Let be "A" the area of the other polygon (in square feet).
By definition, when two figures are similar, the ratio of the lengths corresponding sides can be written as following:
\(\frac{a}{b}\)And the ratio of the areas of two similar figures can be expressed as:
\(\frac{a^2}{b^2}\)Then, the ratio of the areas can be calculated by squaring the ratio of their corresponding sides.
In this case, you can identify that:
\(\begin{gathered} a=6ft \\ b=3ft \end{gathered}\)Then, the ratio of the areas is:
\(k_{\text{areas}=}\frac{(6ft)^2}{(3ft)^2}=4\)Then:
\(\begin{gathered} A=(4)(27ft^2) \\ A=108ft^2 \end{gathered}\)The answer is:
\(108ft^2\)Help, I need to know this extension.
Answer:
10
Step-by-step explanation:
We know that area is 50km^2 and to find area we know the formula it is Area = base * height, 50 = b*5, so b must be 10
The ______ is a collection of all accounts within a company’s accounting system.
The general ledger is a collection of all accounts within a company’s accounting system.
The general ledger is a corporation's financial and economic data record-keeping system, where debit account, as well as credit account records, are being confirmed by a trial balance.
It keeps track of every financial transaction that occurs during the lifespan of a running corporation and stores account information required to generate the corporation's financial performance.
Therefore, we can conclude that the general ledger is a collection of all accounts within a company’s accounting system.
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Two of the sides of a right triangle are 4 and 5. What is the length of the third side? Find all possible answers.
To find the length of the third side of a right triangle when two sides are given, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's assume the two given sides are 'a' and 'b', and the unknown third side is 'c' (the hypotenuse).
Using the Pythagorean theorem:
c² = a² + b²
Substituting the given values:
c² = 4² + 5²
c² = 16 + 25
c² = 41
To find the length of 'c', we need to take the square root of both sides:
c = √41
So, the length of the third side is √41 (approximately 6.40) when rounded to two decimal places.
Therefore, the possible length of the third side of the right triangle is √41.
Step-by-step explanation:
We will use a phayragoras theorem
a^2 +b^2= c^2
let side1=4 be a
let side2=5 be b
let the 3rd side be the hypotnuous=c
therfore 4^2+5^2=c^2
=16+25=c^2
=41=c^2.
therfore c=√41
1. A right triangle LMN is given where: side MN = 8 side NL (the hypotenuse) =
10 What is the length of side LM?*
Step-by-step explanation:
\( \underline{ \underline{ \text{Given}}} : \)
Length of MN ( Base ) = 8 Length of NL ( Hypotenuse ) = 10\( \underline{ \underline{ \text{To \: find}}} : \)
Length of LM ( Perpendicular )\( \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : \)
\( \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}\)
⤑ \( \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }\)
⤑ \( \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }\)
⤑ \( \sf{ \sqrt{100 - 64}} \)
⤑ \( \sf{ \sqrt{36}} \)
⤑ \( \boxed{ \sf{6\: units}}\)
\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}\)
Hope I helped ! ツ
Have a wonderful day / night ! ♡
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John's sister is 8 years less than twice his age. If John is 39, what age is his sister
Answer:
70
Step-by-step explanation:
(39 X 2) - 8 = ?
78 - 8 =?
? = 70
Have a good day!
Alice, Bob, and Carol play a chess tournament. The first game is played between Alice and Bob. The player who sits out a given game plays next the winner of that game. The tournament ends when some player wins two successive games. Let a tournament history be the list of game winners, so for example ACBAA corresponds to the tournament where Alice won games 1, 4, and 5, Caroll won game 2, and Bob won game 3.
Required:
a. Provide a tree-based sequential description of a sample space where the outcomes are the possible tournament histories.
b. We are told that every possible tournament history that consists of k games has probability 1/2k, and that a tournament history consisting of an infinite number of games has zero prob- ability. Demonstrate that this assignment of probabilities defines a legitimate probability law.
c. Assuming the probability law from part (b) to be correct, find the probability that the tournament lasts no more than 5 games, and the probability for each of Alice, Bob, and Caroll winning the tournament.
Answer:
I don't know what you think about it is not going to be a great day of school and I don't know what you think about it is not going to be a great day of school
Write 8% as a fraction. There is no need to simplify your answer.
Answer:
8/100
Step-by-step explanation:
The percentage 8% can be written as \(\frac{8}{100}\) as a fraction.
The percentage is a method of proportionating a given fraction out of 100. x% implies x out of 100 always. The method is used to facilitate comparison is part of a whole when the total figure differs in different cases.
Fraction, on the other hand, is simply the expression of part of a whole. The numerator referring to the part and denominator to the whole. The whole need not be 100.
The percentage 8% means 8 out of 100. Thus the fraction becomes \(\frac{8}{100}\).
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A class has a average height of 68 inches and a standard deviation of 2 inches. What percent of the heights will exceed 72 inches
The percent of the heights of the class which has an average height of 68 inches and a standard deviation of 2 inches that will exceed 72 inches is 2.28%.
How the percentage is computed:We can use the normal distribution calculator to compute the percentage of the heights that will exceed 72 inches, using the following parameters and the z-score, as follows:
The average height of the class = 68 inches
Standard deviation = 2 inches
Sample mean = 72 inches
z score (standard measure) = (x - mean) / standard deviation
z = (72 - 68) / 2
z = 2
The probability that z is greater than 2, using the normal distribution calculator, gives us an area of 0.0228.
Thus, the percent of the heights that will exceed 72 inches is 2.28%.
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name each polynomial by degree and numbers of terms for -8+3x-2x^5
-2x^5 + 3x - 8 Total degree = 5 for this the degree could be 6 if we
consider all the exponents.
Number of terms = 3
2) -9p^3 + 5p^5 Degree = 5 the degree could be 8, if we consider all
the exponents.
Number of terms = 2
3) 4x^6 Degree = 6
Number of terms = 1
4) -3a^5 Degree = 5
Number of terms = 1
5) 3yz^4 + 2x^-4y^3 Total Degree = 4 It could be 4 the highest exponent
Number of terms = 2
\(3yz^4\text{ + }\frac{2y^3}{x^4}\)
6) 4x^4^y-4 + 4xy^-4 - 3x^3y^2 Total degree = 4
Number of terms = 3
\(\frac{4x^4}{y^4}\text{ + }\frac{4x}{y^4}-3x^3y^2\)The result of dividing a two-digit number by the number with its digits reversed is 7 over 4. If the sum of the digits is 12, what is the number?
NO LINKS!!! NOT AN ASSESSMENT OR TEST!!!! NOT MULTIPLE CHOICE!!
a. Sketch a graph to model Seattle's cost structure over the domain [0, 42,000]. Be sure to label the axes and any endpoints where the graph breaks.
b. Describe the function over each part of its domain. State whether it is constant, increasing or decreasing, and state the slope over each part.
Part (a)
The graph is shown below. It's a piecewise function composed of 3 parts: Two flat horizontal segments and a decreasing segment.
Note the use of open holes at points C and E. They tell the reader that the specific point is not part of the function. For example, point C at (8000,0.75) is an open hole since the second piece has x = 8000 excluded. In other words, the domain for the second piece is \(8,000 < x \le 20,000\) which says to exclude 8000 but to include 20,000.
============================================================
Part (b)
The flat parts are due to the two first pieces being constant functions. Regardless of what x is on those portions, the cost per unit stays the same. We see that the cost starts off at 35 cents per unit (green segment), then it jumps to 75 cents per unit (blue segment).
So far the costs have been constant, but once we get to the red curve portion, then the costs decrease as x increases. Note that 1/(200,000) = 0.000005 which means the costs are decreasing by 0.000005 dollars per unit. Let's multiply that by 10,000 to get 10,000*0.000005 = 0.05
So for the red portion, the costs are decreasing by $0.05 per 10,000 units, or they are decreasing by 5 cents per 10,000 units. When x > 20000, the lowest we can get the cost is at 62 cents per unit. This is when production is at max capacity (42,000 units).
If you wanted the cost per unit to be as small as possible, and x didn't have to be larger than 20 thousand, then you'd stick to the green line. However, the drawback here is that you can only produce at max 8000 units.
Answer:
Person above was super helpful!
Step-by-step explanation:
8 ft
10 ft
Find the perimeter of this figure to
the nearest hundredth.
Use 3.14 to approximate .
P = [?] ft
Notice that only half of the circle is included in the figure!
The perimeter of the figure is 4(π + 9)ft.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
Given is a 2 - D figure as shown in the figure attached.
We can write the perimeter as -
P = P{rectangle} + P{semicircle}
P = 2(10 + 8) + (4π)
P = (4π) + (36)
P = 4(π + 9)
Therefore, the perimeter of the figure is 4(π + 9)ft.
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Given the sequence - 3, 4, 11, 18, Amanda was asked to find the 58th term. She wrote the explicit formula below. Her teacher Ms. Felton informs her that her response is incorrect. Explain where she made a mistake. Then correct her mistake. Amanda's Explicit Formula - a58 = 18 + 7(58 - 1) USE COMPLETE SENTENCES/ ESCRIBE EN ORACIONES COMPLETAS a. What is her mistake? b. How should she correct it?
The given sequence is
\(-3,4,11,18\)As you can observe, this sequence as a difference of 7, that is, each new term is the sum of the previous term with seven.
Arithmetic sequences are defined by
\(a_n=a_1+(n-1)d\)Where, in this case, we have
\(\begin{gathered} a_1=-3 \\ d=7 \\ n=58 \end{gathered}\)Replacing these values, we have
\(a_{58}=-3+(58-1)7=-3+(57)7=-3+399=396\)The 58th term is 396.
(a) The reason why Amanda is wrong is she used 18 as the first term which is not correct because 18 is the fourth term of the sequence.
(b) To correct her mistake, she just needs to use -3 as the first term in the formula.
Please answer immediately I beg.
A pyramid and a cone have the same base area and height. The volume
of the pyramid is 175m³. What is the volume of the one? Explain your answer.
The volume of cone is 175 m³
Firstly,
Volume of Pyramid.
The volume (V) of a pyramid is
V = ⅓Ah
Data:
V = 175m³
Calculation:
175 = ⅓× A× h
Ah = 175*3
Ah = 525m³
Secondly,
The volume (V) of a cone is
V = ⅓Ah
Data:
Ah = 525 m³
Calculation:
V = ⅓ A× h
V = 175 m³
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What is 7(w-8)-3(-5w-10)
Answer:
}{7(w-8)}}-3(-5w-10)
7(w−8)−3(−5w−10)
Answer:
22w - 26
\(\large \bold {Solution \: Steps}\)
Use the distributive property to multiply 7 by w−8.\(\small\textsf{7w−56−3(−5w−10)}\)
Use the distributive property to multiply −3 by −5w−10.\(\small\textsf{7w−56+15w+30}\)
Combine 7w and 15w to get 22w.\(\small\textsf{22w−56+30}\)
Add −56 and 30 to get −26.\(\small\textsf{22w - 26}\)
Hope It's Help
find the range of the function y = 1/2x + 2 if the domain is {-4, -2, 0}
The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.
The given function is,
y = 1/2 x + 2.
Also, the domain of the function is {-4, -2, 0}.
Since, the domain of the functions defines the values of x,
And range defines the value of y in function.
The value of y at x = -4
y = 1/2(-4) + 2 = -2 + 2 = 0
At x = -2,
y = 1/2(-2) + 2 = -1 + 2 = 1
At x= 0,
y = 1/2 (0) + 2 = 2
The values of y are 0, 1 and 2.
Hence, the range of the function is {0, 1, 2}.
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Suppose that an individual has a body fat percentage of 15.9% and weighs 159. How many pounds of her weight is made up of fat? Round to the nearest tenth
Answer:
25.3 lb
Step-by-step explanation:
We can multiply the whole by the percentage to find the part. Since 15.9% is equal to 0.159, the weight of fat is 159*0.159 = 25.281. Round this to the nearest tenth, and we get 25.3 pounds.
A jet flies at a rate of 1.3x10^3 feet per hour . Written in scientific notation which is the best estimate of how many feet the jet will travel in 2.8x10^3 hours ?
Answer:
3 * 10^6 if the answer is 3.64 * 10^6, you really ought to argue the meaning of estimate with your instructor.
Step-by-step explanation:
This is a very valuable question. Put your calculator away when you answer it. Using a calculator is sort of cheating.
1.3 * 10^3 roughly is roughly 1 * 10^3
2.8*10^3 hours is roughly 3 * 10^3
Forget the powers for now and just work with the 1 and 3
1*3 equals 3.
10^3 * 10^3 = 10^6 when the base of two numbers is the same (10 in this case) then the powers are added.
10^(3 + 3) = 10^6
So the answer is roughly 3*10^6
Now you can take out your calculator and get the answer.
1.3*10^3 * 2.8 * 10^3 = 3.64 * 10 ^ 6
Notice that the estimate (done in my head) is close enough to tell you what the answer should be. On a test, that's a very handy skill.
Answer:
c
Step-by-step explanation:
Edge2022
Evaluate the expression 3x – 2y + 1 where x = 3 and y = 2
Answer:
6
Step-by-step explanation:
3(3) - 2(2) + 1
9 - 4 + 1
5 + 1
6
If a perpetuity pays a cash flow (C) every time period, forever, how come it is not worth an
infinite amount of money right now? Explain.
Which of the following is a function?
a. picture 1
b. all correct
c. picture 2
d. (6,3), (9,3), (-14,3)
The answer choice which is a function among the given answer choices is; Choice B as they are all correct.
What is a function and what defining property certifies a relation as a function?From conventional mathematics, a function from a set x to a set y assigns to each element of X exactly one element of Y.
The set of values x is called the domain of the function and the set of values y is called the codomain/range of the function.
Functions basically represents the idealization of how a varying quantity depends on another quantity.
It therefore follows from the paragraph above that all of the answer choices are functions.
Therefore, the answer choice which is a function among the given answer choices is; Choice B as they are all correct.
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How to find x here if the perimeter, diagonal, and length is given?
Answer:
see explanation
Step-by-step explanation:
(a)
perimeter (P) is calculated as
P = 2(l + b) ← l is the length and b the breadth
given l = x and P = 20 , then
2(x + b) = 20 ( divide both sides by 2 )
x + b = 10 ( subtract x from both sides )
b = 10 - x
Using Pythagoras' identity in the right triangle
x² + (10 - x)² = 8²
x² + 100 - 20x + x² = 64 ( subtract 64 from both sides )
2x² - 20x + 36 = 0 ( divide through by 2 )
x² - 10x + 18 = 0 ← as required
(b)
solve using the method of completing the square
x² - 10x + 18 = 0 ( subtract 18 from both sides )
x² - 10x = - 18
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 5)x + 25 = - 18 + 25
(x - 5)² = 7 ( take square root of both sides )
x - 5 = ± \(\sqrt{7}\) ( add 5 to both sides )
x = 5 ± \(\sqrt{7}\)
Then
x = 5 - \(\sqrt{7}\) ≈ 2.35 ( to 3 significant figures )
x = 5 + \(\sqrt{7}\) ≈ 7.65 ( to 3 significant figures )
Solve for y -18 = 7y + 9 - 10y
Answer:
I think that is 26y
Step-by-step explanation:
Answer:
the answer for y-18 =7y + 9 - 10y
Step-by-step explanation:
If the Federal Reserve sells $60,000 in Treasury bonds to a bank at 8%
interest, what is the immediate effect on the money supply?
A. It is increased by $64,800.
B. It is decreased by $60,000.
C. It is increased by $60,000.
D. It is decreased by $64,800.
If the Federal Reserve sells $60,000 in Treasury bonds to a bank at 8% interest, the immediate effect on the money supply is B. It is decreased by $60,000.
What decreases the money supply?One of the monetary factors that decreases the money supply in the economic is when the Federal Reserve raises the banks' reserve requirements.
Another factor that can decrease the money supply is the sale of treasury bonds to banks.
Raising the interest rates also decreases the money supply.
Thus, by selling $60,000 in Treasury bonds to a bank at 8% interest, it decreases the money supply.
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Can someone PLEASE HELP!!!!!!
Answer:
Pretty sure it's 8 units long
Parker has 12 blue marbles. Richard has 34
of the number of blue marbles that Parker has.
Part A
Explain how you know that Parker has more blue marbles than Richard without completing the multiplication.
Enter equal to, greater than, or less than in each box.
Multiplying a whole number by a fraction
less than
1 results in a product that is
the original whole number.
Part B
How many blue marbles does Richard have? Enter your answer in the box.
blue marbles
Rate of change In gallons of gas per year from 1995 to 1997???!?
The rate of change In gallons of gas per year from 1995 to 1997 is: C. Δg/Δt = 4 gal/year.
How to calculate the rate of change?In Geometry, the rate of change of the data in this table can be calculated by using this mathematical equation;
Rate of change (slope), m = (Change in y-axis, Δg)/(Change in x-axis, Δt)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph above, we can logically deduce the following data points located on the line:
Points on the x-coordinate = (1995, 1997).Points on the y-coordinate = (530, 538).Substituting the given data points into the rate of change formula, we have the following;
Rate of change (slope), Δg/Δt = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope), Δg/Δt = (538 - 530)/(1997 - 1995)
Rate of change (slope), Δg/Δt = 8/2
Rate of change (slope), Δg/Δt = 4 gallon/year.
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Solve: -5n + 6(5n - 5) = 38 + 8n
Evaluate if a=3, x=2, y=5, and z=4
2y – [4a = (x + 1)]
Answer:
Step-by-step explanation:
3 x y for x=2,
y=3: 3 x y x=2, y=3; Evaluate (z+2)(z-1) for z=5: (z+2)(z-1) z=5.
Given K is the midpoint of line segment CR, line segment MA bisects angle CMR. conclusion?
From the given image, on which you have that MA bisect angle CMR, you can conclude:
- Inside the parallelogram ACMR you have four congruent triangles.
- Angles MKR and CKA are congruent, that is, these angles have the same measure.
- Angles CKM and AKR are congruent.