well, the assumption is that is a rectangle, namely it has two equal pairs, so we can just find the length of one of the pairs to get the dimensions.
hmmmm let's say let's get the length of the segment at (-1,-3), (1,3) for its length
and
the length of the segment at (-1, -3), (-4, -2) for its width
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{length}{L}=\sqrt{[1-(-1)]^2+[3-(-3)]^2}\implies L=\sqrt{(1+1)^2+(3+3)^2} \\\\\\ L=\sqrt{4+36}\implies L=\sqrt{40} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20%28%5Cstackrel%7Bx_1%7D%7B-1%7D~%2C~%5Cstackrel%7By_1%7D%7B-3%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B1%7D~%2C~%5Cstackrel%7By_2%7D%7B3%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Blength%7D%7BL%7D%3D%5Csqrt%7B%5B1-%28-1%29%5D%5E2%2B%5B3-%28-3%29%5D%5E2%7D%5Cimplies%20L%3D%5Csqrt%7B%281%2B1%29%5E2%2B%283%2B3%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20L%3D%5Csqrt%7B4%2B36%7D%5Cimplies%20L%3D%5Csqrt%7B40%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{width}{w}=\sqrt{[-4-(-1)]^2+[-2-(-3)]^2}\implies w=\sqrt{(-4+1)^2+(-2+3)^2} \\\\\\ w=\sqrt{9+1}\implies w=\sqrt{10} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{A=Lw}\implies \sqrt{40}\cdot \sqrt{10}\implies \sqrt{400}\implies \boxed{20}](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B-1%7D~%2C~%5Cstackrel%7By_1%7D%7B-3%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B-4%7D~%2C~%5Cstackrel%7By_2%7D%7B-2%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Bwidth%7D%7Bw%7D%3D%5Csqrt%7B%5B-4-%28-1%29%5D%5E2%2B%5B-2-%28-3%29%5D%5E2%7D%5Cimplies%20w%3D%5Csqrt%7B%28-4%2B1%29%5E2%2B%28-2%2B3%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20w%3D%5Csqrt%7B9%2B1%7D%5Cimplies%20w%3D%5Csqrt%7B10%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20rectangle%7D%7D%7BA%3DLw%7D%5Cimplies%20%5Csqrt%7B40%7D%5Ccdot%20%5Csqrt%7B10%7D%5Cimplies%20%5Csqrt%7B400%7D%5Cimplies%20%5Cboxed%7B20%7D)
If you divide the original equation by "a", you have your answer.
30/a = (a*60)/a = 60*(a/a)
30/a = 60
65 percent as a fraction is 65/100 as a decimal is 0.65
Answer:
The length of the first piece = 41 cm
Step-by-step explanation:
Let the length of the first piece = a
Let the length of the second piece = b
Let the length of the third piece = c
we are given the following:
b = 3a . . . . . (1) (The 2nd piece is 3 times as long as the 1st piece)
c = 6 + a . . . . (2) (the 3rd piece is 6 centimeters longer than the 1st piece)
a + b + c = 211 . . . . . (3) ( the yarn has a total length of 211 centimeters)
Next, let us eliminate two variables, and this can easily be done by substituting the values of b and c in equations 1 and 2 into equation 3. this is done as follows:
a + b + c = 211
a + (3a) + (6 + a) = 211 ( remember that b = 3a; c = 6 + a)
a + 3a + 6 + a = 211
5a + 6 = 211
5a = 211 - 6 = 205
5a = 205
∴ a = 205 ÷ 5 = 41 cm
a = 41 cm
Therefore the length of the first piece (a) = 41 cm
now finding b and c
substituting a into equation 1 and 2
b = 3a
b = 3 × 41 = 123
∴ b = 123 cm
c = 6 + a
c = 6 + 41 = 47
∴ c = 47 cm
Answer:
55
Step-by-step explanation:
difference=8-5=3
if difference is 3 Cole bends=5 times
if difference is 33 Cole bends=(5/3)×33=55 times
