It only works if C is the midpoint of AB
Answer:
(a) 144
(b) 117
(c) 360
(d) 588
(e) 5472
Step-by-step explanation:
To find the LCM of two numbers, first find the prime factorization of each number. Then the LCM is the product of common and not common factors with the larger exponent.
2.
(a)
![72 = 2^3 \times 3^2](https://tex.z-dn.net/?f=72%20%3D%202%5E3%20%5Ctimes%203%5E2)
![144 = 2^4 \times 3^2](https://tex.z-dn.net/?f=144%20%3D%202%5E4%20%5Ctimes%203%5E2)
![LCM = 2^4 \times 3^2 = 8 \times 9 = 144](https://tex.z-dn.net/?f=LCM%20%3D%202%5E4%20%5Ctimes%203%5E2%20%3D%208%20%5Ctimes%209%20%3D%20144)
(b)
![39 = 3 \times 13](https://tex.z-dn.net/?f=39%20%3D%203%20%5Ctimes%2013)
![117 = 3^2 \times 13](https://tex.z-dn.net/?f=117%20%3D%203%5E2%20%5Ctimes%2013)
![LCM = 3^2 \times 13 = 117](https://tex.z-dn.net/?f=LCM%20%3D%203%5E2%20%5Ctimes%2013%20%3D%20117)
(c)
![72 = 2^3 \times 3^2](https://tex.z-dn.net/?f=72%20%3D%202%5E3%20%5Ctimes%203%5E2)
![90 = 2 \times 3^2 \times 5](https://tex.z-dn.net/?f=90%20%3D%202%20%5Ctimes%203%5E2%20%5Ctimes%205)
![LCM = 2^3 \times 3^2 \times 5 = 360](https://tex.z-dn.net/?f=LCM%20%3D%202%5E3%20%5Ctimes%203%5E2%20%5Ctimes%205%20%3D%20360)
(d)
![84 = 2^2 \times 3 \times 7](https://tex.z-dn.net/?f=84%20%3D%202%5E2%20%5Ctimes%203%20%5Ctimes%207)
![147 = 3 \times 7^2](https://tex.z-dn.net/?f=147%20%3D%203%20%5Ctimes%207%5E2)
![LCM = 2^2 \times 3 \times 7^2 = 588](https://tex.z-dn.net/?f=LCM%20%3D%202%5E2%20%5Ctimes%203%20%5Ctimes%207%5E2%20%3D%20588)
(e)
![152 = 2^3 \times 19](https://tex.z-dn.net/?f=152%20%3D%202%5E3%20%5Ctimes%2019)
![288 = 2^5 \times 3^2](https://tex.z-dn.net/?f=288%20%3D%202%5E5%20%5Ctimes%203%5E2)
![LCM = 2^5 \times 3^2 \times 19 = 5472](https://tex.z-dn.net/?f=LCM%20%3D%202%5E5%20%5Ctimes%203%5E2%20%5Ctimes%2019%20%3D%205472)
If we put it into an equation, and x was blue markers, we could say:
7x + x = 32
Then you'd simplify:
8x = 32
Then solve:
8x = 32
÷ 8
x = 4.
So now we know that there are 4 blue markers, we can multiply 4 by 7 to get the amount of red markers, which is 28. Hope this helps!
Answer:
41.4 km per week (rounded)
also:
haha mother joke