When (2x-3) squared is subtracted from 5x squared, what is the result

To find the equation of the tangent plane to the parametric surface, we need to find the partial derivatives of x, y, and z with respect to u and v, evaluate them at the point (u, v) = (2, 1), and use them to construct the equation of the tangent plane.

The partial derivatives of x, y, and z with respect to u and v are:

∂x/∂u = 1, ∂x/∂v = 1

∂y/∂u = 10u, ∂y/∂v = 0

∂z/∂u = 1, ∂z/∂v = -1

Evaluating these partial derivatives at (u, v) = (2, 1), we get:

∂x/∂u = 1, ∂x/∂v = 1

∂y/∂u = 20, ∂y/∂v = 0

∂z/∂u = 1, ∂z/∂v = -1

So the normal vector to the tangent plane is:

N = <1, 20, 1> × <1, 0, -1> = <-20, 0, -20>

This normal vector is perpendicular to the tangent plane, so the equation of the tangent plane can be written as:

-20(x - 2) + 0(y - 5) - 20(z - 0) = 0

Simplifying this equation, we get:

-20x + 20z = -40

Dividing both sides by -20, we get:

x - z = 2

Therefore, the equation of the tangent plane to the given parametric surface at the point (2, 5, 0) is x - z = 2.

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Option A. The dealer has 17 cars for sale. The problem provides us with a ratio of cars to trucks on the lot, which is 11 to 33. This means that for every 11 cars, there are 33 trucks.

We are given that there are currently 51 trucks for sale. We can use this information along with the ratio of cars to trucks to determine how many cars are for sale.

We can start by setting up a proportion with the ratio of cars to trucks:

cars/trucks = 11/33

We can then substitute the given value for trucks:

cars/51 = 11/33

To solve for cars, we can cross-multiply and simplify:

[tex]cars = (11/33) * 51[/tex]

cars = 17

Therefore, the dealer has 17 cars for sale.

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The probability that a piece selected at random and is defective given that it is known to be a plate is 0.0588 or 5.88%.

To calculate the probability, we need to use Bayes' theorem: P(defective|plate) = P(plate|defective) * P(defective) / P(plate).

Therefore, P(defective|plate) = 0.2 * 0.0227 / 0.0818 = 0.0588 or 5.88%.

The probability that a cup will be chosen given that it is defective is 0.4 or 40%.

To calculate the probability, we need to use the information given in the table:

Divide the number of defective cups by the total number of defective products: 10/25 = 0.4 or 40%.

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Complete Question:

The following table shows the relationship of 1100 pieces between good and defective made in a ceramic workshop

cup plate vase total

Good 830 85 1415

Defective 10 5

Overall 510 90

What is the probability that a piece is selected at random and is defective given that it is known to be a plate?

What is the probability that a cup will be chosen given that it is defective?

​

Although both grains and grams are weight-measuring units, they are not interchangeable.

The weight of gunshots, arrows, and gunpowder is often measured in the United States using a unit of mass called a grain. A grain weighs around 0.06479891 grams.

In contrast, a gram is a mass unit in the International System of Units (SI) that is often employed in scientific and practical contexts. There are 15.4323584 grains in one gram.

You may multiply the total number of grains by 0.06479891 to convert grains to grams. If you have 500 grains, for instance, you would convert them to grams as follows: 500 grains x 0.06479891 grams per grain = 32.399455 grams.

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Step-by-step explanation:

You can choose from four main ways to detect outliers:

1.Sorting your values from low to high and checking minimum and maximum values.

2.Visualizing your data with a box plot and looking for outliers.

3.Using the interquartile range to create fences for your data.

4.Using statistical procedures to identify extreme values

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57 kilograms is approximately equal to 125.66334 pounds.

A kilogram (symbol: kg) is the base unit of mass in the International System of Units (SI).

A pound (symbol: lb) is a unit of mass used in the imperial and US customary systems of measurement.

1 kg = 2.2046226218 lbs

1 lbs = 0.45359237 kg

To convert 57 kg to pounds, we need to multiply the value in kilograms by 2.20462,

Since one kilogram is approximately equal to 2.20462 pounds.

Therefore,

57 kg multiplied by 2.20462 gives us:

57 kg x 2.20462 = 125.66334 pounds (rounded to five decimal places)

So 57 kilograms is approximately equal to 125.66334 pounds.

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The interpretation of the slope is that it represents the additional cost per mile driven, beyond the initial charge of $30.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

The equation for the total cost of renting the truck is:

C = 30 + 2.50m

where C is the total cost

m is the number of miles driven.

The slope of the equation is the coefficient of "m", which is 2.50. The slope represents the rate of change of the total cost with respect to the number of miles driven.

In this case, the slope of 2.50 means that for each mile driven, the total cost of renting the truck increases by $2.50.

So, the interpretation of the slope is that it represents the additional cost per mile driven, beyond the initial charge of $30.

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Answer: 0.58

Step-by-step explanation: ..

The order of a matrix is a way to describe its size or dimensions in terms of the number of rows and columns it has.

It is typically represented by the notation m x n, where m is the number of rows and n is the number of columns. For example, a matrix with 3 rows and 4 columns would have an order of 3 x 4.

The order of a matrix is important because it determines how the matrix can be operated on or manipulated, such as in matrix addition, multiplication, or transposition.

It is a fundamental concept in linear algebra and is used extensively in many fields, including mathematics, physics, engineering, and computer science.

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The income plainness of demand for eatery reflections is Income plainness = 200/ 20 = 10

Chance is a way of expressing a volume as a bit of 100. It's frequently denoted using the percent symbol(), which represents" per hundred". For illustration, 25 is original to25/100 or0.25 as a numeric.

By question-

The income plainness of demand measures the responsiveness of the volume demanded of a good or service to a change in income, all other effects being equal .However, it means that the good is a normal good, and the volume demanded increases as income increases, If the income plainness is positive. However, it means that the good is an inferior good, and the volume demanded diminishments as income increases, If the income plainness is negative.

In this case, John's pay increased by 20 percent, and the average number of eatery reflections he consumed increased from one a week to three a week. We can calculate the income plainness of demand for eatery reflections as follows

Income plainness = chance change in volume demanded/ chance change in income

The chance change in volume demanded is

( 3 reflections per week- 1 mess per week)/ 1 mess per week) x 100 = 200

The chance change in income is 20

thus, the income plainness of demand for eatery reflections is

Income plainness = 200/ 20 = 10

Since the income plainness is positive and lesser than 1, we can conclude that eatery reflections are a luxury good for John. Option( b) is the correct answer.

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To use back substitution to solve a system of equations, work backwards from the last equation to the first.

Back replacement is a strategy for settling frameworks of conditions by working in reverse from the last condition to the first. To settle an arrangement of conditions utilizing back replacement, follow these means:

Begin with the last condition in the framework and tackle for the variable with the biggest coefficient.

Substitute this worth into the second-to-last condition and tackle for the relating variable.

Keep subbing values from the tackled conditions into the excess conditions, working in reverse until all factors are settled.

Actually look at the arrangement by subbing the qualities into the first conditions.

Back replacement is a valuable technique for tackling frameworks of conditions, particularly when the conditions are in three-sided structure or when Gaussian disposal has been applied. Be that as it may, it may not be the most proficient technique for bigger frameworks, and different strategies, for example, grid reversal or Cramer's standard might be more suitable

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Answer:

Step-by-step explanation:

792!

Answer:

792

Step-by-step explanation:

First she increases 800 by 10 percent

Since 10 percent of 800 is 80, it becomes 880

then she decreases this result by 10 percent

since 10 percent of 880 is 88, the result becomes 880-88=792

Therefore 792 is the final number

All rational functions having two vertical asymptotes are listed below:

Case 3: f(x) = 1 / (x² - 16)

Case 6: f(x) = (x - 3) / [(x + 3) · (x - 5)]

In this problem we must determine which of the six rational functions have only two asymptotes. Rational functions are expression of the form:

R(x) = P(x) / Q(x)

Where:

Both P(x) and Q(x) are polynomials. There are two asymptotes if the simplified form of R(x) has Q(x) with two real roots. The simplication can be done by means of algebra properties. Finally, we proceed to check each expression:

f(x) = - 2 · (x + 2) / [(x + 2) · (x + 3)]

f(x) = - 2 / (x + 3) (One vertical asymptote)

f(x) = (x - 2) / [(x + 2) · (x - 3)] (Three vertical asymptotes)

f(x) = 1 / (x² - 16)

f(x) = 1 / [(x - 4) · (x + 4)] (Two vertical asymptotes)

f(x) = (x + 4) / (x² - 16)

f(x) = (x + 4) / [(x - 4) · (x + 4)]

f(x) = 1 / (x - 4) (One vertical asymptote)

f(x) = (x - 5) / [(x + 3) · (x - 2) · (x - 5)] (Three vertical asymptotes)

f(x) = (x - 3) / [(x + 3) · (x - 5)] (Two vertical asymptotes)

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The solution set for this equation is {4}, since 4 is the only value that makes the equation true.

You have done a great job of explaining how to check if the numbers 3 and 2 are part of the solution set for the equation 13 = 2x + 5. You correctly substituted each number in for x and simplified the equation to see if it was true or false. You found that both numbers resulted in a false equation, so they are not part of the solution set.

One thing to note is that the solution set for an equation is the set of all values that make the equation true. So, in order to find the solution set for this equation, you would need to solve for x. Here is how you would do that:

13 = 2x + 5

Subtract 5 from both sides of the equation:

8 = 2x

Divide both sides of the equation by 2:

4 = x

So, the solution set for this equation is {4}, since 4 is the only value that makes the equation true.

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Answer: Santa Maria to Los Alamos is approximately 2,612,951.6 centimeters.

Step-by-step explanation:

To convert miles to centimeters, we need to use the following conversion factors:

1 mile = 160,934.4 centimeters

So, to find the distance from Santa Maria to Los Alamos in centimeters, we can use the following calculation:

16.25 miles x 160,934.4 centimeters/mile = 2,612,951.6 centimeters

Therefore, the distance from Santa Maria to Los Alamos is approximately 2,612,951.6 centimeters.

1 mile = 160,934 centimeters

16.25 miles = ?

16.25 * 160,934 = ?

16.25 miles = 2,615,184 centimeters

In metric system distance measured by using kilometres and miles units. Thus, the conversion of one kilometre to mile is equals to the 0.62137119 miles.

To convert from one unit to another, multiply by a conversion factor. Typically, conversion from kilometers to miles is a conversion of distance from kilometers to miles. Kilometers and miles are used to measure the length from one point to another. In the metric system, the kilometer is a unit of length and is considered the International System of Units, while the mile is used as an English and US customary unit. One kilometer is abbreviated as "km" and one mile is abbreviated as "mi". These two measurements are mainly used to measure the geographical area of land. The following conversion values are used to convert distance measurements from kilometers to miles: 1 kilometer = 0.62137119 miles. A conversion factor is required to convert kilometers to miles. This means that 1 km is approximately equal to 0.62137119 miles.

Hence, required value is 0.62137119 miles.

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Answer:

Benny the tiger costs more to feed each day because he eats 12.5 pounds of meat per day, which costs $38.75 ($3.10 x 12.5). Jasmine eats 200 pounds of hay and alfalfa, which costs $0.00, since hay and alfalfa are not typically purchased with money. Therefore, Benny the tiger costs more to feed each day.

The original expression could be log_2(1/3) / log_10(2).

The change of base formula states that:

log_a(x) = log_b(x) / log_b(a)

where a, b, and x are positive real numbers and a, b ≠ 1.

In the given expression, log1/3 / log2, the denominator is log2, which means that the base of the logarithm in the numerator must be 2 raised to some power.

So we can rewrite the logarithmic expression as:

log1/3 / log2 = log_2(1/3) / log_2(2)

Now we can apply the change of base formula, with a = 2, b = 10, and x = 1/3:

log_2(1/3) / log_2(2) = log_10(1/3) / log_10(2)

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Answer: C

Step-by-step explanation:

Answer:

[tex] \sf \: a) \: 27 = 9p \: ; p = 3[/tex]

Step-by-step explanation:

Given information,

→ Simon have 27 pieces of candy.

→ Each person will get 9 pieces.

Now we have to,

→ Find the required equation.

The equation will be,

→ 27 = 9p

→ 9p = 27

=> As each person (p) gets 9 pieces.

Then the value of p will be,

→ 9p = 27

→ p = 27 ÷ 9

→ [ p = 3 ]

Hence, option (a) is correct.

The value of x when y = 8 is 13.5

If y is inversely proportional to x, it means that their product is a constant value.

We can represent this relationship using the formula:

y * x = k

where k is the constant of proportionality.

We are given that y = 27 when x = 4, so we can solve for k:

27 * 4 = k

This gives

k = 108

Now that we know the value of k, we can use it to find x when y = 8:

y * x = k

This guves

8 * x = 108

So, we have

x = 13.5

Hence, when y = 8, the value of x is 13.5.

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The image is an enlargement of the pre-image |s| > 1. The image is a reduction of the pre-image 0 < |s| < 1. The image is the same as the pre-image rotated 180 s = 1.

We double the length of each of the original shape's sides by a quantity known as a scale factor to enlarge a given shape. The shape will become smaller or larger depending on the scale factor, which can range from 0 to 1. If the scale factor is greater than 1, the shape will become larger. The image, for instance, displays a dilation with a scale factor of two.

The image is an enlargement of the pre-image |s| > 1.

The image is a reduction of the pre-image 0 < |s| < 1.

The image is the same as the pre-image rotated 180 s = 1.

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Answer: 3.1 kg

Step-by-step explanation:

Total amount sold of apples and pears = 6.6 kg

Of that 6.6 kg, 3.5 kg is the weight of the apples.

Subtract the weight of the apples from the total weight of the apples and pears.

6.6 kg (total weight) - 3.5 kg (weight of apples) = 3.1 kg (weight of pears)

Answer: B

Step-by-step explanation:

Answer:

81°

Step-by-step explanation:

the sum of the interior angles of a triangle is 180°.

The base of the 10 triangles make a straight line.  180/10 = 18°

The small angle along the base is 18°

180-18 = 162

The other two angles of the triangle must add up to 162. Since this is a isosceles triangle.  The other 2 angles have the same measurements.

162/2 = 81.  The measurement of the angle we are looking for is 81°

According to the paragraph, some people prefer to step away from conflict for the meantime. More time allows them to contemplate their next action.

Conflicts result from conflicts of interest, viewpoints, or even philosophical concepts. The basis of conflict can be personal, racial, class, caste, political, or even international, thus it will always exist in society.

The scenario in the picture shows how people react or respond to conflict and some people prefer to talk about it right away, while some people prefer to give it some time.

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Therefore , the solution of the given problem of unitary method comes out to be  $1,320, $3,960, and $5,280, respectively.

After determining the dimensions of one tiny slice, multiply the sum by two to complete a work using unitary procedure. The unit variable methodology, which just requires an expression, can be used to equation a coded unit from a certain group or set of groups. 40 pens, for example, might cost Rs. 4,000, which would be equal to $1.01 and 4000 pounds. It's possible that one country will have total control over the method employed to do this. Virtually every living creature has a distinctive quality.

Here,

In 2016, the prices for 1, 3, or 4 gold ounces were $1,320, $3,960, and $5,280, respectively.

In 2016, 2 gold ounces would cost $2,640.

1 ounce of gold costing $2 in 2016 is equal to $2 divided by 2 ounces of gold. in 2016.

= $2,640 ÷ 2

= $1,320

The price of 3 grams of gold for 2016 equals the price of One ounce of gold. multiplied by 3.

= $1,320 × 3

= $3,960

cost of one ounce of gold. in 2016 multiplied by 4 to get the price of 4 ounces of gold. in 2016.

= $1320 × 4

= $5,280

The price of 1, 3, and 4 gold ounces each in 2016 is therefore $1,320, $3,960, and $5,280, respectively.

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Answer:

Step-by-step explanation:

Plug in the functions.

(x^2+3x-5) + (2x+1)

Then, combine like terms.

= x^2 + 5x -4

After converting from Celsius to Fahrenheit , we will get 54 Celsius is equivalent to 129.2 Fahrenheit.

To convert Celsius to Fahrenheit, you can use the following formula:

°F = (°C x 9/5) + 32

In this case, to convert 54 Celsius to Fahrenheit, we can substitute 54 for °C in the formula:

°F = (54 x 9/5) + 32

Simplifying this expression, we can first perform the multiplication and division:

°F = (97.2) + 32

Then we can add 97.2 and 32 to get the final answer:

°F = 129.2

It's worth noting that the Celsius and Fahrenheit scales are both used to measure temperature, but they have different starting points and different degrees of scale. Celsius is based on the freezing and boiling points of water, where 0 degrees Celsius is the freezing point and 100 degrees Celsius is the boiling point at sea level.

Fahrenheit, on the other hand, is based on a system of degrees devised by Gabriel Fahrenheit, with 32 degrees being the freezing point and 212 degrees being the boiling point at sea level.

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