need help with two part edulastic question

Need Help With Two Part Edulastic Question

Answers

Answer 1
Know that surface area is squared and volume is cubed.

The surface area of a rectangular prism can be calculated using the formula:
A=2(wl+hl+hw)
A is the area, w is the width, l is the length, and h is the height.
A=2·(6.5·11+10·11+10·6.5)
A=493in^2
The surface area of this rectangular prism is 493in^2.

The volume of a rectangular prism can be calculated using the formula:
V=l x w x h
V=6.5·10·11
V=715in^3
The volume of this rectangular prism is 715in^3.

Hope this helped!

Related Questions

..................................................................................................................

Answers

Answer:

(-3, -2)

Step-by-step explanation:

In terms of a scatterplot, an outlier is an individual data point that lies at an unusually extreme position relative to the other data points in the scatterplot.

To determine which of the given ordered pairs would be considered an outlier for the given scatterplot, plot the ordered pairs and observe how far away they are from the line of best fit.

After plotting the ordered pairs on the scatterplot (see attachment), we can see that point (-3, -2) is farthest away from the line of best fit. The other three points are very close to the line of best fit.

Therefore, (-3, -2) would be considered an outlier comparatively to the other ordered pairs.

Answer: Your answer is (-3, -2)

Step-by-step explanation: Outlier means the one that stands out in the bunch. So when you look at the coordinates of (-3, -2) you can see it is the farthest of the bunch. If you look at the other answers you can see that they are not as far away as (-3, -2)

P(R) = 1/3 P(R & W) = 2/19

What is P(W|R)?

Group of answer choices

9/16

19/51

6/19

51/19

Answers

The probability of event W occurring given that event R has occurred is 6/19. Among the given answer choices, the correct probability is 6/19.

To find P(W|R), we can use the conditional probability formula:

P(W|R) = P(W & R) / P(R)

Given that P(R) = 1/3 and P(R & W) = 2/19, we can substitute these values into the formula:

P(W|R) = (P(R & W)) / P(R) = (2/19) / (1/3)

To divide by a fraction, we can multiply by its reciprocal

P(W|R) = (2/19) * (3/1) = 6/19

Therefore, the probability of event W occurring given that event R has occurred is 6/19.

Among the given answer choices, the correct probability is 6/19.

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What is the slope of a line passing through the points (2,3)
and (5,3)?
Enter your answer as a number, like this: 42

Or, if the slope is undefined, enter a lowercase letter "u," like this: u

Answers

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 3 ) and (x₂, y₂ ) = (5, 3 )

m = [tex]\frac{3-3}{5-2}[/tex] = [tex]\frac{0}{3}[/tex] = 0

a line with a slope of zero is a horizontal line parallel to the x- axis


For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of
your response as Part A, Part B, and Part C.
Part A: Suppose event A and event B are mutually exclusive. Is the statement P(A and B)-0 true?
Part 9: Explain why or why not to support your answer to Part A.
Part C: Provide an example to support your explanation.

Answers

Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

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PLEASE HELP
Question 7 (5 points)
60°
a
30°
The triangle above has the following measures.
=10 yd
b=10√3 yd
Use the 30-60-90 Triangle Theorem to find the
length of the hypotenuse. Include correct units
Show all your work

Answers

A^2 + B^2 = C^2

100 + 300 = C^2

Sqrt(400) = 20

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

The sum of the measures of the exterior angles of a convex 21-gon is 360°.

Given,

Convex 21- gon

Polygon is a plane figure with a finite number of straight line segments.

Convex polygons are those in which none of their interior angles are greater than 180°.

Now,

The sum of exterior angles of any regular polygon is 360°.

Hence,

The sum of the measures of the exterior angles of a convex 21-gon is 360°.

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4. Higher Order Thinking A national TV
news show conducted an online poll to find
the nation's favorite
comedian. The
website showed
the pictures of
5 comedians and
asked visitors of the
site to vote. The news
show inferred that
the comedian with
the most votes was
the funniest comedian
in the nation.


a. Is the inference valid? Explain.



b. How could you improve the poll? Explain.

Answers

No, the inference is not valid because it excluded those who were not online and so did not see the poll.

To improve the poll, the news show could have conducted it in a more representative manner by surveying a larger sample of people from a variety of backgrounds

How to improve the poll ?

The poll's results may have been influenced by various factors, including but not limited to the order in which the comedians were presented, the demographics of the respondents, and the fact that it was conducted online, possibly excluding those without internet access. Overall, the poll's representative accuracy is questionable.

To enhance the accuracy of the survey, the broadcast could have implemented a more inclusive method by polling a wider range of individuals from diverse backgrounds. An alternate method for conducting the poll would have been by personal or telephonic means, enabling individuals without internet connectivity to participate.

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What numbers are missing from the pattern below? Enter your answer, using
a comma to separate each number.
57, 53, 49, 45, ?, ?, ?, ?, 25, 21, 17, 13
Answer here

Answers

The numbers that are missing from the pattern are 41, 37, 33, and 29

How to determine the numbers that are missing from the pattern

From the question, we have the following parameters that can be used in our computation:

57, 53, 49, 45, ?, ?, ?, ?, 25, 21, 17, 13

The above pattern is an arithmetic pattern that has the following features

First term = 57

Common difference = 4

using the above as a guide, we have the following:

Next term = 45 - 4 = 41

Next term = 41 - 4 = 37

Next term = 37 - 4 = 33

Next term = 33 - 4 = 29

Hence, the numbers that are missing from the pattern are 41, 37, 33, and 29

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she uses 3 inch by 3 foot strips of nylon. She will cut 12 separate peices. What are the side lengths of each piece? Round to the nearest tenth​

Answers

The solution is: 114 inches of wood, in inches, did Maya use in all.

Here, we have,

First, we must remember:

1 foot = 12 inches

Knowing that, let's solve the exercise:

• She made 5 strips, and in each one she used 14 inches of wood.

So, 5 * 14 = 70 inches

• 3 strips, each with 1 foot. So, 3 * 12 = 36 inches

• 4 strips, each with 1/6 foot. So, 4 * 2 = 8 inches

In all, she used 70 + 36 + 8 = 114 inches of wood.

Hence, The solution is: 114 inches of wood , in inches, did Maya use in all.

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complete question:

Maya cut a length of wood into strips to make 5 small picture frames. She used 4 inches of wood for each frame. For another project she cut another length of wood into 3 strips of 1 foot each and 4 strips of = foot 3 4 each. How much wood, in inches, did Maya use in all? Show your work.

I want to buy a house in 4 years. I need a down payment of $50,000. How much do I need to have today in order to have a down payment, if I can earn 3%?

Answers

To calculate the amount you need to have today in order to have a down payment of $50,000 in 4 years with an annual interest rate of 3%, you can use the concept of compound interest.

The formula to calculate the future value (FV) of an investment with compound interest is:

FV = PV * (1 + r)^n

Where:
FV = Future Value
PV = Present Value (initial investment)
r = Interest rate per period
n = Number of periods

In this case, you want to find the present value (PV), so we rearrange the formula:

PV = FV / (1 + r)^n

Plugging in the values:
FV = $50,000
r = 3% = 0.03
n = 4 years

PV = $50,000 / (1 + 0.03)^4
PV = $50,000 / (1.03)^4
PV = $50,000 / 1.1255
PV ≈ $44,444.44

Therefore, you would need to have approximately $44,444.44 today in order to have a down payment of $50,000 in 4 years, assuming an annual interest rate of 3%.

HELPPP MEEE PLEASEE WITH THIS QUESTION

Answers

The values of x and y are given as follows:

x = 18.[tex]y = 6\sqrt{10}[/tex]

What is the geometric mean theorem?

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases for this problem are given as follows:

2 and x.

The altitude is given as follows:

6.

Hence the length x is given as follows:

2x = 6²

2x = 36

x = 18.

Applying the Pythagorean Theorem, the length y is given as follows:

y² = 18² + 6²

y² = 360

[tex]y = \sqrt{36 \times 10}[/tex]

[tex]y = 6\sqrt{10}[/tex]

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need help urgently, don’t think the answers i have are right and i don’t know how to do it!!!

Answers

Answer:

See attached graphy-intercepts =   [tex]\dfrac{3}{2}[/tex]

Roots: x = - 3
Vertical asymptote: x = -2
Horizontal asymptote y = 1End behavior
[tex]\mathrm{as}\:x\to \:+\infty \:,\:y\to \:1,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:y\to \:1[/tex]
Table:
x                y-4            1/2 - 3            0-1               20               3/21                4/32                5/43               6/5Note that the function is undefined at x = -2

Step-by-step explanation:

Given function is

[tex]f(x) = \dfrac{\left(x^2-9\right)}{\left(x^2-x-6\right)}[/tex]

Part 1

Graph attached

y-intercepts can be found by finding f(0) ie the value of f(x) at x = 0

[tex]f(0) = \dfrac{\left(0^2-9\right)}{\left(0^2-0-6\right)} = \dfrac{-9}{-6} = \dfrac{3}{2}[/tex]


Roots of a function can be found by setting f(x) = 0 and solving for x

Setting f(x) = 0

==> [tex]\dfrac{x^2-9}{x^2-x-6} = 0\\\\[/tex]

We can factor the numerator  as follows:
x² - 9 = (x + 3) (x -3)     since (a + b)(a-b) = a² - b²

Denominator can be factored as follows
x² - x - 6 = (x-3)(x+2)

So
[tex]f(x) = \dfrac{(x + 3)(x-3)}{(x-3)(x+2)}\\\\[/tex]

The (x-3) term cancels leaving
[tex]f(x) = \dfrac{x+3}{x+2}[/tex]

Setting this equal to 0 gives
[tex]\dfrac{x+3}{x+2} = 0[/tex]

This is 0 when x + 3 = 0 or x = -3

So there is only one root and that is x = -3

Asymptotes

The vertical asymptote occurs when at a value of x when the denominator becomes 0

The given function has been factored as
[tex]f(x) = \dfrac{x + 3}{x + 2}[/tex]

The denominator becomes 0 at x = -2
Vertical asymptote is x = - 2

To find the horizontal asymptote use the fact that when the degrees of the numerator and denominator are equal, the horizontal asymptote is given by
[tex]y=\dfrac{\mathrm{numerator's\:leading\:coefficient}}{\mathrm{denominator's\:leading\:coefficient}}[/tex]

The degree of the numerator x + 3 is 1 and the degree of the denominator x + 2 is also 1

So the horizontal asymptote is y = 1/1 = 1

y = 1 is the horizontal asymptote

End behavior is the behavior of the function as x → ±∞  

This is determined by examining the leading term of the function and determining what its behavior is as x → ±∞

In the function
[tex]f(x) = \dfrac{x + 3}{x + 2}[/tex]
which is the factored form of the originally given function
the domain of x = all real numbers with the exception of -2 since at x = -2, the function is undefined

The end behavior can be determined by finding the limit of f(x) as x tends to infinity

[tex]\lim _{x\to \infty \:}\left(\dfrac{x+3}{x+2}\right)\\\\\dfrac{x+3}{x+2} \text{ can be transformed by dividing by x both numerator and denomiator :}\\\\\\=\dfrac{\dfrac{x}{x}+\dfrac{3}{x}}{\dfrac{x}{x}+\dfrac{2}{x}}\\\\\\=\dfrac{1+\frac{3}{x}}{1+\dfrac{2}{x}}[/tex]

[tex]\lim _{x\to \infty \:}\left(\dfrac{x+3}{x+2}\right) \\\\\\\\=\lim _{x\to \infty \:}\left(\dfrac{1+\dfrac{3}{x}}{1+\dfrac{2}{x}}\right)\\\\\\\\=\dfrac{\lim _{x\to \infty \:}\left(1+\dfrac{3}{x}\right)}{\lim _{x\to \infty \:}\left(1+\dfrac{2}{x}\right)}[/tex]

[tex]\lim _{x\to \infty \:}\left(1+\dfrac{3}{x}\right) = 1\\\\\lim _{x\to \infty \:}\left(1+\dfrac{2}{x}\right) = 1[/tex]

[tex]\lim _{x\to \:-\infty \:}\left(\dfrac{x+3}{x+2}\right) = 1[/tex]

End behavior
[tex]\mathrm{as}\:x\to \:+\infty \:,\:y\to \:1,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:y\to \:1[/tex]

Table:
x                y

-4            1/2

- 3            0

-1               2

0               3/2

1                4/3

2                5/4

3               6/5

Note that the function is undefined at x = -2

2 A car dealer, at a year-end clearance, reduces the price of last year's models by a certain amount. If a certain four-door model has been sold at a discounted price of Birr 51,000, with a discount of Birr 9,000, what is the percentage of discount?

Answers

The four-door model is sold at 15% discount.

Discount is the difference between list price and selling price.

List price is the original price of the product set by the seller.

Selling price is the price at which the product is actually sold.

We know that percentage of discount is:

Discount % = (Discount/ List price) * 100

where Discount= List price- Selling price

       ⇒ List price= Discount + Selling Price

       ⇒ List price = 9000 + 51000 = Birr 60,000

Calculating the discount percentage based on above mentioned results:

Discount % = (Discount/ list price)*100

⇒ (9,000/60,000)*100 = 15%

Therefore the percentage of discount for the four-door model sold at discounted price of Birr 51,000 with discount of Birr 9,000 is 15%.

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Show that the partition of G into left cosets of H is different from its partition into right cosets?

Answers

It is shown below that the partition of G into left cosets of H is different from its partition into right cosets when n ≥ 3.

How to prove right cosets?

Let us first find the left cosets of H in G:

H = {1, s₀}

s₁H = {s₁, s₁s₀}

s₂H = {s₂, s₂s₀}

s₃H = {s₃, s₃s₀, s₂s₁, s₂s₁s₀}...

Now, find the right cosets of H in G:

H = {1, s₀}

Hs₁ = {s₁, s₀s₁}

Hs₂ = {s₂, s₀s₂}

Hs₃ = {s₃, s₀s₃, s₁s₂, s₀s₁s₂}...

Observe that the left cosets of H in G and the right cosets of H in G are not the same when n≥3. This is because s₁s₀ is not in H, but s₀s₁ is in H.

Therefore, the left coset s₁H is not the same as the right coset Hs₁. Similarly, s₂s₁s₀ is not in H, but s₀s₁s₂ is in H, so the left coset s₃H is not the same as the right coset Hs₃.

Thus, it is shown that the partition of G into left cosets of H is different from its partition into right cosets when n≥3.

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Which of the following statements is true?

√9 is rational and √10 is rational.

√9 is irrational and √10 is irrational.

√9 is rational and √10 is irrational.

√9 is irrational and √10 is rational.​

Answers

Answer:

[tex]\sqrt{9}[/tex] is rational and [tex]\sqrt{10}[/tex] is irrational

Step-by-step explanation:

The square root of 9 is 3 and the square root of 10 is a decimal that never stops.

Final answer:

The square root of 9 (√9) is rational because it results in an integer, which can be expressed as a fraction (3/1). However, the square root of 10 (√10), yields an approximate decimal that cannot be precisely expressed as a fraction, hence is an irrational number. Thus the statement √9 is rational and √10 is irrational is true.

Explanation:

In Mathematics, a rational number is a number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. Irrational numbers are numbers that cannot be expressed as fractions.

The square root of 9 is √9, which equals 3. This can be expressed as a fraction (3/1), so √9 is rational.

However, the square root of 10 is √10, which equals to approximately 3.16227766017. This cannot be accurately expressed as a fraction, so √10 is irrational.

Therefore, the true statement among the options provided is: √9 is rational and √10 is irrational.

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Math
Florida's B.E.S.T. Standards: Grade 8 GG.5 Make predictions 38C
Recommendations
Submit
times
Skill plans
4) If you spin the spinner 55 times, what is the best prediction possible for the number of
times it will not land on yellow?
You have prizes to r

Answers

Answer:

Assuming that the spinner is fair (i.e., each color has an equal chance of being landed on), we can find the best prediction for the number of times the spinner will not land on yellow by using probability.

There are 6 colors on the spinner, so the probability of the spinner landing on yellow is 1/6. The probability of the spinner not landing on yellow is therefore:

1 - 1/6 = 5/6

This means that for each spin of the spinner, there is a 5/6 probability that it will not land on yellow. If we spin the spinner 55 times, we can expect the number of times it will not land on yellow to be:

55 x 5/6 = 45.83

However, since we cannot have a fractional number of spins, we need to round to the nearest whole number. The best prediction for the number of times the spinner will not land on yellow is therefore 46.

I do not understand why the answer is a) for this equation: y'=2y+x. I assumed that the answer is c) or a), because numbers in the equation are positive, but I'm not sure this is the correct method here​

Answers

The slope field for the differential equation would be D . Graph D .

What are slope fields ?

A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .

The length of line segments represents the magnitude, while the direction indicates the sign of the slope.

The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.

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The figure below is a net for a square pyramid. What is the surface area of the square pyramid, in square inches?

Answers

Answer:

183.89

Step-by-step explanation:

S = square area + area of 4 triangles =

7.1^2 + 4*0.5*9.4*7.1 = 183.89

Answer: your answer is 266.44 square inches

Explanation: Triangles:

6.1x7.6=46.36in

Each triangle is 46.36in

46.36x4=185.44in

Rectangle:

9x9=81in

The rectangle is 81in

All together:

185.44+81=266.44in

So the square is the easiest do 4×4=16

The triangles its just Base×Height/2 in that order so 4×3=12/2=6

Mulitply 6 by 4 because there's 4 triangles and add 16 so 6×4=24+16=40

Hope this helped:)

Find the inverse of the function.
f-¹(x) =
+
f(x) =
1
x - 2
X # 2
, X = 0

Answers

Answer:

The given function is:

f(x) = 1/(x - 2), x ≠ 2

0, x = 2

To find the inverse of the function, we need to solve for x in terms of f(x).

Let y = f(x)

Case 1: When y = 0

If y = 0, then x = 2 as per the definition of the function.

Case 2: When y ≠ 0

y = 1/(x - 2)

1/y = x - 2

x = 1/y + 2

So, the inverse function is:

f-¹(x) = 2, x = 0

1/(x - 2), x ≠ 0 and x ≠ 2

Step-by-step explanation:

please helpppp me i can not figure this out it is an attachment

Answers

If they both start riding at the same time and ride at their current rates, the time is that A. Amy will have to wait 0.5 minute for Sebastian.

How to explain the information

Let v be the speed of Amy and Sebastian.

Option A states that Amy will have to wait 0.5 minutes for Sebastian. This implies that Sebastian is faster than Amy since he catches up to her within half a minute.

Therefore, Amy will have to wait 0.5 minute for Sebastian. This was calculated thus:

V = 3.0 - 2.5

v = 0.5

Therefore, Amy will have to wait 0.5 minute for Sebastian.

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

The interior angles of the trapezium is as follows:

∠P = 80°∠L = 100°∠N = 70°∠M = 110°

How to find the angle in a quadrilateral?

The sum of interior angles in a quadrilateral is 360 degrees. Therefore, the diagram above is a trapezium with 4 sides.

Let's find the measure of each interior angles

2x + 2x + 20 + 2x - 10 + 3x - 10 = 360

9x  = 360

divide both sides by 9

x = 360 / 9

x = 40

Therefore, each interior angles is as follows:

2x = 2(40) = 80 degrees

2x + 20 = 2(40) + 20 = 100 degrees

2x - 10 = 2(40) - 10 = 70 degrees

3x - 10 = 3(40) - 10 = 110 degrees

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Y varies directly as x, and y=9 when x = 27

Answers

If y varies directly as x, when x = 15, the value of y is equal to 5.

If y varies directly as x, we can express this relationship using the formula y = kx, where k is the constant of proportionality.

Given that y = 9 when x = 27, we can substitute these values into the equation:

9 = k x 27

To solve for k, we divide both sides of the equation by 27:

k = 9 / 27

k = 1/3

Now that we know the value of k, we can use it to find y for any other value of x.

Let's find y when x = 15:

y = (1/3) x 15

y = 5

Therefore, when x = 15, y is equal to 5.

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The complete question:

Y varies directly as x, and y=9 when x = 27.

Find the value of y, when x =15.

There are 15 ushers and 9 technicians helping at the Harper Middle School fall play.

Answers

The ratio of technicians to all the helpers at the Harper Middle School fall play is 9 : 24.

What is the ratio of technicians to all the helpers at the Harper Middle School fall play?

The ratio of technicians to all helpers can be calculated by dividing the number of technicians by the total number of helpers.

the ratio of technicians to all helpers = number of technicians/number of helpers

Number of technicians = 9

Total number of helpers = 15 ushers + 9 technicians = 24

The ratio of technicians to all helpers = 9 / 24

The ratio will then be:

The ratio of technicians to all helpers =  9 : 24

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Complete question:

There are 15 ushers and 9 technicians helping at the Harper Middle School fall play. What is the ratio of technicians to all helpers?

Simplify (4x5y³)(-3x³y²).
O-12x85
Ox³y5
O-12x³y6
O-12x¹5,6

Answers

Answer:

-12x⁸y⁵

Step-by-step explanation:

Exponent law:

         xᵃ * xᵇ = xᵃ ⁺ ᵇ

In exponent multiplication, if bases are same, add the exponents.

Multiply the co-efficient.Multiply the variable using the exponent law.

(4x⁵y³) (-3x³y²) = 4*(-3) * x⁵⁺³ * y³⁺²

                        = -12x⁸y⁵

The radius of a circle is 14 yards. What is the circle's circumference?
Use 3.14 for ​.

pls help

Answers

Answer:

Circumference = 87.92 yd

Step-by-step explanation:

We know that formula for circumference (C) of a circle is

C = πd, where d is the diameter.

We know that the diameter is twice the measure of the radius, so we can find the diameter of the circle by multiplying the radius by 2:

d = 2r

d = 2 * 14

d = 28 yd

Now, we can find circumference, remembering to use 3.14 for π

C = 3.14 * 28

C = 87.92 yd

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:

A.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

hope it helps you

Help I don’t know this answer

Answers

Answer:

15*8*10-7*8*11=584

Step-by-step explanation:

N
50°
AOMN~ ARPQ
Find 0.
M
Ө
0 = [?]°
<
P
70°
R

Answers

Answer:

60°

Step-by-step explanation:

In similar triangles, the corresponding angles are congruent.

          ∠O = R

          O = 70°

In ΔOMN,

      ∠O + ∠M + ∠N = 180     {Angle sum property of triangle}

       70 + 50 + Ф    = 180

               120 + Ф  = 180

Subtract 120 from both sides,

                        Ф  = 180 - 120

                         Ф = 60°  

Please help with this I am struggling bad thank you all

Answers

p = speed of the plain in still air

w = speed of the wind

when going headwind, the plane is not really going "p" fast, is really going slower, is going "p - w", because the wind is subtracting speed from it, likewise, when going with the wind the plane is not going "p" fast, is really going faster, is going "p + w", because the wind is adding its speed to it.

we also know that on the way over he flew 2000 miles and on the way back he flew again the same 2000 miles back.

[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&2000&p-w&10\\ \textit{with the wind}&2000&p+w&8 \end{array}\hspace{3.5em} \begin{cases} 2000=(p-w)(10)\\\\ 2000=(p+w)(8) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{2000=(p-w)10}\implies \cfrac{2000}{10}=p-2\implies 200=p-w\implies \boxed{200+w=p} \\\\\\ \stackrel{\textit{using the 2nd equation}}{2000=(p+w)8}\implies \cfrac{2000}{8}=p+w\implies 250=p+w \\\\\\ \stackrel{\textit{substituting "p" from above}}{250=(200+w)+w}\implies 250=200+2w\implies 50=2w\implies \cfrac{50}{2}=w \\\\\\ \boxed{25=w}\hspace{10em}\stackrel{ 200+(25) }{\boxed{225=p}}[/tex]

Determine the solutions of a 2x2 system of linear equations given the augmented matrix representation

| 1 5 0 |
| 0 0 0 |

Answers

The general format of the solution to the system of equations in this problem is given as follows:

(x, -1/5x).

How to solve the system of equations?

Considering the augmented matrix for the system, the system of equations in the context of this problem is defined as follows:

x + 5y = 0.0x + 0y = 0.

The second equation is true for any ordered pair (x,y), hence the system has an infinite number of solutions.

The infinite number of solutions has the format given as follows:

x + 5y =  0

5y = -x

y = -x/5.

Hence the ordered pair is:

(x, -1/5x).

More can be learned about a system of equations at https://brainly.com/question/13729904

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