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.
Related Questions
A triangular prism has a height of 3 ft, a width of 5 ft, and a length of 8 ft. Find the volume.
a
90 ft3
b
60 ft3
c
150 ft3
d
120 ft3
Answers
Answer
120 ft3
Step-by-step explanation:
Length×Width×Height
(8ft×5ft×3ft)
5×3= 15 ft
15×8= 120 ft3
Name the component that changes its resistance as the temperature changes.
Answers
Answer:
Thermistor
Step-by-step explanation:
Answer:
thermistor
Step-by-step explanation:
it is a special typeof variable resistive element that changes its physical resistance when exposed to changes in temperature.
help!!! I will give brainiest to whoever gets both
Answers
Answer:
She has to buy 48 inches of ribbon
Step-by-step explanation:
We know that the pillow is a square with an area of 144. This means that all the side lengths must be the same. If we take the square root of 144 we get 12 which is the length of one side of the square. Because there are four sides to a square, we multiply this by 4. So 12 x 4 = 48 inches of ribbon.
find the gcf 27y^3z and 45x^2y
Answers
Answer:
Gcf 9
Step-by-step explanation:
Factors of 27y^3z = 1,3,5,9,27,y,y^2. Factors of 45x^2y = 1,3.5,9,15,45,x,y. CF = 1,3,5,9,y. GCF = 9.
Rodney is making three pizzas. The recipe says that, for one pizza, he needs 2 cups of flour, 2 teaspoons of instant active dry yeast, 2 cloves of garlic, 1 tablespoon of olive oil, and some other ingredients. Rodney is out of flour and goes to the store to buy a bag containing 20 cups of flour. How much flour will he have left over after making the pizzas?*
Answers
Answer:
+20+-+6+=+14+
He will have 14 cups leftover
Step-by-step explanation:
The function f (x) = 4(3) can be used to determine the number of
bacteria in a petri dish after x weeks. How much bacteria will there be in 4
weeks?
Answers
Which table shows a linear relationship?
OA
OB
1
X
0
2
0
С
1
2
A
Ос
5
7
10
у
7
y
12
18
CD
Hint:
Is the change in x constant and is the change in y
constant.
0
1
B
x
2
1
2
0
D
16
30
У
8
16
24
Answers
Answer:
Its C
Step-by-step explanation:
Because its c
Find the weekly wage before deductions for following data.
Hours worked Rate in dollars Weekly Wage
32.0
at $6.65
$
36.5
at $8.20
$
37.6
at $8.15
$
.
31.7
at $10.65
$
36.0
at $8.84
$
Answers
Answer:
Did I do something wrong because you never did text me back
Step-by-step explanation:
$34
at 9.00
Mark needs to buy 42 stamps to send out invitations tor his birthday party. Will 3 sheets of stamps be enough? How do you know?
Answers
someone help me please!
Answers
Answer:
1) 44 toilet rolls
2) 15 packs
3) 72 yogurts
4) 4 packs
Step-by-step explanation:
1) 4 x 11 = 44 in 11 packs
2) 60÷4= 15 packs
3) 12 ×6= 72
4)42÷12=3.5=4
Factorise m2 - 10m + 24 =0
Answers
Answer:
(m-6) (m-4).
Step-by-step explanation:
m2-6m-4m+24
m(m-4)-6(m-4).
therefore answer is (m-6) (m-4).
Richard rolls a fair dice 420 times.
How many times would Richard expect to roll a four?
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]
When Deion was born, his grandfather gave him a 7.5-gram gold coin as a present. Today, Deion read in the newspaper that a gram of gold is worth $50.04. How much money is the gold coin worth?
20 POINTSSSSSSSSSSSSSS
FAST HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Step-by-step explanation:
1 garm = $50.04
7.5 gram = 50.04 × 7.5 = $375.3
An outlier is a data value that differs greatly from other
values in a data set.
Complete the statements about the outlier rule.
If any values in the data set are
the upper boundary, then
those values are upper outliers.
If any values in the data set are
the lower boundary, then
those values are lower outliers.
Answers
Answers:
Box 1: Greater thanBox 2: Less thanSo,
If any values in the data set are greater than the upper boundary, then those values are upper outliers.If any values in the data set are less than the lower boundary, then those values are lower outliers.The general rule is that the upper boundary is found computing Q3+1.5*IQR, where IQR is the interquartile range. Recall that IQR = Q3-Q1. The Q1 and Q3 are the first and third quartiles respectively.
Another rule is that the lower boundary is found by computing Q1 - 1.5*IQR
On a box and whisker plot, outliers are points that are not connected to the main plot itself. You can think of them as islands far from the mainland.
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:
Box 1: Greater than Box 2: Less thanLearn more about Outliers here -
https://brainly.com/question/3631910
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Julie weighs five watermelons and rounds the weighs to the nearest hundredth which of the weights round to 7.43 pounds
Answers
Options :
7.423 pounds
7.437 pounds
7.413 pounds
7.425 pounds
Answer:
7.425
Step-by-step explanation:
Rounding each option to the nearest hundredth:
The second digit after the decimal point is the hundredth digit, if the next digit (thousandth digit) is more than or equal to 5, then it is rounded to 1 and added to the hundredth digit value, if otherwise, it is rounded to zero.
7.423 = 7.42 (nearest hundredth)
7.437 = 7.44 (nearest hundredth)
7.413 = 7.41 (nearest hundredth)
7.425 = 7.43 (nearest hundredth)
In a flower garden, there are 6 tulips for every 7 daisies. If there are 54 tulips, how many daisies are there? A. 69
B. 65
C. 61
D. 63
Answers
Answer:
D
Step-by-step explanation:
Answer:
61
Step-by-step explanation:
54+ 7 = 61 yuhhhhh
Help! I will mark brainliest
Answers
Answer:
[tex]4[/tex] x [tex]10^{6}[/tex]
Step-by-step explanation:
Answer:
4*10^6
Step-by-step explanation:
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:
https://brainly.com/question/19755382.
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PLS HELP ! URGENT
will mark brainliest
Answers
Answer:
6^36
Step-by-step explanation:
6^9x4
6^36
Y 9. ΔΧΥΖ» Δ. ~^_ A. XYT; YZT B. XTY; YTZ C. TXY, ZYT Z T Х D. YXT; TYZ
Answers
Answer:
A
Step-by-step explanation:
Find the class mark of the class 160- 165
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
So, the class mark of the class is
= (Upper limit + lower limit) ÷ 2
= (160 + 165) ÷ 2
= 162.5
Hence, the classmark of the class is 162.5
The graph H shows the height, in meters, of a
rocket 1 seconds after it was launched.
a. Find H0). What does this value
represent?
b. Describe the domain of this function.
c. Describe the range of this function.
Answers
Answer:
a) H0 = 15 m, is the initial height, the height of the rocket at time 0 s.
b) [tex]D=[0,5][/tex]
c) [tex]R=[0,35][/tex]
Step-by-step explanation:
a) H0 is the initial height. It means the height of the rocket at time 0 s.
This value is 15 m.
b) The domain is all values of t between 0 and 5 seconds.
[tex]D=[0,5][/tex]
c) The range is all values of height from 0 to 35 meters.
[tex]R=[0,35][/tex]
I hope it helps you!
2. How would you find the
rate of change in a table.
You would divide what
Over-what?...
Answers
y/x
what is the area of circle whose diameter is 32 inches? use π=3.14
Answers
Answer:
803.84
Step-by-step explanation:
Radius is half of the diameter.
32/2=16
3.14*16^2=803.84
Answer:
803.84 in^2.
Step-by-step explanation:
Radius = 1/2 * 32 = 16
Area = 3.14 * 16^2
= 803.84.
what is another way to represent the expression- f + (0.50 x f)?
A) 1.5f
B) 150f
C) f + 1.5
D) f + 150
Answers
two complentary angles are drawn such that one angle is 10 more than seven times the other angle find the measure of each angle
Answers
Answer:
10° and 80°
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
8x + 10 = 90 ( subtract 10 from both sides )
8x = 80 ( divide both sides by 8 )
x = 10
and 7x + 10 = 7(10) + 10 = 70 + 10 = 80
Thus the 2 angles are 10° and 80°
Simplify 7(2x + 3) please?
Answers
=14x+21 hope it helps
Answer:
14x + 6
Step-by-step explanation:
use the distributive property
Hope this helped! Have a nice day! Plz mark as brainliest!!! :D
-XxDeathshotxX
Why is it important to include a conclusion at the end of an argument? to answer a question to restate the claim to introduce an idea to show understanding
Answers
to restate the claim
Find each Quotient answer quick 2mins left don't troll
Answers
Answer:
18/125 92/105
Step-by-step explanation:
Answer:
1) 9/50
2) 92/105
Step-by-step explanation:
1)[tex]\frac{3}{5} /4\frac{1}{6} =\frac{3}{4} /\frac{25}{6} \\\\\frac{3}{4} *\frac{6}{25} =\frac{9}{50}[/tex]
2) [tex]\frac{23}{7} /\frac{15}{4} =\frac{23}{7} *\frac{4}{15} \\\\=\frac{92}{105}[/tex]