Let
x be the distance that the truck has left to travel
t be the the time
The total distance is 1675 miles
The average speed is 55 miles per hour
The equation that represents the distance that the truck has left to travel with respect to time is
55t + x =1675
x = -55t + 1675
Answer: In order to begin figuring that out, we need to know how both of their plans work.
Answer: (-4, -1)
Step-by-step explanation:
Starting at point (-4, -2) and translating 3 units up means we add 3 to -2.
So the new point is now (-4, 1).
Now we reflect over the x-axis which means the y-value of 1 becomes negative.
So the final point is (-4, -1)
Part (A)
We have n = 5 sides, so the measure of any exterior angle of a regular pentagon is E = 360/n = 360/5 = 72
Each interior angle is therefore 180-E = 180-72 = 108 degrees.
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Alternatively, you could use the formula below with n = 5
i = interior angle
i = 180(n-2)/n
i = 180(5-2)/5
i = 180(3)/5
i = 540/5
i = 108
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<h3>Answer: 108 degrees</h3>
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Part (B)
We're told that CDF is 70 degrees. From part (A) we know that angle CDE is 108 degrees, so this must mean that angle EDF is 108-70 = 38 degrees.
Similarly, angle FEA is 85 degrees, which subtracts from angle AED to get 108 - 85 = 23 degrees. This is the measure of angle DEF.
So far we found
angle EDF = 38
angle DEF = 23
Let's call these x and y for shorthand. Let z be the missing third angle of triangle DFE.
So,
x+y+z = 180
38+23+z = 180
61+z = 180
x = 180-61
x = 119
Interior angle DFE is 119 degrees.
Note how 90 < x < 180 showing we have an obtuse angle. It is not a reflex angle because the statement 180 < x < 360 is false.
So we subtract the value of x from 360
360-x = 360-119 = 241
This is the reflex angle DFE
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<h3>Answer: 241 degrees</h3>
W is in the lower left corner located at (-1,-2)
W' is in the upper left corner located at (-2,1)
Notice that the original Y value (-2) became the new X value (-2) and the original X value (-1) is the inverse of the new Y value (1).
If you look at the coordinates of the other two pints you would see it was the same transformation.
When the X and Y coordinates switch like this, it is a 90 degree clockwise rotation around the origin.
