To draw the geometric mean in a right triangle, first draw a perpendicular from the right angle to the hypotenuse, creating two smaller triangles. Then use the properties of similar triangles or the Pythagorean theorem to find the geometric mean, which is the length of the perpendicular you drew.
Explanation:To draw the geometric mean in a right triangle, you can use the following step-by-step method:
Identify the right triangle within which you want to find the geometric mean. Assume this triangle has sides of lengths a and b, with c being the hypotenuse.Drop a perpendicular from the right angle to the hypotenuse, subdividing the original triangle into two smaller right triangles. This line segment will be the geometric mean, which we can label as x.Apply the properties of similar triangles or the Pythagorean theorem. The two smaller triangles will be similar to the original right triangle and to each other.The geometric mean x relates to the segments of the hypotenuse (which can be labeled d and e, where d + e = c), through the relationships x² = ad and x² = be.Since x is the geometric mean between a and b, the equations can also be written as x = √(ad) and x = √(be).Finally, measure the length of the perpendicular line you have drawn with a ruler to get the magnitude of the geometric mean x, or calculate it using the relationships stated.The Pythagorean theorem, a² + b² = c², can also be helpful in finding the lengths of the segments on the hypotenuse if they are not given.
which function grows at the fastest rate for increasing values of x?
f(x)=4x2+9x
h(x)=2x
g(x)=18x
Answer with explanation:
The given functions in x are
1. f(x)=4 x² + 9 x
2. h(x)= 2 x
3. g(x)=18 x
To check whether the function is increasing or not , there are two ways
1. The graph of function is sloping Upwards.
2. For, two real x number ,that is if , a ≥ b, then , f(a) ≥ f(b).
All the three given function in x, are increasing because ,for increasing , x , value of function increases.
For Integral numbers,
⇒Function 1
f(x)=4 x² + 9 x
f(1)=4×1²+9×1
=4 +9
=13
f(2)=4×2²+9×2
=4 × 4 +18
=16 +18
= 34
f(2) - f(1)=34 - 13
= 21
→→Function B
h(x)= 2 x
h'(x)=2
Rate of change of function is constant, which is equal to 2.
→→Function C
g(x)=18 x
g'(x)=18
Rate of change of function is constant, which is equal to 18.
≡⇒→Rate of change of function ,f(x) is maximum among three functions.That is, f(x)=4 x² + 9 x , has highest rate of increasing, for increasing value of, x.
Jordan bought 9/16 of a pound of sunflower seeds and divided them evenly into 9 snack bags for his lunch. What is the weight of sunflower seeds in each snack bag? 1/16 of a pound 1/9of a pound 16/81 of a pound 81/16 pounds
Answer:
A
Step-by-step explanation:
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67,456 divided by 32
Whats 16 + 4 plese help!!
What is the equation of the line in slope-intercept form?
7. When dy/dx = (x -6)1/2, what does y equal?
now how do u find the approximate area of a circle
diane places 2 drawers with the same width and height on top of each other. what is the combined volume of the 2 drawers?
The rectangle is divided into 4 equal parts. What is the name of the 4 equal parts?
Melanie’s bedroom walls are 45% painted. The area of her walls totals 420 square feet. What is the number of square feet of Melanie’s walls that still need to be painted?
The percentage of Melanie's walls that still needed to be painted is 55 % and the number of walls is 231 feet²
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the percentage of Melanie's walls that still needed to be painted be A
Now , the equation will be
The total number of walls = 420 feet²
The percentage of Melanie's walls that are painted = 45 %
So , the remaining percentage A = 100 - percentage of Melanie's walls that are painted
The percentage of Melanie's walls that still needed to be painted A = 55 %
And , the number of walls that needed to be painted = percentage of Melanie's walls that still needed to be painted A x total number of walls
On simplifying , we get
The area of walls that needed to be painted = ( 55/100 ) x 420
The area of walls that needed to be painted = 231 feet²
Hence , the area of Melanie's wall to be painted is 231 feet²
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I do this question yet get nothing close to the choices. Please help me and explain how I solve the areas.
Jefferson high school is looking to expand its student parking lot by expanding the existing lot as shown below
PLEASE HELP!
an electrician charges $80 an hour. his apprentice earns $42 an hour. the apprentice works on a job 3 hours less than the plumber. together they earn $850. how many hours did they each work?
find vaule of w if the sides of the triangle are w-10° w-38°. and w+36°
HELP
Seth watched 14 episodes of his favorite TV show in 10.5
hours. He spent the same amount of time watching each episode. What is the unit rate of hours to episodes? Remember to include units! (Example: 0.3 hours per episode)
2is more than a number v
A newspaper writer will write an article about the mean age of voters. She will estimate by selecting a sample of voters and calculating their mean age. Which method should the writer use to select the sample?randomly select 100 people who voted in the last election
select 100 people who voted in the last election and are more than 30 years old
select 100 people who voted for the most popular candidate in the last election
randomly select 100 people who read the newspaper
How much money is 2/3 of 15
Solve the equation. z/32 + 5/8 =13/16
True Or false, And why?
Milton purchases a 6-gallon aquarium for his bedroom. To fill the aquarium with water, he uses a container with a capacity of 1 quart. How many times will Milton fill and empty the container before the aquarium is full?
Help.
How many pieces 3/7 of a foot each can I make out of 7/2 feet of rope?
Final answer:
To find out how many 3/7 foot pieces can be made from 7/2 feet of rope, divide the total rope length by the length of one piece, resulting in 8 whole pieces with a small amount left over.
Explanation:
The question asks how many pieces of rope, each measuring 3/7 of a foot, can be made from a total length of 7/2 feet. To find the answer, you need to divide the total length of the rope (7/2 feet) by the length of each piece (3/7 foot), which is a division problem involving fractions:
(7/2) ÷ (3/7) = (7/2) × (7/3) = 49/6.
This means you can cut the rope into 49/6 pieces. Since you can't have a fraction of a physical piece of rope, the practical answer is that you can make 8 whole pieces of rope, each 3/7 of a foot long, with a little bit of rope left over.
You can make 8 full pieces of rope that are each 3/7 of a foot long from 7/2 feet of rope, with a small leftover piece.
Explanation:The question asks how many pieces of rope measuring 3/7 of a foot each can be made from 7/2 feet of rope. To find this, we divide the total length of rope by the length of one piece:
Total length of rope: 7/2 feet
Piece length: 3/7 foot
We divide 7/2 by 3/7, which is the same as multiplying 7/2 by the reciprocal
of 3/7 (which is 7/3):
(7/2) * (7/3) = 49/6
This simplifies to 8 1/6, which means you can make 8 full pieces of rope that are each 3/7 of a foot long, with a small piece leftover.
factor the polynomial
3y^3−9y^2=
will is 23% taller than wanda so wills height is ___ % of wanda’s height
Since Wanda's height represents 100% and Will is 23% taller, then Will's height is 123% of Wanda's height.
Explanation:The question tells us that Will is 23% taller than Wanda. In terms of understanding this percentage in relation to Wanda's height, it helps to see Wanda's height as 100% because 100% represents a whole, in this case, Wanda's entire height. If Will is 23% taller, then his height is 100% of Wanda's plus an additional 23%. Thus, Will's height is 123% of Wanda's height.
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Find the surface area of the pyramid.
A. 64 in.2
B. 56 in.2
C. 88 in.2
D. 118 in.2
Answer:
I believe it may be A.
Step-by-step explanation:
The formula looks complicated so I'm going to simplify it.
SA = 1/2 (4 * side of base * height) + side of base^2
Using this, we can get our answer.
1/2 (4 * 4 * 6) + 4^2
1/2 * 96 + 16
48 + 16
64
Thus the answer should be 64in. ^2
The surface area of the pyramid is 64 inch².
What is Surface area?A three-dimensional shape's surface area is the sum of all of its faces. To calculate the surface area of a shape, we add the areas of each face.
Here the pyramid has 4 triangles and one square.
Side of base square = 4 inch
Height of Triangle = 6 inch
Then, area of base
= side²
= 4²
= 16 inch²
and, Area of Triangle = 1/2 x base x height
= 1/2 x 4 x 6
= 12 inch²
So, the Surface Area of pyramid
SA = 1/2 (4 x t) + side²
= 12 x 4 + 16
= 48+ 16
= 64 inch²
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which relationship between the legs and the hypotenuse of the right triangle is correct?
Translate the algebraic expression below into words
g-12
Answer:
a number 12 less than g
Step-by-step explanation:
g -12 is a number 12 less than g
What is the LCM of 6 and 9?
what is thw quadractic formula of this
Hello!
[tex]\sf 7n^{2} -6n+10=0\\\\x = \dfrac{-b~\±~\sqrt{b^{2} -4ac} }{2a} \\\\\\x = \dfrac{-(-6)~\±~\sqrt{(-6)^{2} -4~\times~7~\times~10} }{2~\times~7}\\\\\\x =\boxed{\dfrac{6\±\sqrt{-244} }{14} }[/tex]
Bill Gates wants to construct an in ground swimming pool for his dog. he wants it's length to be 8 yards shorter than twice it's width. he then wants to surround it with a concrete walkway 6 yards wide. he can only afford 570 square yards of concrete. what should the dimensions be of the pool ?
Please find the attached file for a better understanding of the solution provided here:
ABCD is the swimming pool and PQRS is the extent of the swimming pool plus the concrete walkway which is 6 yards wide.
Now, we know that the length is 8 yards shorter than twice it's width. Thus,
l=2w-8
Now the area of the region, A'B'QP will be: length x width. Now, the length here is l+6+6=2w-8+12=2w+4 and width is 6.
Thus, area of the region A'B'QP is (2w+4)x6=12w+24
Likewise, the area of the region D'C'RS will similarly be 12w+24 too.
Now, the area of the region BB'C'C will be 6 x w=6w
Similarly, the area of the region AA'D'D will be 6 x w=6w
Therefore, the total area of the walk way will be:
[tex] 2(12w+24)+2\times 6w=570 [/tex]
[tex] 24w+48+12w=570 [/tex]
[tex] 36w+48=570 [/tex]
[tex] \therefore w=14.5 [/tex]
Therefore, length, l will be:
[tex] l=2w-8=2\times 14.5-8=29-8=21 [/tex]
Therefore, the dimensions of the swimming pool are:
Length, l= 21 yards and Width, w=14.5 yards
How many quarter pound buyers can george make out of 3 and 1/2 pounds of ground beef?