Answer:
y = √55
Step-by-step explanation:
All the triangles are similar, so the ratio of short side to hypotenuse is the same for all:
5/y = y/(5+6)
y^2 = 55
y = √55
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<em>Comment on the geometry</em>
There are three "geometric mean" relationships that apply to this geometry.
- the altitude BD is the geometric mean of BC and BA (√30)
- the long side of the large triangle is the geometric mean of the longer segment of the hypotenuse and the whole hypotenuse (x = √66)
- the short side of the large triangle is the geometric mean of the shorter segment of the hypotenuse and the whole hypotenuse (y = √55)
If you were aware of the last of these relationships, you could write down the answer without any "work."
y = √(5(5 +6)) = √55
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The geometric mean is the n-th root of the product of n numbers. When there are 2 numbers, it is the square root of their product.
Answer:
2 1/10 and 21/10
Step-by-step explanation:
2.1 is 2 + 0.1 when expanded.
2 is just 2 and then 0.1 as a fraction is 1/10. The mixed number would be 2 1/10.
The improper fraction is just 21/10 (convert the mixed number into improper form).
Converting from mixed number to improper: <u>Multiply the number in the front (in this case 2) by the denominator. </u>
<u />
<u>That is 2 x 10 which is 20. Then add that number (20) to the numerator. 20 + 1 is equal to 21. </u>
<u />
<u>21 would be our numerator and the denominator would stay the same (10). </u>
21/10 is the improper form.
Let us suppose the number is x. Now we try to make an algebraic expression going step by step.
Step 1:
Five times the number means 5 multiplied by x.
So it becomes 5x.
Step 2:
Sum of 14 and five times the number means 5x+14.
Step 3:
Number multiplied by -8 means -8x.
Step 4:
Subtract the expression in step (3) from expression in step (2)
5x+14-(-8x)
Now we can simplify it further,
5x+14+8x
Combining like terms,
13x+14
Answer: The final expression becomes 13x+14.
Check out the attached image. I drew what I think your book is showing. The figure on the left is triangle ABC without any extended segments. The figure on the right has segment AB extended shown in red. This forms the exterior angle x
The rule that connects x, y and z together is the remote interior angle theorem. It says that adding two interior angles is going to be equal to the exterior angle that is not touching either interior angle. The "remote" part means "far away" so just think of the two angles that are furthest way or not touching the exterior angle in question.
In terms of algebra, the rule is
x+y = z
The correct answer to that would be b
