Simplify the rational expression, if possible.
9y/y^2 − 81

I don't know what to do ;-;

Answer:

Area is 126.5 inches^2

Step-by-step explanation:

Mathematically, to calculate the area of the trapezoid, we use the following mathematical formula;

A = 1/2(a + b) h

here, a and b represents the two parallel sides which is 9 and 14 inches here and h which is the height is 11

Plugging these values into the equation, we have

A = 1/2(9 + 14)11

= 1/2(23)11 = (23*11)/2 = 126.5 inches^2

Given that the surface area of a rectangular prism is 200 cm², we need to determine the dimensions of the rectangular prism that would have the greatest volume.

To determine the length, width, and height of the rectangular prism that would have the greatest volume, we need to use the following formulas:

Surface area of a rectangular prism = 2(lw + lh + wh)

Where l = length,

w = width,

and h = height.

Volume of a rectangular prism = lwh

Using the surface area formula:2(lw + lh + wh)

= 200lw + lh + wh

= 100

Equation 1: w = (100 - lh) / (l + h)

Volume of a rectangular prism = lwh

= l(lh - lh² / (l + h))

Rearranging the equation:V = l³h / (l + h) - lh² / 1

Where V represents volume.To determine the dimensions of the rectangular prism that would have the greatest volume, we need to find the maximum value of the equation above.

To do this, we need to differentiate the equation with respect to l, then equate it to zero. Differentiating with respect to l gives:

(dV/dl) = h(lh + h²) / (l + h)² - h² / (l + h)²

= h(lh - h²) / (l + h)²

Equating to zero:h(lh - h²) / (l + h)² = 0lh - h²

= 0h(l - h)

= 0

Therefore, l = h.

Substituting into equation 1:

w = (100 - lh) / (l + h)

= (100 - l²) / (2l)

Differentiating with respect to l gives:(dw/dl) = (l² - 100) / 2l²

Equating to zero:(l² - 100) / 2l²

= 0l²

= 100l

= ±10 cm

Since the dimensions of a rectangular prism cannot be negative, l = 10 cm.

Substituting into w = (100 - l²) / (2l):

w = (100 - 100) / 20

= 0cm

Substituting l and w into equation 1: lw + lh + wh = 10010h + 0h

= 100h

= 10 cm

Therefore, the length, width, and height of the rectangular prism that would have the greatest volume with a surface area of 200 cm² are:

Length = 10 cm

Width = 0 cm

Height = 10 cm

Therefore, the rectangular prism is a square pyramid. The length and height are equal to 10 cm while the width is equal to 0 cm. The volume of the rectangular prism is equal to 500 cm³.

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The statement that if Σan and Σbn are both convergent series with positive terms, then Σanbn is also convergent is false.

The given statement that if Σan and Σbn are both convergent series with positive terms, then Σanbn is also convergent can be proved false by providing a counterexample. That is, we can provide an example of two convergent series with positive terms whose product series is divergent. To prove the given statement false, we can take the following example series:an = 1/n2bn = n

Then, Σan and Σbn both converge.

We can show this as follows: Σan = 1/12 + 1/22 + 1/32 + 1/42 + … is a well-known convergent p-series with p = 2. Σbn = 1 + 2 + 3 + 4 + … is a divergent series.

However, the product series Σanbn is a divergent series. We can show this as follows:Σanbn = (1/1) + (2/4) + (3/9) + (4/16) + …= Σ(1/n)

This series is known as the harmonic series, which is a well-known divergent series.

Therefore, the given statement is false.

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9514 1404 393

Answer:

  x = 7

Step-by-step explanation:

The angle bisector divides the sides proportionally.

  (3x -12)/6 = 21/14

  3x -12 = 9 . . . . . . . multiply by 6 and simplify

  x -4 = 3 . . . . . . . .  divide by 3

  x = 7 . . . . . . . . . . . add 4

Answer:\(1\frac{1}{2}\)

Answer:

2cos(330º)

Step-by-step explanation:

both equal to √3

Expressing 4cos2(165°) – 2 as a single trignometric function, it will be written as : 2cos(330º)

Trigonometric function can be defined as real functions in mathematics that forms a relationship between an angle of a right-angled triangle to the ratio of the length of two sides.

Trigonometric function is very important as it is mostly concerned with functions of angles and their application in calculation

In conclusion, to express 4cos2(165°) – 2 as a single trignometric function, it will be written as : 2cos(330º)

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Answer:

5

Step-by-step explanation:

41 - 32 = 9

5/9 x 9 = 5

Answer:

Linear Equation: y=-44000x+88922000

Year 2009: $526000

By year 2021, they have no more fund

Step-by-step explanation:

Slope formula is difference of y/difference of x. 79000-70200/2003-2005=

-88000/2=-44000.

To find the y intercept, x=0.

It should be year 0. 44000x2003=88132000+790000=88922000

Now put it into y=mx+b

y=-44000x+88922000

Plug in 2009.

It should equal 526000.

The third-place runner would have been 50.0 meters behind the winner when the winner crossed the finish line.

a) Computation on the assumption that each runner ran at his average speed for the entire race:

The difference in time between the winner and the third-place runner is 10.07 – 9.72 = 0.35 seconds.

Therefore, the third-place runner was behind the winner by a distance of:

(100 m)/(9.72 m/s – 10.07 m/s)

= 1,000 m/(-0.35 m/s)

≈ 285.7 m

(Note: The answer is negative because the third-place runner was behind the winner. The magnitude of the answer represents the distance that the third-place runner was behind the winner.)

b) Computation on the assumption that after an initial acceleration phase, world-class sprinters run at a speed of 12.0 m/s:

If the runners reach a constant speed of 12.0 m/s after an initial acceleration phase, then they will cover the first 50 meters in a time of t = d/v = 50 m/12.0 m/s = 4.17 s.

During this time, the winner would have covered an additional 50 meters and finished the race, while the third-place runner would have covered a distance of only d = v*t = 12.0 m/s x 4.17 s = 50.0 m.

So, the third-place runner would have been 50.0 meters behind the winner when the winner crossed the finish line.

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In the two scenarios, the third-place runner was 3.47m and 4.2m behind when the winner crossed the finish line, assuming constant average speed and a speed of 12m/s respectively.

To answer this question, you need to understand the concept of average speed which is calculated by dividing the total distance traveled by the total time taken.

a) In the first scenario, assuming, both runners maintained a constant speed throughout the race. The speed of the winner is 100m / 9.72s = 10.28 m/s and the speed of the third-place runner is 100m / 10.07s = 9.93 m/s.

When the winner crossed the finish line, the third-place runner was still running for (10.07s - 9.72s) = 0.35s. At his average speed he was (9.93m/s * 0.35s) = 3.47m behind.

b) In the second scenario, if both runners reached the same speed of 12m/s after an initial acceleration phase, the time they spent at this speed will vary.

When the winner crossed the finish line, the third-place runner still needed (10.07s - 9.72s) = 0.35s to finish. At the speed of 12m/s, he was (12m/s * 0.35s) = 4.2m behind.

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If f is an increasing function and g is a decreasing function, then fog will be a decreasing function (option b).

The behavior of the composite function fog when f is an increasing function and g is a decreasing function. To answer this question, let's examine the properties of fog.

1. f is an increasing function: This means that if x1 < x2, then f(x1) < f(x2).
2. g is a decreasing function: This means that if y1 < y2, then g(y1) > g(y2).

Now, let's analyze the behavior of fog(x):

fog(x) = f(g(x))

Let's consider two points x1 and x2 such that x1 < x2.

Since g is a decreasing function, we have:
g(x1) > g(x2)

Now, as f is an increasing function, when we apply f to both sides, we get:
f(g(x1)) > f(g(x2))

This translates to:
fog(x1) > fog(x2)

Since x1 < x2, and fog(x1) > fog(x2), we can conclude that the composite function fog is a decreasing function.

So, the answer to your question is: If f is an increasing function and g is a decreasing function, then fog will be a decreasing function (option b).

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41/7 is approximately 5.86

5.86 is greater than 1

Therefore, 41/7 as a fraction IS greater than one.

Hopefully, that helped! :)

The graph of the equation is plotted and attached

The solution of the equation is at the point (-7, -8)

To find the solution of a graph, you need to identify the point or points where the graph intersects the axis or axes, depending on the number of dimensions of the graph.

The given equation is a linear equation hence the graph will be straight lines. The equations are

-2x  y = 6

x - y = 1

Examining the graph the point of the intersection of the two graphs is seen to be at the point (-7, -8)

Therefore we say that the solution of the equation plotted is (-7, -8)

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Adding the area of the base and the area of the triangular faces, we get the total surface area of the pyramid: 36 + 12sqrt(34) square cm.

The solid right pyramid has a height of 4 cm and a square base with sides of 6 cm. We need to find the volume and total surface area of the pyramid.

To calculate the volume of a pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height. In this case, the base is a square with sides of 6 cm, so the area of the base is B = 6^2 = 36 square cm. Plugging in the values, we have V = (1/3)(36)(4) = 48 cubic cm. Therefore, the volume of the pyramid is 48 cubic cm.

To calculate the total surface area of the pyramid, we need to find the area of the base and the area of the four triangular faces. The area of the base is 36 square cm. The area of each triangular face can be calculated using the formula A = (1/2)bh,

where b is the base of the triangle (the side of the square base) and h is the height of the triangle (the slant height of the pyramid). In this case, the base b is 6 cm and the height h can be found using the Pythagorean theorem: h = sqrt((6/2)^2 + 4^2) = sqrt(18 + 16) = sqrt(34) cm.

Therefore, the area of each triangular face is A = (1/2)(6)(sqrt(34)) = 3sqrt(34) square cm. Since there are four triangular faces, the total area of the triangular faces is 4 * 3sqrt(34) = 12sqrt(34) square cm.

Adding the area of the base and the area of the triangular faces, we get the total surface area of the pyramid: 36 + 12sqrt(34) square cm.

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Answer:

A

Step-by-step explanation:

Answer: their difference in elevation is 188 feet

Step-by-step explanation:

The overall answer of three parts :

The slope is positive. As the size of the home​ increases, the price should also increase.

(a) The variables and units in this regression are:

i) Size of homes ( x )  ( measured in \(ft^2\) )

ii) Selling price in ( y ) ( measured in dollars )

(b) Units of the slope will be :

unit of slope = dollar per square foot (i.e.  y / x )

(c) According to the above slope

The slope will be positive given that the increase of home size is directly proportional to the increase in price.

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The given question is incomplete, complete question is:

A random sample of records of sales of homes from February 15 to April 30, 1993, from the files maintained by the Albuquerque Board of Realtors gives the Price and Size (in square feet) of 117 homes. A regression to predict Price (in thousands of dollars) from Size has an R-squared of 71.4%. The residuals plot indicated that a linear model is appropriate.

Required:

a. What are the variables and units in this regression?

b. What units does the slope have?

c. Do you think the slope is positive or negative? Explain.

Answer:

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Step-by-step explanation:

The distance between the building and the ladder is 34.876 foot.

A triangle in which one of the angle measure is equal to 90 degree is called a right triangle.

The ladder forms a right triangle with the building and the ground,

The length of the triangle is 40 foot

The angle made by the ladder is 29.32 degree

By using Trigonometric Ratios

cos 29.32 = Base /  Hypotenuse

cos 29.32 = Base / 40

0.8718 × 40 = Base

Base = 34.876 foot

Base is the distance between the building and the ladder.

Base of the ladder = 34.876 foot

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Answer:

, hope u understand and happy

Answer:

Oral traditions are things that have been passed down from generations, such as folktales, pieces of art, stories, and more

Step-by-step explanation:

Answer:

Based on the given graph, we can see that the bars representing salaries above $175,000 span a total of 7 employee salaries. Since each bar spans a width of $50,000, we can estimate that the total number of employees making at least $175,000 is approximately 7 multiplied by 50,000 divided by 10,000, which equals 35%. Therefore, the owner can justify the claim that on average an employee makes at least $175,000 by stating that approximately 35% of the current employees already make at least that amount. However, it's important to note that this calculation is based on estimates and assumptions and should not be used as a definitive answer.

This real-world problem has the limitations 75< x <110 and 0< y\(\leq\) 50, hence:

option (C) is the best choice.

The term "inequality" refers to a mathematical expression in which both sides have mathematical signs that are either less than or greater than one another, and the expression is one where the two sides are not on equal footing.

We have:

Your senior vacation is scheduled to include a class trip to a beach. Only when it's between 75 and 110 degrees do guests at the resort get access to the pool. 50 passengers can go with you.

Let y be the number of passengers and x be the temperature

75 to 110 degrees are the range of the temperature.

75 < x < 110

50 passengers can go with you.

0 < y ≤ 50

In order to illustrate this real-world issue, the limitations are 75 <x <110 and 0< y \(\leq\)50.

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The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

If the diagonals of a quadrilateral divide each other proportionally, it is a trapezium.

Let's consider a quadrilateral ABCD, where the diagonals AC and BD intersect at point E. If the diagonals divide each other proportionally, it means that AE/CE = BE/DE.

To prove that the quadrilateral is a trapezium, we need to show that one pair of opposite sides is parallel.

Using the proportionality condition, we can rewrite it as (AE/CE) = (BE/DE) = 1.

By the Converse of the Basic Proportionality Theorem, we know that if two lines are cut by a transversal such that corresponding angles are equal, then the lines are parallel. In this case, AE is parallel to CD, and BE is parallel to AD.

Therefore, we have shown that AB || CD, which is the definition of a trapezium.

If the diagonals of a quadrilateral divide each other proportionally, it can be concluded that the quadrilateral is a trapezium.

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Answer:

d

Step-by-step explanation:

A=pi•r^2 (this is the equation for the area of a circle)

So the diameter is the line going through the circle which in this case is 14, but we need the radius which is half of that being 7

A=pi•7^2

which will be about

153.94

Answer:

7

Step-by-step explanation:

because you take the 6 and the 9 and you see how far apart from each pother that would be 3 so the you add that to the 4 and you get 7.   :)

The standard deviation of a sample proportion is given by the formula:

σ = sqrt((p * (1 - p)) / n)

where σ is the standard deviation, p is the sample proportion, and n is the sample size.

If we want the standard deviation to be one-half of what it was for a sample of size 100, we can write the following equation:

(sqrt((p * (1 - p)) / n)) / 2 = sqrt((p * (1 - p)) / 100)

To simplify the equation, we can square both sides:

((p * (1 - p)) / n^2) / 4 = (p * (1 - p)) / 100

Simplifying further:

100 * n^2 = 4 * 1

n^2 = (4 * 1) / 100

n^2 = 0.04

Taking the square root of both sides:

n = sqrt(0.04)

n = 0.2

Therefore, the sample size should be 0.2. However, since the sample size must be a positive integer, we round it up to the nearest whole number. Therefore, the sample size should be 1.

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The fifth roots of 1024 are complex numbers with different magnitude and angles. The five fifth roots of 1024 are approximately 2, 2cis(72°), 2cis(144°), 2cis(216°), and 2cis(288°).

To find the fifth roots of 1024, we need to determine complex numbers z such that z^5 = 1024. We can express 1024 as 1024cis(0°) in polar form, where the magnitude is 1024 and the angle is 0°.Using De Moivre's theorem, we can find the fifth roots by taking the principal root of the magnitude and dividing the angle by 5.

The principal fifth root has a magnitude of the principal fifth root of 1024, which is approximately 2. Taking the angle of 0° and dividing it by 5, we get 0°.The other four roots can be found by adding multiples of 72° to the angle. These roots have the same magnitude of 2 and angles of 72°, 144°, 216°, and 288°.

Therefore, the five fifth roots of 1024 are approximately 2, 2cis(72°), 2cis(144°), 2cis(216°), and 2cis(288°). These complex numbers represent the solutions to the equation z^5 = 1024.

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Answer: First question for the slope that passes through (-7, -2) and (6,-2) is m = 0. For the line that passes through (5, 3) and 5, -7) is m = 1/0.

I hope this helps!

Step-by-step explanation:

(−7,−2) and (6,−2)

(x₁,y₁) = (−7,−2)

(x₂,y₂) = (6,−2)

y₂ − y₁ / x₂−x₁

= −2 − −2 / 6 − −7

= 0/13

m = 0

m = y₂ − y₁ / x₂ − x₁

= −7 − 3 / 5 - 5

= −100

m = 1/0

The appropriate sample space for this experiment is { I  M P S}

The list of potential outcomes or results for the experiment is represented by the word MISSISSIPPI in the notation above. It is represented using a set notation, where the elements of the set are the possible outcomes.

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Answer:

the value of y equal to 122

Answer:the sum of y is equal to 122