Answer:
Step-by-step explanation:
Let t represent the time it took Emanuel to drive home from college. If the total round trip took 11 hours, it means that the time it took
Emanuel to drive from home back to college would be (11 - t) hours.
Emanuel drove home from college traveling an average speed of 70 mph.
Distance = speed × time
Distance covered by driving from college to home is
70 × t = 70t
He drove back to the college the following week at an average speed of 62.7 mph.
Distance covered by driving back to college from home is
62.7(11 - t) = 689.7 - 62.7t
Since the distance travelled is the same, then
689.7 - 62.7t = 70t
70t + 62.7 = 689.7
132.7t = 689.7
t = 689.7/132.7
t = 5.19 hours.
Therefore, the time that it took Emanuel to drive from home back to college is
11 - 5.19 = 5.81 hours
Answer:
1/16 of a gallon
Step-by-step explanation:
total = 1/4 gallon
split into 4 containers
1/4 ÷ 4 = 1/4 • 1/4 = 1/16
1/16 of a gallon
Answer:
(h + g)(10) = -6
Step-by-step explanation:
Step 1: Define
h(x) = 3x + 3
g(x) = -4x + 1
Step 2: Find (h + g)(x)
(h + g)(x) = 3x + 3 + -4x + 1
(h + g)(x) = -x + 4
Step 3: Substitute and Evaluate
(h + g)(10) = -10 + 4
(h + g)(10) = -6
Answer: 216 square units
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Explanation:
A common pythagorean triple you may be familiar with is the 3-4-5 right triangle. This has two legs of 3 and 4, and a hypotenuse of 5. The perimeter is 3+4+5 = 7+5 = 12. Note how this is a factor of 72.
If we multiply the perimeter (12) by 6, then 12*6 = 72. So we have scaled the triangle by a factor of 6. Each length is 6 times longer
the side length 3 becomes 3*6 = 18
the side length 4 becomes 4*6 = 24
the side length 5 becomes 5*6 = 30
The new perimeter is 18+24+30 = 42+30 = 72
The last step is to find the area. The two legs of this triangle are the base and height
area = 0.5*base*height
area = 0.5*18*24
area = 9*24
area = 216
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Or you could find the area of the 3-4-5 right triangle to get
area = 0.5*base*height = 0.5*3*4 = 6
then multiply by 36 to get 6*36 = 216. The 36 is the square of the scale factor 6 we applied above. The new lengths are 6 times longer, so the new area is 6^2 = 36 times larger.
