Answer: rate of train A = 120 km/h
rate of train B = 101 km/h
Step-by-step explanation:
Let x = the speed of train A
Let y = the speed of train B
One train travels 19 km/h slower than the other. Let train B be the slower train. Therefore,
x = y + 19 - - - - - - - - - -1
Recall
Speed = distance/time
Distance = speed × time
If they meet in 3 hours, it means that train A has travelled a distance of
x × 3 = 3x km
And train B has travelled a distance of y × 3 = 3y km
Train A and Train B were 663 kilometers apart when they left their respective destinations. They left at the same time and travelled towards each other. This means that if they meet in 3hours time, they must have covered a total of 663 km. Therefore,
3x + 3y = 663 - - - - - - - - - 2
Substituting x = y + 19 into equation 2, it becomes
3(y + 19) + 3y = 663
3y + 57 + 3y = 663
6y + 57 = 663
6y = 663 - 57 = 606
y = 606/6 = 101 km/h
x = y + 19 = 101 + 19
x = 120 km/h
Answer:
15
Step-by-step explanation:
using the 3 : 4 : 5 triangle triple:
we see that this triangle follows the same ratio
9:12 = 3:4, so the hypotenuse = 5*3 = 15
ANSWER: 15
Answer:
130.25 ft.
Step-by-step explanation:
The semi circle has a length 1/2 of the circumference of the circle with a diameter of 25
C = πd = 3.14(25)
So, the semi circle has a length = 1/2(3.14)25) = 39.25
The distance for the rectangle = 33 + 25 + 33 = 91
Therefore, the total perimeter = 91 + 39.25 = 130.25
Answer:
Step-by-step explanation:
<u>Given vertices of a triangle:</u>
- A(4, 12), B(14, 6), and C(-6, 2)
Let the circumcenter is point M(x, y)
We know that the circumcenter is equidistant from each of the vertices.
<u>Use distance formula:</u>
- AM = √(x - 4)² + (y - 12)²
- BM = √(x - 14)² + (y - 6)²
- CM = √(x + 6)² + (y - 2)²
<u>All three distances are equal:</u>
- AM = BM = CM ⇒ AM² = BM² = CM² ⇒
- (x - 4)² + (y - 12)² = (x - 14)² + (y - 6)² = (x + 6)² + (y - 2)²
<u>Square of each:</u>
- AM² = x² - 8x + 16 + y² - 24y + 144 = x² + y² - 8x - 24y + 160
- BM² = x² - 28x + 196 + y² - 12y + 36 = x² + y² - 28x - 12y + 232
- CM² = x² + 12x + 36 + y² - 4y + 4 = x² + y² + 12x - 4y + 40
<u>Comparing the squares, we get following system:</u>
- -8x- 24y + 160 = -28x - 12y + 232 ⇒ 20x - 12y = 72 ⇒ 5x - 3y = 18
- - 8x - 24y + 160 = 12x - 4y + 40 ⇒ 20x + 20y = 120 ⇒ x + y = 6
<u>Solve by substitution, x = 6 - y:</u>
- 5(6 - y) - 3y = 18
- 30 - 8y = 18
- 8y = 12
- y = 1.5
<u>Find x:</u>
So the circumcenter is M(4.5, 1.5)
Answer:
Can you take a pic of the problem if you can't type it out?
Step-by-step explanation:
