corey has 42 feet of fencing around his garden. The garden is rectangular in shape, and its length is equal to twice the width minus 3 feet. Define the variables, and write a system of equations to find the length and width of the garden

To find the visible part of the longitude line from an altitude of 5 miles, we can use the Law of Sines in combination with the given angle of 173.7 degrees. The resulting arc length signifies what portion of the Earth is visible from this altitude.

This question pertains to plane geometry and spherical geometry. Given that the angle formed by the lines of sight to the northern and southern horizons is 173.7 degrees when flying at an altitude of 5 miles, we can find the visible part of the longitude line using the Law of Sines.

Imagine a figure with a central angle of 173.7 degrees and a radius of 5 miles (the altitude of the airplane). Here, the radius of Earth is 3959 miles. Thus, from the center of the Earth to the airplane is a total of 3959+5 = 3964 miles.

Using the law of sines, we have: (sin(173.7 deg) / s) = (1 / 3964). Simplifying this gives us the arc length, s, which is the visible part of the longitude line. This visible part signifies the portion of the Earth you can see from the airplane's perspective.

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Using the horizon line formula, D = 112.88 km x √h, where h is the height in kilometers, we can determine the length of the longitude line visible from 5 miles up. This calculation takes into account, but barely modifies for not looking at a perfect 180-degree angle.

In order to find out how much of the longitude line directly under the plane is visible from 5 miles high, we need to apply some mathematical and geographical concepts. The key concept here is the idea of the horizon line, which is the furthest point you can see from a given point of elevation.

Using the formula D = 112.88 km x √h, where h is the height in kilometers (in this case, 5 miles or approximately 8.05 km), you would calculate D = 112.88 km x √8.05. This calculation gives you the distance to the horizon or how much of the line directly beneath the plane is visible.

However, the student's question also mentions an angle of 173.7 degrees - it represents nearly a complete observable circle from the airplane (as 180 degrees would be a complete straight line view). So, the observable part of longitude from the plane will also be correspondingly reduced by a very small amount, since we are not looking at a perfect 180 degrees.

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The probability that Sarawong recovers at least five pages of his math homework is 56.6%, using the combinatory principles of probability.

To solve the problem, we need to calculate the probability that Sarawong recovers at least five pages of his math homework after a gust of wind blows the pages out of his hands. This is a probability problem, which is under the field of mathematics. We first need to understand the total possibilities of the pages he could recover, which is combinations of six math pages and four English pages, that is 10 pages pick 7 pages. We add up the probabilities that he recovers 5, 6, or all 7 math pages. We also need to consider that there is no particular order in which the pages are recovered.

The total number of ways to select 7 pages from 10 can be calculated by 10 choose 7, which is 120.

The number of ways to select 5 math pages out of 6 and 2 English pages out of 4 is 6 choose 5 times 4 choose 2, which equals 60. The probability of this case is 60 / 120 which is 0.5.

The number of ways to select 6 math pages and 1 English page is 6 choose 6 times 4 choose 1, which is also 4. The probability is 4 / 120 which is 0.033.

The number of ways to select all math pages is 6 choose 6 and 4 choose 1, which totals 4. The probability is also 4 / 120 which is 0.033.

Therefore, the total probability that Sarawong recovers at least 5 of his math pages is 0.5 + 0.033 + 0.033 = 0.566, or 56.6%. This is the mathematical solution to the problem.

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Sadie will make 3 gallons of punch.

First, let's convert all the measurements to the same unit, such as gallons.

1 gallon = 4 quarts

1 gallon = 8 pints

1 gallon = 16 cups

Now, let's convert each ingredient:

1. Lemon-lime juice: 8 quarts = 8/4 = 2 gallons

2. Vanilla ice cream: 4 pints = 4/8 = 0.5 gallons

3. Orange juice: 8 cups = 8/16 = 0.5 gallons

Now, let's sum up the amounts of each ingredient:

2 gallons (lemon-lime juice) + 0.5 gallons (vanilla ice cream) + 0.5 gallons (orange juice) = 3 gallons

Complete question: Using 8 quarts lemon-lime juice , 4 pints vanilla ice cream , 8 cups orange juice .How many gallons of punch will Sadie make?

The volume of box which is not used is (1728 - 288π) inch³.

Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.

If the diameter of the soccer ball is 12 inches.

So, Volume of box

= length x width x height

= 12 x 12 x 12

= 1728 inch³

and, Volume of ball

= 4/3 πr³

= 4/3π (6)³

= 864/3 π

= 288 π inch³

So, the volume of box which is not used

= 1728 - 288π

Learn more about Volume here:

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Answer:

[tex]\text{The difference is }\frac{x^2+4x-1}{x(x+2)}[/tex]        

Step-by-step explanation:

Given two expression, we have to find the difference of these two.

[tex]\frac{x+5}{x+2}-\frac{x+1}{x^2+2x}[/tex]

[tex]=\frac{x+5}{x+2}-\frac{x+1}{x(x+2)}[/tex]

[tex]\text{Taking (x+2) common from the denominator }[/tex]

[tex]=\frac{1}{x+2}((x+5)-\frac{x+1}{x}[/tex]

[tex]=\frac{1}{x+2}(\frac{x(x+5)-(x+1)}{x})[/tex]

[tex]=\frac{1}{x+2}(\frac{x^2+5x-x-1}{x}[/tex]

[tex]=\frac{1}{x+2}(\frac{x^2+4x-1}{x})[/tex]

[tex]=\frac{x^2+4x-1}{x(x+2)}[/tex]

which is required difference.

Answer:

630 cm 3 is the answer to the question

Answer:

D.  x^2 = -16y

Step-by-step explanation:

got it right on edge

Answer:

It is q i  think

Step-by-step explanation:

Answer: 25

Step-by-step explanation:

Pythagorean theorem

c=√a²±b²

So it was 7=A

And it was 24=b

solving that it gives us 25

This isn’t that much of help sorry but this is the basic info on how to solve it you can learn more by searching videos about the Pythagorean thermom.

Hope this helps-A

The maximum width of the slot is 25cm (Option A).

To find the maximum width of the mail slot, we need to calculate the length of the diagonal (the dotted line) in the rectangle. The diagonal of a rectangle can be found using the Pythagorean theorem.

Given:

- The length of the rectangle (one side) = 24 cm

- The height of the rectangle (other side) = 7 cm

The formula for the diagonal [tex]\( d \)[/tex] is:

[tex]\[ d = \sqrt{(length)^2 + (height)^2} \][/tex]

Substituting the given values:

[tex]\[ d = \sqrt{24^2 + 7^2} \][/tex]

[tex]\[ d = \sqrt{576 + 49} \][/tex]

[tex]\[ d = \sqrt{625} \][/tex]

[tex]\[ d = 25 \, \text{cm} \][/tex]

So, the maximum width of the mail slot is 25cm.

Full Question:

Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.

The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.

What is the maximum width of the mail slot?

A) 25

B) 31

C) 22

D) 20

To express ln x + a ln y - b ln z as a single logarithm, use the properties of logarithms.

To express ln x + a ln y - b ln z as a single logarithm, we will use the properties of logarithms. The key properties we will use are:

Using these properties, we can simplify the expression:

ln x + a ln y - b ln z = ln x + ln(y^a) - ln(z^b)= ln (x(y^a)/(z^b))

So, the given quantity can be expressed as a single logarithm: ln (x(y^a)/(z^b))

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