Which one of the equations is equivalent to the given equation? 2x + 3y = 10

The dimensions of the rectangular garden which minimize the cost is equal to 9.6ft and 14.6ft respectively.

As given in the question,

Cost of brick wall is equal to $40/ft

Cost of metal fencing is equal to $20/ft

Let 'x' and 'y' are the dimensions of the rectangular garden

Area of the rectangular garden = 142 square feet

⇒ 142 = xy

⇒x = 142/y

Costing of four side fencing 'C' = 40x + 20x + 20y + 20y

⇒ C = 60x + 40y

⇒C = 60(142/y) + 40y

⇒C = 8520/y + 40y

Differentiate with respect to y

dC/dy = -8520/ y² + 40

Put dC/dy = 0

-8520/ y² + 40 = 0

⇒y² = 8520/40

⇒y = √213

⇒ y= 14.6 ft

⇒ x= 142/14.6

     = 9.7 ft

Therefore, the dimensions of the rectangular garden with the given area which minimize the cost is equal to 14.6ft and 9.7ft.

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For the given function, the critical point is (-1,2), relative extrema is is 2, and saddle points is zero.

To find the critical points of a function, we need to find where the partial derivatives of the function are equal to zero or do not exist. In other words, we need to find the points where the function is not changing with respect to x and y. The partial derivative of f(x,y) with respect to x is:

fx = 2x + 2

And the partial derivative of f(x,y) with respect to y is:

fy = 2y - 4

To find the critical points, we set both partial derivatives to zero and solve for x and y:

fx = 2x + 2 = 0

=> x = -1

fy = 2y - 4 = 0

=> y = 2

So, the critical point of the function is (-1, 2).

To determine whether this critical point is a relative maximum, minimum, or saddle point, we need to look at the second partial derivatives of the function. The second partial derivative of f(x,y) with respect to x is:

fx = 2

And the second partial derivative of f(x,y) with respect to y is:

fy = 2

The mixed partial derivative of f(x,y) with respect to x and y is:

fy = 0

To classify the critical point, we can use the second derivative test.

If fx and fy are both positive (or both negative) at the critical point, then the critical point is a relative minimum (or maximum), respectively.

If fx and fy have different signs, then the critical point is a saddle point. If the second derivative test is inconclusive, then we need to use additional methods to determine the nature of the critical point.

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Complete Question:

Find the critical points, relative extrema, and saddle points of the function. (If an answer does not exist, enter DNE.) f(x, y) = x² + y² + 2x - 4y + 2

Answer:

51:120

Step-by-step explanation:

since 120 is length in mm, it is the y value

since 50 is width in mm it is the x value

51mm:120mm

The whole given data sets can have their median calculated after being arranged either in an ascending or descending order. That is option A,B,C,D and E.

The median of a data set is defined as the data that is found at the center, otherwise known as the measure of center of a data set, after being arranged in ascending or descending order.

For example the median of option A) is calculated as follows:

Data set= 23,62,68,73,75,77

Median = 68+73/2 = 70.5

Therefore the median is between 68 and 73 which is = 70.5

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The table can be summarized as follows:

|          | Has a dog | Does not have a dog |

|----------|-----------|---------------------|

| Has a cat     | 2         | 3                   |

| Does not have a cat | 12        | 10                  |

To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.

The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.

The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.

So, the probability that a student chosen randomly from the class has a cat is 5/27.

Answer: 20

Step-by-step explanation: If you look at how 4 got to 8 you multiplied it by two, so therefore, you multiply 10 by 2 also to get twenty.

Answer:

Step-by-step explanation

if in triangle 1 it’s four and its 8 in the 2nd one

multiply each number on the first triangle

f-e 20

Answer:

4 ( a+2)

Step-by-step explanation:

The average rate of change is

(f(a) - f(2))/(a-2)

f(a) = 4a^2 -8

f(2) = 4*2^2 -8 = 4*4 -8 = 16-8 = 8

(4a^2 - 8  - 8))/(a-2)

(4a^2 -16) / (a-2)

Factor the numerator

4( a^2 -4) / (a-2)

4( a-2)(a+2) / (a-2)

Cancel

4 ( a+2)

The value of x in the given figure is 8.

In the given figure there are two lines which are parallel.

We have to find the value of x.

In the straight line the sum of angles is 180 degrees.

8x+1+115=180

8x+116=180

Subtract 116 from both sides:

8x=180-116

8x=64

Divide both sides by 8:

x=64/8

x=8

Hence, the value of x in the given figure is 8.

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Answer:

Step-by-step explanation:

d + 2d = 120

3d = 120

d = 40 m

east distance was 40cos30 + 80cos120 = -5.35898 m

north distance was 40sin30 + 80sin120 = 89.282032

as 30° and 120° bearings are 90° apart, Jason needs to walk

D = √(d² + (2d)²) = d√5 or 40√5 meters or about 89.44 m to return to his original position.

we could also use √(-5.35898² + 89.282032²) = 89.44 m

direction will be

θ = arctan -89.28/5.359 = -86.565° or a bearing of 273.4°

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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The difference between the depths in February and July is 31 feet.

The method of measuring depth depends on what we are trying to measure the depth of. Here are some general methods for measuring different types of depth:

Depth of water: The depth of water can be measured using a sounding device such as a sonar or a simple depth gauge. A sonar uses sound waves to determine the distance from the water's surface to the bottom. A depth gauge is a simple device that measures the distance from the surface of the water to the bottom using a weight and a line.

Depth of a hole: The depth of a hole can be measured using a tape measure or a ruler. Simply insert the measuring device into the hole and measure the distance from the top of the hole to the bottom.

Depth of a trench: The depth of a trench can be measured using a measuring tape or a surveyor's level. Place the measuring device at the edge of the trench and measure the distance from the top of the trench to the bottom.

Depth of a pool: The depth of a pool can be measured using a pool depth marker or by using a measuring tape. A depth marker is usually located on the side of the pool and indicates the depth at various points. Alternatively, you can use a measuring tape to measure the distance from the surface of the water to the bottom of the pool.

Depth of a well: The depth of a well can be measured using a well sounder or a tape measure. A well sounder is a device that sends a signal down the well and measures the time it takes for the signal to bounce back. The time it takes is then used to calculate the depth of the well. Alternatively, a tape measure can be used to measure the distance from the surface of the water to the bottom.

Given, In February, it measured 6 ft deep, or |−6| and in July, it was 25 ft deep, or |−25|.

The difference between the depths in February and July is:

|−6| − |−25| = 6 − (−25) = 6 + 25 = 31

Therefore, the correct choice is B) 31 feet.

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There are two angles for the sine function such that sin θ = - 0.093: (i) 185.3°, (ii) 354.7°.

In this problem we must determine two values of the angle of the sine function such that its result is - 0.093. According to the features of the trigonometric function, sine is negative for angles between 180° and 360°.

Since trigonometric functions are trascendent functions, we can only obtain approximate values of the angle by means of inverse trigonometric functions and numerical methods. There are two possible solutions:

sin⁻¹ - 0.093

θ₁ ≈ 185.336° or θ₂ ≈ 354.664°

θ₁ ≈ 185.3° or θ₂ ≈ 354.7°

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The 0.2 mm spacers will be utilized in order to achieve the correct valve clearance.

On motorcycle and automobile engines, valve clearances essentially refer to the gap or distance between the top of the valve stem and the camshaft that controls it.

The exhaust valves in an automobile engine release the burned gases, while the intake valves permit air and fuel into the cylinder.

Given that:

The difference in between the current and clearance range is:

However, for clearance to be positioned within 0.18 mm - 0.22 mm. The required spacers to be used are 0.04 mm, and 0.08 mm in conjunction with:

The mean value = 3.04

Therefore, for us to approach and get to the value of 3.02, the required spacers to be that must be added are:

Therefore, we can conclude that the 0.2 mm spacers will be utilized in order to achieve the correct valve clearance.

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Answer: mannn i dunno either i’m tryna figure out the same thing

Step-by-step explanation:

The value of k in the expression is equal to 2.

The expression is in the form of Cubic polynomial. A cubic polynomial is the one which can be written in the form y = ax³ + bx² + cx + d where a, b, c and d are coefficients and x, and y are independent and dependent variables respectively.

here, we have,

given that,

The cubic polynomial,

f(x) = 2x^4 + 6x^3 – 10x^2 + kx – 10 ,has a factor equal to (x-1).

If it is the factor, then x = 1 is the solution of cubic polynomial

and at x = 1 the value of f(x) = 0.

2x^4 + 6x^3 – 10x^2 + kx – 10 = 0

2(1)^4 + 6(1)^3 – 10(1)^2 + k(1) – 10 = 0

2 + 6 -10 + k = 0

k - 2 = 0

=> k = 2, which is the required value.

Hence, The value of k in the expression is equal to 2.

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The value of the given equation 3 2/3x = 2 2/5 is 36/55.

A mixed number is one that combines a whole number and a legal fraction. A number that contains both an integer (whole number) and a correct fraction is known as a mixed number or mixed fraction.

Pretzels, peanuts, Cheerios, and of course, rice and corn Chex are all included in this mix, which is why it is called a mix. Mixed numbers are those that contain both an integer and a fraction.

A mixed fraction is a fraction that is represented by both its quotient and remainder. For instance, 2 1/3 is a mixed fraction, where 2 is the quotient and 1 is the remainder. Therefore, a mixed fraction is a combination of a whole number and a proper fraction.

3 2/3x= 2 2/5

11/3 x=12/5

55x=36

x=36/55

Therefore, the value of the given equation 3 2/3x = 2 2/5 is 36/55.

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Answer:

5880 ways

Step-by-step explanation:

For selections like this, we solve using the combination theory. Recall that

nCr = n!/(n-r)!r!

Hence given to find the number of ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies,

= 10C6 * 8C4

= 10!/(10-6)!6! * 8!/(8-6)!6!

= 10 * 9 * 8 * 7 * 6!/4 *3 *2 * 6! * 8 * 7 * 6!/2 * 6!

= 210 * 28

= 5880 ways

The arrangement can be done in 5880 ways

Check the picture below.

Answer:

(c) Pi/4

Step-by-step explanation:

3pi/4 = (3 x 180) / 4 = 135 degrees

135 degrees is equivalent to (180 degrees - 135 degrees) 45 degrees

45 degrees = Pi/4

Therefore, the reference angle of 3pi/4 is Pi/4

Thus, the correct option is (c) Pi/4

The reference angle for 3π/4 is π/4.

So, the correct answer is c) π/4.

Given is an angle 3π/4, we need to find its reference angle,

The reference angle is the acute angle formed between the terminal side of an angle and the x-axis in the coordinate plane.

To find the reference angle for an angle, you need to consider the position of the terminal side of the angle in the coordinate plane and determine the acute angle formed.

In this case, we are given the angle 3π/4. To find the reference angle, we need to consider the position of the terminal side of this angle.

The angle 3π/4 lies in the second quadrant of the coordinate plane, where both the x-coordinate and y-coordinate are negative.

To find the reference angle, we need to find the acute angle formed by the terminal side with the x-axis. In the second quadrant, this acute angle is formed by the vertical line connecting the terminal side to the x-axis.

If we draw a vertical line from the terminal side of 3π/4, it intersects the x-axis at π/4.

Therefore, the reference angle for 3π/4 is π/4.

So, the correct answer is c) π/4.

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Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

the real solutions are the ones that actually cross the x-axis.

so the real solutions are (-5, 0) (-1,0) (4,0) and (8,0)

Answer:

9m  +3

Step-by-step explanation:

6m-4+3m+7

Combine like terms

6m+3m    -4+7

9m  +3

Answer:

−3⋅(5m+7)

Step-by-step explanation: