
![-16\:](https://tex.z-dn.net/?f=-16%5C%3A%3C3-x%5Cleq%2040)
We subtract 3 to get
![-19\:](https://tex.z-dn.net/?f=-19%5C%3A%3C-x%5Cleq%2037)
Divide through by -1 to obtain;
![19\:>x\ge-37](https://tex.z-dn.net/?f=19%5C%3A%3Ex%5Cge-37)
Or
![-37\leq x\:](https://tex.z-dn.net/?f=-37%5Cleq%20x%5C%3A%3C19)
Answer:mmmmmmmso;/mvsklllllllllllllllnvslxlnxnmlkx.vmkmd
Step-by-step explanation:nmkl iscvcjniknikosvnjivmvms cfdujnncsbnosnojsvnoj dvjnsvnjvnklvsnkl
Answer: Options 1, 3, 5
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals, so since the slope of the given line is 1/3, we need to find lines with a slope of -3.
- Option 1 has a slope of -3.
- Option 2 has a slope of 3.
- Option 3 has a slope of -3.
- Option 4 has a slope of 1/3.
- If we subtract 3x from both sides, we get y=-3x+7, so option 5 has a slope of -3.
Answer:
(a) See attachment for tree diagram
(b) 24 possible outcomes
Step-by-step explanation:
Given
![Urn\ 1 = \{B_1, R_1, R_2, R_3\}](https://tex.z-dn.net/?f=Urn%5C%201%20%3D%20%5C%7BB_1%2C%20R_1%2C%20R_2%2C%20R_3%5C%7D)
![Urn\ 2 = \{R_4, R_5, B_2, B_3\}](https://tex.z-dn.net/?f=Urn%5C%202%20%3D%20%5C%7BR_4%2C%20R_5%2C%20B_2%2C%20B_3%5C%7D)
Solving (a): A possibility tree
If urn 1 is selected, the following selection exists:
![B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]](https://tex.z-dn.net/?f=B_1%20%5Cto%20%5BR_1%2C%20R_2%2C%20R_3%5D%3B%20R_1%20%5Cto%20%5BB_1%2C%20R_2%2C%20R_3%5D%3B%20R_2%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_3%5D%3B%20R_3%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_2%5D)
If urn 2 is selected, the following selection exists:
![B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]](https://tex.z-dn.net/?f=B_2%20%5Cto%20%5BB_3%2C%20R_4%2C%20R_5%5D%3B%20B_3%20%5Cto%20%5BB_2%2C%20R_4%2C%20R_5%5D%3B%20R_4%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_5%5D%3B%20R_5%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_4%5D)
<em>See attachment for possibility tree</em>
Solving (b): The total number of outcome
<u>For urn 1</u>
There are 4 balls in urn 1
![n = \{B_1,R_1,R_2,R_3\}](https://tex.z-dn.net/?f=n%20%3D%20%5C%7BB_1%2CR_1%2CR_2%2CR_3%5C%7D)
Each of the balls has 3 subsets. i.e.
![B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]](https://tex.z-dn.net/?f=B_1%20%5Cto%20%5BR_1%2C%20R_2%2C%20R_3%5D%3B%20R_1%20%5Cto%20%5BB_1%2C%20R_2%2C%20R_3%5D%3B%20R_2%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_3%5D%3B%20R_3%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_2%5D)
So, the selection is:
![Urn\ 1 = 4 * 3](https://tex.z-dn.net/?f=Urn%5C%201%20%3D%204%20%2A%203)
![Urn\ 1 = 12](https://tex.z-dn.net/?f=Urn%5C%201%20%3D%2012)
<u>For urn 2</u>
There are 4 balls in urn 2
![n = \{B_2,B_3,R_4,R_5\}](https://tex.z-dn.net/?f=n%20%3D%20%5C%7BB_2%2CB_3%2CR_4%2CR_5%5C%7D)
Each of the balls has 3 subsets. i.e.
![B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]](https://tex.z-dn.net/?f=B_2%20%5Cto%20%5BB_3%2C%20R_4%2C%20R_5%5D%3B%20B_3%20%5Cto%20%5BB_2%2C%20R_4%2C%20R_5%5D%3B%20R_4%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_5%5D%3B%20R_5%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_4%5D)
So, the selection is:
![Urn\ 2 = 4 * 3](https://tex.z-dn.net/?f=Urn%5C%202%20%3D%204%20%2A%203)
![Urn\ 2 = 12](https://tex.z-dn.net/?f=Urn%5C%202%20%3D%2012)
Total number of outcomes is:
![Total = Urn\ 1 + Urn\ 2](https://tex.z-dn.net/?f=Total%20%3D%20Urn%5C%201%20%2B%20Urn%5C%202)
![Total = 12 + 12](https://tex.z-dn.net/?f=Total%20%3D%2012%20%2B%2012)
![Total = 24](https://tex.z-dn.net/?f=Total%20%3D%2024)
Answer: the perimeter is 214. AB's half is 32.5 and BC's whole is 65
Step-by-step explanation: 10x-5 and 12x-26 are equal, as shown by the marks on their lines, so we can set them equal to each other to solve for x. when solved x=7. then plug 7 into each equation to get 65. lastly add up 84+65+65 to get 214.