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Answer: Yes it can form a triangle and its a right triangle.
Step-by-step explanation:
Using the Pythagorean theorem we can see that the longest side (20) is our hypotenuse. From there you just check if its true. :)
Answer:
Total length of ribbon to line the long sides will be 22 in
Step-by-step explanation:
In the given figure of kite if we draw a line "h" vertically will form two right angle triangles.
Then by applying Pythagoras theorem in both the triangles.
h²= (3x + 5)² + (2x + 1)² ------(1)
h²= (5x + 1)² + 5² ------(2)
By equating both the equations
(3x + 5)² + (2x + 1)² = (5x + 1)² + 25
9x² + 25 + 30x + 4x² + 4x + 1 = 25x² + 10x + 1 + 25
13x² + 34x + 26 = 25x² + 10x + 26
13x² - 25x² + 34x - 10x + 26 - 26 = 0
- 12x² + 24x = 0
12x² - 24x = 0
x² - 2x = 0
x(x - 2) = 0
x = 2
Now we will put x = 2 in the measure of sides of the kite.
Side 1 = (3x + 5)
= 3×2 + 5
= 11
Side 2 = (5x + 1)
= 5×2 + 1
= 11
Side 3 = (2x + 1)
= 2×2 + 1
= 5
Therefore, Total length of ribbon to line the long sides will be = 11 + 11
= 22 in.
The equation is
time= distance/rate
and the train is going 300 miles
the car is going 200 miles
the train goes 20 miles faster than the car
fitting the numbers into the equation
200/r=300/(r+20)
cross multiply
200/r = 300/(r+20)
200(r+20) = 300r
distributive property
4000+200r=300r
subtract 200r from both sides to add like terms
4000=100r
divide 100 from each side to get r by itself
40 = rate of car
60 = rate of train
Answer:
56 ways.
Step-by-step explanation:
This question is solved by using combinations and permutations chapters in the math book.
To put it simply, we need to find the number of 3 horse combinations we can make from 8 horses. This requires the combinations formula:
here n is the total number of objects to choose from, and r is the number of objects we require in the combination or group.
Since there are 8 horses, n= 8
Since we need to choose only 3 of them, and order does not matter, r= 3
Solving the equation above using these inputs gives us 56 unique ways we can choose the three winners.
