Perimeter = 2(L + W)
2(L + 10) = 50
2L + 20 = 50
2L = 30, L = 15
Solution: the length is 15 inches
Answer:
A
Step-by-step explanation:
Deshaun charges $40 per hour.
So if Deshaun and Silvio work for 5 hours, then it would be $40(5) which would be more expensive than Silvio's with $60 + 20(5). Silvio gets $60 with $20 per hour.
Deshaun would get $200 while Silvio would get $160.
Let's break this down into what each piece is.
One flat= one whole= 1
One rod= one tenth= 0.1
One unit= one hundredth= 0.01
a) We have 1 flat, 3 rods, and 7 units. Using what we know, we have 1 whole, 3 tenths, and 7 hundredths. So, this is 1 + 0.3+ 0.07. This equals 1.37.
b) 1 flat, 37 units. This is 1 whole, and 37 hundredths. When there are two digits that you want to put in the hundredths place, put the digit furthest to the right in the hundredths place (excluding decimals) and place the rest of the number to the left accordingly. So for us, 37 hundredths would be .37, not .037. Add up 1 and .37, and we have 1.37.
c) 13 rods, 7 units. This is like the last problem. We have two digits wanted to go in the tenths place, but that isn't possible. So, we take the digit all the way to the right and put it in the tenths place (3). Now, we take out remaining digits (1), and put it in the next space to the left. Our rods= 1.3. Now for our units. We have 7, so that equals 0.07. Add it together, and now we have 1.37.
All of the problems equal 1.37. This shows how many ways a number can be represented.
Hope this helped! If it's still confusing, feel free to comment. have a nice day!
Answer:
f = 7.5h
Step-by-step explanation:
The graph is a straight line through the origin, so represents a proportional relation. For some value of k, you have ...
f = k×h
The constant of proportionality can be found from any of the points on the graph. I generally find it convenient to use points where the line crosses a grid intersection. (h, f) = (2, 15) is one such point.
k = f/h = 15/2 = 7.5
Your equation is ...
f = 7.5h
<span>28.4 miles.
This problem effectively creates a triangle with the data you're giving being SAS (side, angle, side) and then asks you for the length of the 3rd side. So let's first determine the sides and angle of the triangle.
1st side, the ship leaves at 1 pm and travels for 4 - 1 = 3 hours at 12 mph. So the length of the side is 12 * 3 = 36 miles.
2nd side, the ship leaves at 2 pm and travels for 4-2 = 2 hours at 15 mph. So the length of the side is 15 * 2 = 30 miles
The included angle. The key thing to realize is that the angle isn't either of the ship headings. It's the difference between the headings. So we have one ship with a heading of 70 degrees and the other ship with a heading of 120 degrees. So there's a difference of 120 - 70 = 50 degrees between the two ships.
So we have
side 1 = 36 miles, side 2 = 30 miles, included angle = 50 degrees.
Since we we only know the lengths of the adjacent sides to the known angle, we should use the law of cosines to solve for the unknown side (if we had a known angle and knew the length of the opposite side to the angle, we would use the law of sines).
The law of cosines is:
c^2 = a^2 + b^2 - 2ab cos θ
where
a,b = adjacent sides to known angle
c = side opposite to known angle
θ = known angle
Let's substitute the known values and calculate
c^2 = a^2 + b^2 - 2ab cos θ
c^2 = 36^2 + 30^2 - 2*36*30 cos 50
c^2 = 1296 + 900 - 2160*0.64278761
c^2 = 1296 + 900 - 1388.421237
c^2 = 807.5787631
c = 28.41793031
So at 4 pm, the distance between the ships is 28.4 miles.</span>
