Answer:
27 miles.
Step-by-step explanation:
Here I attach the draw of the coordinates.
Tony traveled 3 segments. The first was from (12,6) to (12, 15), where, leting 12 constant, he moved from 6 to 15 in the ordinates axis, which implies 9 units. This is the section 1 in the draw.
Then he moved from point B to C. If you notice, this distance is the hypotenuse on the the triangle DBC. We can find this value using Pitagoras' theorem:
DB^2 + CD^2 = CB^2
With DB=15 and CD=8 (12 minus 4 = 8)
15^2 + 8^2 = 289
So CB^2=289
Applying sqr root:
CB = 17
So, the second section has a measure of 17 units.
Finally, the 3rd section is the hypotenuse of the DAC triangle and we can use Pitagoras to solve it:
CD^2 + AD^2 = CA^2
8^2 + 6^2 = CA^2
64 + 36 = 100
So, CA=10
In the 3r section we traveled 10 units.
So, in total he traveled 10 + 17 + 9 = 36 units
As every unit is 0.75 miles he traveled 36*0.75 miles:
36*0.75 = 27 miles
He traveled in total 27 miles!!
43.99 times 7% in decimal form which is 0.07 then it equals 3.0793 and if you want how much it would coat then you add 3.0793 and 43.99 I hope that helped
First let's find the angles a and b.
We have then:
sin a = 4/5
a = Asin (4/5)
a = 53.13 degrees.
cos b = 5/13
b = Acos5 / 13
b = 67.38 degrees.
We now calculate cos (a + b). To do this, we replace the previously found values:
cos ((53.13) + (67.38)) = - 0.507688738
Answer:
-0.507688738
Note: there is another way to solve the problem using trigonometric identities.
Answer: 4 ties or draws
8 wins, 4 ties, 20 losses
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Explanation:
The ratio 2:1:5 is of the format wins:ties:losses where getting a draw is the same as getting a tie.
So one possibility is that they won 2 matches, tied once, and lost 5 matches. The only problem is that it doesn't fit with the statement that "The team lost 12 more matches than they won."
We could guess-and-check our way to the answer, but I think using algebra is the most efficient route.
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Let x = number of ties
2x = number of wins and 5x = number of losses
Note the ratio 2x:x:5x reduces to 2:1:5 after dividing everything by x.
Since the team lost 12 more matches than they won, this means,
loss count = (win count) + 12
5x = (2x) + 12
5x-2x = 12
3x = 12
x = 12/3
x = 4
The team tied 4 times and has 2x = 2*4 = 8 wins and 5x = 5*4 = 20 losses.
The ratio 8:4:20 reduces to 2:1:5 when you divide all parts by the GCF 4.
Also, the gap between 8 wins and 20 losses is 20-8 = 12 to help fully confirm we have the correct answer.
