It looks like it goes through (0,-3) and (1,2), so the gradient is (change in y)/(change in x) ->
(-3-2)/(0-1) = 5
So y=5x+b
Then as we know it passes the y axis at (0,-3) so b= -3
So we have y=5x-3
You can always draw a right-angled triangle where the sloped side c is the line between the two points of interest, and a and b are the sizes of the horizontal and vertical lines.
Then apply c = √(a²+b²)
Answer:
h = 3.62
Step-by-step explanation:
First, as both triangles have the same angles we can use the relationship of areas and sides corresponding to similar triangles as follows:
Now we know that the new triangle has sides of 4.18. Then, as these triangles are equilateral we can use the Pythagorean Theorem to find the height:
Finally the height of this new triangle is 3.62 cm
Answer:
745.5
Step-by-step explanation:
To answer this question we need to find the perimeter and multiply it by three. To do that we can start by adding 85 yards plus 85 yards for both sides of the rectangle which equals 170. Then we need to add the circumference of the semicircles. To do that we can use the formula C = 2(3.14)r. for that we need to find the radius which is the diameter divided by 2 which is 12.5. Then we can plug that into the formula to get C=(2)(3.14)(12.5). After solving that we get 78.5 which we can add to 170 to get the perimeter which is 248.5 . However we are NOT done since jasmine is running 3 laps we need to multiply 248.5 by 3 to get an answer of 745.5.
keeping in mind that any line parallel to MN will have the same exact slope as MN's.
![\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-6}{4-2}\implies \cfrac{-6}{2}\implies \cfrac{-3}{1}\implies -3~~\checkmark \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B6%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B4%7D~%2C~%5Cstackrel%7By_2%7D%7B0%7D%29%20%5C%5C%5C%5C%5C%5C%20slope%20%3D%20m%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B0-6%7D%7B4-2%7D%5Cimplies%20%5Ccfrac%7B-6%7D%7B2%7D%5Cimplies%20%5Ccfrac%7B-3%7D%7B1%7D%5Cimplies%20-3~~%5Ccheckmark%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
