Answer: width = 300
<u>Step-by-step explanation:</u>
Area (A) = Length (L) x width (w)
Given: A = 268,500
L = 3w - 5
w = w
268,500 = (3w - 5) x (w)
268,500 = 3w² - 5w
0 = 3w² - 5w - 268,500
0 = (3w + 895) (w - 300)
0 = 3w + 895 0 = w - 300
-985/3 = w 300 = w
Since width cannot be negative, disregard w = -985/3
So the only valid answer is: w = 300
For this case we must follow the steps below:
step 1:
We place each of the given points on a coordinate axis
Step 2:
We join the AC points (represented by the orange line)
We join the BD points (represented by the blue line)
It is observed that the resulting figure after placing the 4 points on a coordinate axis, turns out to be a rhombus.
In addition, the blue and orange lines turn out to be perpendicular, that is, they have an angle of 90 degrees between them. This can be verified by finding the slopes of each of the two straight lines (blue and orange), which must be opposite reciprocal, that is, they comply:
In this case, the slope of the orange line is and that of the blue line is
Then , it is verified that they are perpendicular.
Thus, the conclusion is that ABCD is a rhombus and AC is perpendicular to BD.
Answer:
See attached image
Option D
Answer:
3.90 meters.
Step-by-step explanation:
Since Amy needs ribbon for her art project, and she plans to buy 3.84 meters of that material, but the store only sells said product by the tenth of a meter, in order to get closer to the desired size she will have to buy 39 pieces of 10 cm (one tenth of a meter), that is, she must buy 3.90 meters, of which there will be 6 centimeters of the product left over.
Answer:
Answer is 12
Step-by-step explanation:
f(g(-2))
=f((-2)^2+2)
=f(6)
=-1/2×6^2+5×6
=12
<u>First Train:</u>
Time taken = 9 hours (2pm to 11pm)
Let the speed be x
Distance = Time x Speed = 9x
<u>Second Train:</u>
Time taken = 5 hours (6pm to 11pm)
Speed = x + 48
Distance = Time x Speed = 5(x + 48)
Since both the distance they traveled are the same, we equate the distance to solve for x.
<u>Solve for x:</u>
9x = 5(x + 48)
9x = 5x + 240
4x = 240
x = 60
<u>Find the speed:</u>
x = 60 mph
x + 48= 108 mph
Answer: The spend of the two trains are 60 mph and 108 mph.