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VikaD [51]
3 years ago
5

(Geometry) The answers are x = 15 and y = 9 but I don't know how. Help me understand this

Mathematics
1 answer:
Kryger [21]3 years ago
4 0

Check the picture below.

\bf \stackrel{\measuredangle DAC}{4y+2x}~~=~~\stackrel{\measuredangle BCA}{9y-x}\implies 2x=5y-x\implies 3x=5y\implies \boxed{x=\cfrac{5y}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle DAB}{[(4y+2x)+35]}~~+~~\stackrel{\measuredangle ADC}{5x+4}~~=~~180\implies 4y+2x+5x+39 = 180 \\\\\\ 4y+7x+39=180\implies 4y+7x=141\implies \stackrel{\textit{substituting "x"}}{4y+7\left( \boxed{\cfrac{5y}{3}} \right)} = 141

\bf 4y+\cfrac{35y}{3}=141\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( 4y+\cfrac{35y}{3} \right)=3(141)}\implies 12y+35y=423 \\\\\\ 47y=423\implies y=\cfrac{423}{47}\implies \blacktriangleright y = 9 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{x=\cfrac{5y}{3}}\implies x = \cfrac{5(9)}{3}\implies \blacktriangleright x = 15 \blacktriangleleft

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two bike riders ride around in a circular path. The first rider completes one round in 15 minutes and the second rider completes
katrin2010 [14]

Answer:

Rider 1 does one round in 15 min, and will complete another in each consecutive multiple of 15 min

Rider 2 does one round in 18 min, and will complete another in each consecutive multiple of 18 min

Assuming that they start together, they will complete another round together in a time that is both multiples of 15min and 18 min.

Then we need to find the smallest common multiple between 15 and 18.

To smallest common multiple between two numbers, a and b, is equal to:

a*b/(greatest common factor between a and b).

Now, the greatest common factor between 15 and 18 can be found if we write those numbers as a product of prime numbers, such as:

15 = 3*5

18 = 2*3*3

The greatest common factor is 3.

Then the smallest common multiple will be:

(15*18)/3 = 90

This means that after 90 mins, they will meet again at the starting place.

3 0
3 years ago
the location on point k is shown on the number line below. what fraction is represented by the location of point k
Xelga [282]
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Hope this helped☺☺
7 0
3 years ago
Read 2 more answers
Need help ASAP! What is this
ikadub [295]

180 - 64= 116

116 divided by 4 = 29

x=29

Have a good day:>

8 0
3 years ago
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a car moves with the speed of 40 km/h for 15 minutes and then with a speed of 60 km/h for the next 5 minutes find the total dist
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Answer: 8

Step-by-step explanation:

Umm idk

4 0
3 years ago
How do I solve this?
Anni [7]
I hope this helps you




4^3/3.x^2/3.y^3/3


4.y.x^2/3
3 0
3 years ago
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