The altitude to the hypotenuse of a right triangle divides the hypotenuse into 15 inches and 30 inch segments. Explain or show how to find the exact length of the altitude including the correct value. Then explain or show how to find the length of each leg including the correct values.
Answers
9514 1404 393
Answer:
CX = 15√2 inches
BC = 15√3 inches
AC = 15√6 inches
Step-by-step explanation:
In this geometry, all of the triangles are similar:
ΔABC ~ ΔACX ~ ΔCBX
Corresponding segments are proportional in similar triangles, so we have ...
AX/CX = CX/BX = (long leg)/(short leg)
Filling in the numbers, we get
30/CX = CX/15
CX² = 15×30
CX = 15√2 . . . . . exact length of the altitude (inches)
__
Similarly, we can form proportions with the legs:
AB/BC = CB/BX
BC² = (BX)(AB) = (45)(15)
BC = 15√3 . . . inches
and
AC/AB = AX/AC
AC² = (AX)(AB) = (30)(45)
AC = 15√6 . . . inches
_____
Additional comment
You may notice that each of the segments we're interested in is the root of a product involving segments of the hypotenuse. This "root of a product" is called the geometric mean. Here, the three geometric mean relations are ...
altitude = geometric mean of hypotenuse segments
short side = geometric mean of short segment and whole hypotenuse
long side = geometric mean of long segment and whole hypotenuse
__
Strictly speaking the geometric mean is the n-th root of the product of n items. Here, there are only 2 items, so it is the square root of their product.
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Complementary angles sum to 90°
let one angle be x then the other angle is 7x + 10 , so
x + 7x + 10 = 90
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at 9.00
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If any values in the data set are
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If any values in the data set are
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Answers
Answers:
Box 1: Greater thanBox 2: Less thanSo,
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What are Outliers?
If a number in distribution is more than 1.5 times the length of the box away from either of the upper and lower quartile of the distribution, then that number is said to be an outlier.
The lower quartile is [tex]Q_1[/tex] and the upper quartile of distribution is [tex]Q_3[/tex]
Then lower boundary is given by [tex]=Q_1-1.5\times IQR[/tex]
The Upper boundary is given by [tex]=Q_3+1.5\times IQR[/tex]
If any number or value of the distribution is greater than [tex]Q_3+1.5\times IQR[/tex] then that is called Upper Outlier.
Similarly, if any value or number of the distribution is less than [tex]Q_1-1.5\times IQR[/tex] then that is called Lower Outlier.
So the answers in the boxes are given by:
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FAST HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Step-by-step explanation:
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Answers
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Answer:
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Step-by-step explanation:
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у
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Answer:
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Answer:
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Answer:
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Answers
Answer
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answers
Answer:
the classmark of the class is 162.5
Step-by-step explanation:
The computation of the class mark is shown below:
Given that
160 - 165
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= (160 + 165) ÷ 2
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Answers
Answer:
Gcf 9
Step-by-step explanation:
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what is another way to represent the expression- f + (0.50 x f)?
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B) 150f
C) f + 1.5
D) f + 150
Answers
solve for x: 3^(x+3)=9
Answers
Answer:
-1
Step-by-step explanation:
To solve equations like this we need to use the following rule
[tex]x^y=z\\y=log_xz[/tex]
We have
[tex]3^{x+3}=9\\x+3=log_39\\x+3=2\\x= -1[/tex]
Which function is the inverse of f(x)=9x-3
Answers
Answer:
The screenshot of my test is below
Step-by-step explanation:
The inverse function is [tex]f^{-1} (x)[/tex]=(x+3)/9.
The given function is f(x)=9x-3.
How to find the inverse of a function?Steps for finding the inverse of a function f(x).
Replace f(x) with y in the equation describing the function.Interchange x and y. In other words, replace every x with a y and vice versa.Solve for y.Replace y with [tex]f^{-1} (x)[/tex].Now, y=9x-3
Interchange x and y. That is x=9y-3.
Solve for y.
That is, 9y=x+3
⇒y=(x+3)/9
⇒[tex]f^{-1} (x)[/tex]=(x+3)/9
Therefore, the inverse function is [tex]f^{-1} (x)[/tex]=(x+3)/9.
To learn more about the inverse function visit:
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