Answer:
1
Step-by-step explanation:
Three side lengths that meet the requirements of the triangle inequality will form exactly one triangle.
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The triangle inequality requires the sum of the short sides be at least as long as the long side. Here, we have 3 + 4.69 = 7.69 > 7, so we satisfy the triangle inequality.
The side lengths can be arranged in clockwise or counterclockwise order, least to greatest. Each triangle is a reflection of the other, so they are considered to be the same triangle (congruent).
To get it into standard you need to simplify
6y - 12 = -3x add 12 to both sides
6y = -3x + 12 add 3x to both sides
3x + 6y = 12
And that is in standard which is A + B = C
You want to find values of v (number of visors sold) and c (number of caps sold) that satisfy the equation
... 3v + 7c = 4480
In intercept form, this equation is
... v/(1493 1/3) + c/640 = 1 . . . . . divide by 4480
Among other things, this tells us one solution is
... (v, c) = (0, 640)
The least common multiple of 3 and 7 is 21, so decreasing the number of caps sold by some multiple of 3 and increasing the number of visors sold by that same multiple of 7 will result in another possible solution.
The largest multiple of 21 that is less than 4480 is 213. Another possible solution is (0 +213·7, 640 -213·3) = (1491, 1)
We can also pick some number in between, say using 100 as the multiple
... (0 +100·7, 640 -100·3) = (700, 340)
In summary, your three solutions could be
... (visors, caps) = (0, 640), (700, 340), (1491, 1)
9514 1404 393
Answer:
Step-by-step explanation:
The speed against the wind is ...
4680 mi/(8 h) = 585 mi/h
The speed with the wind is ...
5720 mi/(8 h) = 715 mi/h
The speed of the airplane in still air is the average of these speeds:
(585 +715)/2 = 650 mi/h . . . speed in still air
The speed of the wind is the difference between the airplane speed and the speed in the wind:
715 -650 = 65 mi/h . . . speed of the wind
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<em>Additional comment</em>
If p and 'a' represent the speeds of the plane and the air, the speeds with and against the wind are ...
p + a = with
p - a = against
If we average these, we get ...
((p +a) +(p -a))/2 = (with + against)/2
p = (with + against)/2 . . . . . . . the formula we used above
