Answer:
The total number of 50 cent coins in the bag = 36.
Step-by-step explanation:
Let x be the number of 50 cents coins and y be the number of $1 bills.
We have been given that the total amount of money in the bag is $36. We can represent this information as:
We are also told that there are twice as many 50 cents coins as $1 bills. We can represent this information as:
Now we will use substitution method to solve our given system of equations. Upon substituting equation (2) in equation (1) we will get,
Now let us substitute y=18 in equation (2) to find our x.
Therefore, there are 36 fifty cent coins in the bag.
Kory and Leanne will meet each other again after 36 minutes from starting i.e. at 10:36 am .
<u>Step-by-step explanation:</u>
Here we have , Leanne runs a lap in 12 minutes. Kory runs a lap in 9 minutes. We need to find out that If they both start running at 10 am, at what time will they both cross the start together again . Let's find out:
Kory runs a lap in 9 minutes and , Leanne in 12 minutes , in order to find at what time will they both cross the start together again we will find LCM of 9 & 12 :
⇒ 
⇒ 
So ,LCM of 9 & 12 is 36 .That means Kory and Leanne will meet each other again after 36 minutes from starting i.e. at 10:36 am .
In clear way , Kory will run race as :
1st lap = 9 minutes
2nd lap = 18 minutes
3rd lap = 27 minutes
4th lap = 36 minutes , i.e. at 10:36 am he'll complete his 4th lap
For , Leanne
1st lap = 12 minutes
2nd lap = 24 minutes
3rd lap = 36 minutes i.e. at 10:36 am he'll complete his 3rd lap .
This means Kory & Leanne will meet at 10:36 am completing there 4th and 3rd lap respectively .
Answer: n=8 cm
Step-by-step explanation:
You can solve this problem by applying the "Intersecting chords theorem". You must follow the proccedure below:
1. Let's represent each length, as below:
(P will be the point of intersection)
AP=4 cm
CP=6 cm
DP=3 cm
BP=n
2. Therefore, you have:
APxCP=BPxDP
APxCP=nxDP
3. Now, you must clear "n", as below:
n=APxCP/DP
4. When you substitute each value into n=APxCP/DP, you obtain:
n=(4 cm)(6 cm)/3 cm
n=24 cm²/3 cm
5. Finally, the result is:
n=8 cm