The perimeter of the pentagon is:
\(AB + BC + CD + DE + EA = \sqrt{(10)} + \sqrt{(25)} + \sqrt{(13)} + \sqrt{(5)} + 6 = 23.1\)
To find the perimeter and area of a regular polygon, we need to know the number of sides, the length of each side, and the apothem, which is the distance from the center of the polygon to the midpoint of a side. However, in this problem, we are not given enough information to determine whether the polygon is regular or not.
Instead, we can find the perimeter and area of the pentagon with the given vertices using the distance formula to find the length of each side, and then using the formula for the area of a polygon:
Perimeter:
To find the length of each side, we can use the distance formula:
\(AB = \sqrt{((3-1)^2 + (1-4)^2)} = \sqrt{(10)\)
\(BC = \sqrt{((0-3)^2 + (5-1)^2)} = \sqrt{(25)\)
\(CD = \sqrt{((2-0)^2 + (8-5)^2)} = \sqrt{(13)\)
\(DE = \sqrt{((1-2)^2 + (10-8)^2)} = \sqrt{(5)\)
\(EA = \sqrt{((1-1)^2 + (4-10)^2) }= 6\)
Therefore, the perimeter of the pentagon is:
\(AB + BC + CD + DE + EA = \sqrt{(10)} + \sqrt{(25)} + \sqrt{(13)} + \sqrt{(5)} + 6 = 23.1\)
Area:
To find the area of the pentagon, we can divide it into five triangles and then use the formula for the area of a triangle:
Area of triangle ABC = (1/2) * AB * h1, where h1 is the perpendicular distance from C to line AB.
Area of triangle BCD = (1/2) * BC * h2, where h2 is the perpendicular distance from E to line BC.
Area of triangle CDE = (1/2) * CD * h3, where h3 is the perpendicular distance from A to line CD.
Area of triangle DEA = (1/2) * DE * h4, where h4 is the perpendicular distance from B to line DE.
Area of triangle EAB = (1/2) * EA * h5, where h5 is the perpendicular distance from C to line EA.
To find each height, we can use the formula for the distance from a point to a line:
\(h1 = |(2-1)(1-4) - (3-1)(0-4)| / \sqrt{((2-1)^2 + (3-1)^2)} = \sqrt{(10)} / 2\)
\(h2 = |(4-1)(3-1) - (3-1)(5-1)| / \sqrt{((4-1)^2 + (3-1)^2) }= \sqrt{(13)} / 2\)
\(h3 = |(4-2)(4-5) - (1-2)(8-5)| / \sqrt{((4-2)^2 + (8-5)^2)} = \sqrt{(5)} / 2\)
\(h4 = |(8-10)(1-8) - (2-1)(10-8)| / \sqrt{((8-10)^2 + (2-1)^2) }= \sqrt{(13)} / 2\)
\(h5 = |(4-1)(4-10) - (1-1)(5-4)| / \sqrt{((4-1)^2 + (5-1)^2)} = 3 \sqrt{(10)} / 2\)
Therefore, the area of the pentagon is:
Area = Area of triangle ABC + Area of triangle BCD + Area of triangle CDE + Area of triangle DEA + Area of triangle EAB
\(= (1/2) * \sqrt{(10)} * (\sqrt{(13)}/2) + (1/2) * \sqrt{(25)} * (\sqrt{(13)}/2) + (1/2) * \sqrt{(13)} * (\sqrt{(5)}/2) + (1/2) * \sqrt{(5)} * (\sqrt{(13)}/2) + (1/2) * 6 * (3 \sqrt{(10)}/2)\)
≈ 27.5
Therefore, the approximate perimeter of the pentagon is 23.1 units, and the approximate area of the pentagon is 27.5 square units.
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Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y=−8
x=4
Choose the correct answer below.
A.
Perpendicular
B.
Neither
C.
Parallel
Answer:
A. Perpendicular
Step-by-step explanation:
**I recommend going to desmos; desmos is a graphing calculator and is super useful!
When the genetic material was first being isolated and studied, there was a controversy about it being protein or DNA. Those that backed protein as the genetic material almost got it's right. Explain. What was the connection between the two molecules that was missed
According to the information we can infer that the connection between proteins and DNA that was missed during the controversy was the role of DNA as the carrier of genetic information, while proteins played a crucial role in executing the instructions encoded in DNA.
What was the connection between the two molecules that was missed?During the early stages of studying genetic material, there was a controversy between proteins and DNA as the carrier of genetic information. Those who supported proteins overlooked the crucial role of DNA in carrying genetic instructions. In 1944, an experiment demonstrated that DNA, not proteins, transmitted genetic information.
The overlooked connection was that DNA carries instructions for building proteins. DNA's specific nucleotide sequences encode the information needed to synthesize proteins, which fold into functional structures. While proteins exhibit complexity and diversity, it is DNA that serves as the blueprint for building proteins and carrying genetic information.
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6x+2y-3z=-17
7x-5y+z=72
2x+8y+3z=-21
Answer:
what exacly are you trying to figure out
Step-by-step explanation:
Noah’s soccer team played 12 games and won 10 of these. The ratio is 10:2 what is the percentage of the game won?
The equation A equals P equals quantity 1 plus 0.05 over 4 end quantity all raised to the power of 4 times t represents the amount of money earned on a compound interest savings account with an annual interest rate of 5% compounded quarterly. If after 15 years the amount in the account is $12,065.51, what is the value of the principal investment? Round the answer to the nearest hundredths place.
$5,725.90
$6,339.61
$10,014.53
$11,481.12
The value of the principal investment is given as follows:
$5,725.90.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
t = 15, A(t) = 12065.51, r = 0.05, n = 4.
Hence the principal can be obtained as follows:
P(1 + 0.05/4)^(4 x 15) = 12065.51
2.1072P = 12065.51
P = 12065.51/2.1072
P = $5,725.90
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At charles school, 15 of the 75 students in seventh grade play in the jazz band. How many seventh graders play in the jazz band?.
The jazz band has 15 seventh graders playing according to the ratio.
What is the ratio?A ratio, which is a number, is a way to represent one quantity as a portion of another. A ratio can only be compared when the two numbers in it have the same unit. To compare two objects, ratios are utilized.
Given One fifth of the 75 seventh graders at Charles School participate in the jazz band.
Presented as a ratio
75 pupils, or 1/5 of them, participate in the jazz band.
75 pupils out of the total play in the jazz band.
15 kids in total participate in the jazz band.
15 seventh graders are therefore playing in the jazz band in accordance with the ratio.
Hence, The jazz band has 15 seventh graders playing according to the ratio.
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Which of the following is an advantage of a lossless compression algorithm over a lossy compression algorithm
A lossless compression algorithm preserves all of the original data, while a lossy compression algorithm may discard some of the original data.
A lossless compression algorithm is a type of data compression algorithm that preserves all of the original data without any loss. This means that when the original data is uncompressed, it is exactly the same as when it was compressed. On the other hand, a lossy compression algorithm is a type of data compression algorithm that discards some of the original data in order to reduce the size of the file. This means that when the original data is uncompressed, it may not be exactly the same as when it was compressed.
The advantage of a lossless compression algorithm over a lossy compression algorithm is that it preserves all of the original data, while a lossy compression algorithm may discard some of the original data.
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Carl stands 2. 47m from a tree. The angle of elevation to the tree is 34. 7
The height of the tree is approximately 1.68 meters. Note that this calculation assumes that Carl is standing directly on level ground and that his eye level is at the same height as the base of the tree. If these assumptions are not true, the calculation may not be accurate.
To solve this problem, we can use trigonometry. Let's assume that the height of the tree is represented by "h". Then, we can set up the following equation:
tan(34.7) = h / 2.47
We can then solve for "h" by multiplying both sides by 2.47:
h = tan(34.7) * 2.47
h ≈ 1.68 meters
Therefore, the height of the tree is approximately 1.68 meters. Note that this calculation assumes that Carl is standing directly on level ground and that his eye level is at the same height as the base of the tree. If these assumptions are not true, the calculation may not be accurate.
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Solve dy/dx = xy, y(0) = 2. Find the interval, on which the solution is defined.
Answer:
The interval on which the solution is defined depends on the domain of the exponential function. Since e^((1/2)x^2 + ln(2)) is defined for all real numbers, the solution is defined on the interval (-∞, +∞), meaning the solution is valid for all x values.
Step-by-step explanation:
o solve the differential equation dy/dx = xy with the initial condition y(0) = 2, we can separate the variables and integrate both sides.
Starting with the given differential equation:
dy/dx = xy
We can rearrange the equation to isolate the variables:
dy/y = x dx
Now, let's integrate both sides with respect to their respective variables:
∫(dy/y) = ∫x dx
Integrating the left side gives us:
ln|y| = (1/2)x^2 + C1
Where C1 is the constant of integration.
Now, we can exponentiate both sides to eliminate the natural logarithm:
|y| = e^((1/2)x^2 + C1)
Since y can take positive or negative values, we can remove the absolute value sign:
y = ± e^((1/2)x^2 + C1)
Next, we consider the initial condition y(0) = 2. Substituting x = 0 and y = 2 into the solution equation, we get:
2 = ± e^(C1)
Here, we see that e^(C1) is positive since it represents the exponential of a real number. So, the ± sign can be removed, and we have:
2 = e^(C1)
Taking the natural logarithm of both sides:
ln(2) = C1
Now, we can rewrite the general solution with the determined constant:
y = ± e^((1/2)x^2 + ln(2))
Jorge tiene que viajar de Cancún a Tijuana realizando escala en el D.F. De Cancún salen 2 vuelos diferentes al D.F. Y del D.F. Salen 6 vuelos diferentes. ¿Cuál es el total de combinaciones que puede elegir Jorge?
Answer:
12.
Step-by-step explanation:
Dado que Jorge tiene que viajar de Cancún a Tijuana realizando escala en el D.F., y de Cancún salen 2 vuelos diferentes al D.F. mientras que del D.F. salen 6 vuelos diferentes hacia Tijuana, para determinar cuál es el total de combinaciones que Jorge puede elegir se debe realizar el siguiente cálculo:
2 x 6 = X
12 = X
Así, Jorge puede realizar 12 combinaciones diferentes para elegir sus vuelos.
Given Triangle ABC if sides AB is congruent to side AC, and angle B = 5x +9 , C = 8x-30 Then, find the value of X
Answer:
x = 13
Step-by-step explanation:
When we say side AB is congruent to Side AC it means both side are the same.
This is written Mathematically as:
AB = AC
We are asked to find x
angle B = 5x +9 , angle C = 8x-30
5x + 9 = 8x - 30
Collect like terms
9 + 30 = 8x - 5x
8x - 5x = 30 + 9
3x = 39
Divide both sides by 3
x = 39/3
x = 13
Taylor has 16 crayons, 12 markers, 8 pencils, and 4 pens in his locker. What is the ratio of markers to total items in Taylor’s locker?
Answer:
3:7
Step-by-step explanation:
12:28
6:14
3:7
brainliest please
Which of the following expressions does not represent “half of three times a quantity b”?
A. 2/3b
B. 0.5(3b)
C. 3/2b
D. 1.5b
What is the interest practice of combining campaign contributions from several sources into one larger contribution from the group, so as to increase the groups impact on the candidate
The interest practice described in the question is known as "bundling." Bundling refers to the act of combining individual campaign contributions from multiple sources into a single larger contribution from a group or organization.
Bundling allows interest groups or individuals to pool their resources and present a more substantial contribution to a candidate. By consolidating smaller contributions into a larger sum, bundlers can demonstrate greater financial support and influence.
This practice is often employed by special interest groups, lobbyists, or individuals with shared political objectives who want to maximize their influence on the political process. Bundlers can leverage their collective financial power to gain access to candidates, shape policy agendas, and potentially gain favorable treatment or influence over decision-making.
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If P = (-3,-2) and Q = (1, 6) are the endpoints of the diameter of a circle, find the equation of the circle.
(x +?)^2 + (y - ?)^2 = ?
Answer:
(x+1)²+(y-2)²= 20
Step-by-step explanation:
P = (-3,-2)
Q = (1, 6)
Center (h, k)
C = ((-3+1)/2 , (-2+6)/2)
C = (-2/2 , 4/2)
C = (-1 , 2)
Radius = Distance from the center to point Q
R = √((1-(-1))² + (6-(2))²)
R = √((2)² + (4)²)
R = √(4+ 16)
R = √20
Equation
(x-h)²+(y-k)²= R²
(x-(-1))²+(y-2)²= (√20)²
(x+1)²+(y-2)²= 20
In a standard deck of cards, P(heart)
Answer:
1/4
Step-by-step explanation:
probabillty of hearts. deck of cards is 52 there are 13 hearts so its 13/52 or 1/4
A DMM in ABC stock on the NYSE is approached at the same time by a floor broker who wishes to buy ABC stock at the market and another floor broker who wishes to sell ABC stock at the market. The DMM buys the stock from the floor broker who wants to sell; and then immediately sells that stock for $.01 more to the floor broker who wants to buy. This is an example of:
The DMM buys the stock from the floor broker who wants to sell; and then immediately sells that stock for $.01 more to the floor broker who wants to buy. This is an example of scalping or trading ahead.
Designated Market Maker (DMM) on the New York Stock Exchange (NYSE), the DMM has certain obligations and responsibilities to maintain fair and orderly markets for the stocks they oversee. They are expected to provide liquidity by facilitating trades and maintaining an orderly market.
However, in the scenario you provided, the DMM takes advantage of the situation by executing a trade with a floor broker who wants to sell ABC stock and immediately selling it to another floor broker who wants to buy at a slightly higher price. By doing so, the DMM profits from the price difference, earning an extra $.01 per share.
This practice goes against the principles of fair and orderly markets, as the DMM is essentially prioritizing their own profit over providing fair execution prices for buyers and sellers. It can be considered unethical and may be subject to regulatory scrutiny or penalties, as it undermines the integrity and fairness of the market.
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Hi! Can somebody pls explain to me how to do one of these problems pls......
will give brainliest lol
Answer:
1. Y = -3x
2. Y = -2
3. Y= x + 2
4. Y = 2/3x -1
I HAVE A FELLING
The ellipse x^2/2^2 + y^2/4^2 = 1
can be drawn with parametric equations. Assume the curve is traced clockwise as the parameter increases. If x = 2 cos(t) then y = __
The parametric equations for the ellipse x^2/2^2 + y^2/4^2 = 1, traced clockwise as the parameter increases, are:
x = 2cos(t)
y = -2sin(t)
To find the corresponding y-value for a given x-value on the ellipse, we can rearrange the equation:
x^2/2^2 + y^2/4^2 = 1
y^2/4^2 = 1 - x^2/2^2
y^2 = 4^2(1 - x^2/2^2)
y = ±2sqrt(1 - x^2/2^2)
Since the curve is traced clockwise as the parameter t increases, we can set x = 2cos(t) and y = -2sqrt(1 - x^2/2^2) to trace the lower half of the ellipse:
x = 2cos(t)
y = -2sqrt(1 - (2cos(t))^2/2^2)
y = -2sqrt(1 - cos^2(t))
Using the identity sin^2(t) + cos^2(t) = 1, we can solve for sin(t):
sin^2(t) = 1 - cos^2(t)
sin(t) = ±sqrt(1 - cos^2(t))
Since we want the negative value to trace the lower half of the ellipse, we have:
y = -2sin(t)
Therefore, the parametric equations for the ellipse x^2/2^2 + y^2/4^2 = 1, traced clockwise as the parameter increases, are:
x = 2cos(t)
y = -2sin(t)
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Describe the distribution of streak lengths. What is the typical streak length for this?
We can see that the distribution of Kobe Bryant's distribution is somewhat similar to that of the distribution of streak lengths for the simulated shooter. The distribution of Kobe Bryant's is fewer longer compared to streak lengths. Using the comparison, I found no evidence that the hot hand model fits shooting patterns because if the hot hand model is held for Kobe,I could have more length of Kobe but in this case, the length is only up to 4
A streak length of 1 means a hit followed by a miss.
3 hits in one run and he has 6 misses. The calc_streak user-defined function loaded with the
data can be used to calculate the length of all shooting streaks and examine their distribution.
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(-8) • 2/3 = I dont know and yea I'm confused lol
A coast guard ship patrols an area of 125 square miles . The area the ship patrols is a square . About how long is each side of the square round to nearest mile ! PLEASE HELP
Answer:
11
Step-by-step explanation:
If it is a square, both sides will be equal. Therefore, you need to find out what number times itself equals 125. In the end, you just have to solve \(\sqrt{125}\) which is 11.1803...When you round that number, you get 11.
What is the multiplication sentence for the following diagram?
Answer:
welllllllll thats is the confusion diagram
What is the height, to the nearest tenth of a foot, of a tree that creates a 35-foot shadow when the sun is at an angle of elevation of 35⁰? (do NOT type in units, just the value)
The height of the tree is approximately 20.1 feet.
What is the height of a tree that produces a 35-foot shadow when the sun is at an angle of 35 degrees?To determine the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the length of the shadow) of a right triangle.
tan(35°) = height of tree / 35 feet shadow
Rearranging this formula, we get:
height of tree = 35 feet shadow x tan(35°)
Plugging in the given values and using a calculator, we get:
height of tree = 35 x tan(35°) ≈ 20.1 feet
Therefore, the height of the tree is approximately 20.1 feet.
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Please help trying to answer it can be with or without step with step
tell weather 9(w−9) −2 = −7 + 7(w−8) is one soultion no solution or infinty solution
Answer:
One Solution
Step-by-step explanation:
Calculating 9(w−9) −2 = −7 + 7(w−8)
is on paper is w = 10.
Hope this helps you! :))
Please let me know if its incorrect
what is x (its a parralleligram)
Check the picture below.
Suppose that some consumer's preference, using a Cobb-Douglas utility function U, where U: U(b, c) =b ^50 c^50 . Assuming that the consumer is able to buy $84 on two goods, b and c, where P b =6, and Pc = 7 1. Find the most - preferred, affordable bundle 2. Define the income expansion point 2. Consumer preferences are characterized axiomatically. These axioms of consumer choice give formal mathematical expression to fundamental aspects of consumer behavior and attitudes towards the objects of choice. Explain the axioms of consumer choice and present them in terms of binary relations.
The most-preferred, affordable bundle can be found by maximizing the utility function subject to the budget constraint.
How can we find the most-preferred, affordable bundle?To find the most-preferred, affordable bundle, we need to maximize the utility function U(b, c) = b^50 * c^50 subject to the budget constraint. The budget constraint can be expressed as P_b * b + P_c * c = I, where P_b and P_c are the prices of goods b and c respectively, and I is the consumer's income.
In this case, P_b = 6, P_c = 7, and the consumer's income is $84. We can substitute these values into the budget constraint and rearrange it to solve for one variable in terms of the other. For example, we can solve for b in terms of c or vice versa.
Once we have the relationship between b and c, we can substitute it into the utility function and maximize it to find the combination of b and c that gives the highest utility. This will give us the most-preferred bundle that is affordable.
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i inserted a picture of the question 6, i can give you the answer to the previous question if it helps
For
\(w^2-3w=350\)To be a perfect square trinomial, we need to find a such that
\(\begin{gathered} (w-a)^2=w^2-3w+b \\ b\to\text{constant} \end{gathered}\)Thus,
\((w-a)^2=w^2-2aw+a^2\)Then,
\(\begin{gathered} \Rightarrow w^2-2aw+a^2=w^2-3w+b \\ \Rightarrow-2a=-3 \\ \Rightarrow a=\frac{3}{2} \end{gathered}\)Furthermore,
\(\begin{gathered} \Rightarrow a^2=b \\ \Rightarrow\frac{9}{4}=b \\ \end{gathered}\)We need to add 9/4 to both sides of the equation, resulting in
\(\begin{gathered} w^2-3w+\frac{9}{4}=350+\frac{9}{4} \\ \Rightarrow(w-\frac{3}{2})^2=\frac{1409}{4} \end{gathered}\)HELP ME FOR BRAINETEST
Answer:
1 7/8
Step-by-step explanation:
The answer is 1 7/8.