Answer:
Step-by-step explanation:
The geometric mean relations for this geometry tell you the length of each segment (x or y) is the root of the product of the hypotenuse segments it touches.
x = √(9×5) = (√9)(√5) = 3√5
y = √(9×(9+5)) = (√9)(√14) = 3√14
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<em>Additional comment</em>
The geometric mean of 'a' and 'b' is √(ab).
The geometric mean relations derive from the fact that the three triangles in this geometry are similar. That means corresponding sides are proportional.
Segment x is both a long side (of the smallest triangle) and a short side (of the medium-size triangle). Then it will be involved in proportions involving the relationship of the long side and the short side of the triangles it is part of:
long side/short side = x/5 = 9/x
x² = 5·9
x = √(9×5) . . . . as above
In like fashion, y is both a long side and a hypotenuse, so we have ...
long side/hypotenuse = y/(9+5) = 9/y
y² = (9+5)(9)
y = √(9×14) . . . . . as above
The same thing holds true on the other side of the triangle. The unmarked segment is both a short side and a hypotenuse, so its measure will be the geometric mean of 14 and 5, the hypotenuse and its short segment.
Answer:
x = -5
Step-by-step explanation:
You are often told to start a problem like this by clearing fractions. Multiply the equation by the least common denominator of the fractions. Here, that value is 6.
4x -3 = 2 +5x . . . . multiply the equation by 6
-5 = x . . . . . . . . . . . add -2-4x to both sides
The solution is x = -5.
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If you're comfortable with arithmetic using fractions, you can "cut to the chase." Subtract 2/3x+1/3 from both sides:
(2/3x -1/2) -(2/3x +1/3) = (1/3 +5/6x) -(2/3x +1/3)
-1/2 -1/3 = 5/6x -2/3x . . . . simplify a little
-5/6 = 1/6x . . . . . . . . . . . . .simplify more
-5 = x . . . . . . multiply by 6
Answer:
What do you need help with
Step-by-step explanation:
Answer: There are 5 guards on each team.
Step-by-step explanation:
Since we have given that
Number of forwards in basketball league = 32
Number of guards in basketball league = 80
We need to find the greatest number of teams possible.
We will find "H.C.F. of 32 and 80.
Since H.C.F. of 32 and 80 = 16
Number of guard would be
Hence, there are 5 guards on each team.