two people start walking in different directions from the same point. one walks south at 4 mph and the other walks west at 3 mph. at what rate is the distance between the walkers increasing two hours later?

Answer:

the aswer is 154

Step-by-step explanation:

multiple

Answer:

3 and half

Step-by-step explanation:

half of seven is 3.5

The a = 0.Substituting the values of a, b, and c in the general equation, we get:y = 0x² + 2x + 3The quadratic function is:y = 2x + 3Answer: The quadratic function is y = 2x + 3.

The given table illustrates the values of a quadratic function. Here is how you can find the quadratic function:Step 1: Write the general form of a quadratic function y = ax² + bx + c, where y is the dependent variable and x is the independent variable. a, b, and c are constants that affect the shape and position of the parabola.Step 2: Substitute the values from the table for x and y to form a system of equations.Step 3: Solve the system of equations to find the values of a, b, and c. Once you have found these values, substitute them into the quadratic equation to get the quadratic function.

The given table is as follows:x   |  0   |  2   |  4  |   6y   |  3   |  1   |  -1  |   -3Step 2:Form a system of equations using the values in the table. Here are the equations:y = a(0)² + b(0) + cy = a(2)² + b(2) + cy = a(4)² + b(4) + cy = a(6)² + b(6) + cStep 3:Solve the system of equations.Using the first equation, y = c. Hence, we have:y = 0²a + 0b + c3 = cThe value of c is 3.Using the second equation, we have:y = 2²a + 2b + 3y = 4a + 2b + 3Subtracting the two equations, we get:- 2a - b = - 2a + b = 2b = 4Therefore, b = 2.Substituting the values of b and c into the first equation, we get:3 = a(0)² + 2(0) + 3

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9514 1404 393

Answer:

  use the slope formula

Step-by-step explanation:

Usually, you are asked for an average slope over some interval. The slope is calculated on that interval the same as it would be if you were given two points, one at each end of the interval.

  m = (y2 -y1)/(x2 -x1)

For example, if you wanted to know the slope on the interval [1, 2] hours, the points you would use would be ...

  (hours, miles) = (1, 25) and (2, 75)

The corresponding slope on that interval is ...

  m = (75 -25)/(2 -1) = 50 . . . . miles per hour

__

You can identify four (4) regions on this graph in which the slope is constant:

  (0, 1) . . . slope is 25 mph

  (1, 2) . . . slope is 50 mph, as computed above

  (2, 3) . . . slope is 0 (the rider has stopped)

  (3, 5) . . . slope is 25 mph

Over different intervals, you need to identify the points involved and use the formula to compute the average slope.

Answer:

Step-by-step explanation:

2

Answer:

Step-by-step explanation:

y = ax

-3 = a×2            {divide both sides by 2}

a = -³/₂

Answer:

my algebra calculator says that x=10.09

the .09 has a line over it btw!

Finding the smallest possible integer value of k requires analyzing the given equation and determining the conditions under which one root is less than 1 and the other is greater than 1.

The equation is:

2^(2x) - 2(k-1)^(2x) + k = 0

Let's break down the conditions step by step.

1. Square root less than 1:

To make the square root less than 1, we need to substitute x = 1 into the equation and get a positive value. So if x = 1, then

2^(2*1) - 2(k-1)^(2*1) + k > 0

4 - 2(k-1)^2 + k > 0

Extensions and simplifications:

4 - 2(k^2 - 2k + 1) + k > 0

4 - 2k^2 + 4k - 2 + k > 0

-2k^2 + 5k + 2 > 0

2k^2 - 5k - 2 < 0 xss=removed xss=removed xss=removed xss=removed > 0.

Now we can combine both conditions to find the smallest integer value of k.

2k^2 - 5k - 2 < 0 > 0 (Condition 2)

By solving these conditions simultaneously, we can find the range of values of k that satisfy both conditions and determine the smallest integer value of k. However, this process requires calculations and algebraic manipulations beyond the scope of simple text-based answers.

It is recommended to use an algebraic calculator or software to solve the equation and find the smallest integer value of k that satisfies the given conditions. 

Answer:

\(4\sqrt{10}\)

Step-by-step explanation:

\(\sqrt{160}\)

\(\sqrt{16 * 10}\)

\(4\sqrt{10}\)

because 16 is a perfect square root and it splits into 4 * 4 while 10 isnt a perfect square root so it stays inside.

Answer:

4\(\sqrt{10}\\\)

Step-by-step explanation:

To reduce a radical of a square root, you want to find a perfect square that multiplies into that number. 16 is a perfect square (of 4) and can be divided into 160. so \(\sqrt{160\\}\) becomes \(\sqrt{16}\) x  \(\sqrt{10}\) (because 16 x 10 = 160) then we simplify the square root of 16 to be 4. We leave the square root of 10 because it cannot be simplified.

Hope this helps!

:)

Answer:

3

Step-by-step explanation:

-5 + 8 = 3

keep inverse opposite:

-5 => -5

- => +

-8 => 8

Answer:

I would say a 20, 30-ish degree angle, maybe 45 degrees, somewhere in that continuum

Answer: Correct option is B)

Put x=3y=4

(3x+4y):(5x+6y)=(3×3+4×4):(5×3+6×4)

                                      =(9+16):(15+24)

                                      =25:39

Step-by-step explanation:

The answer to the question is True. This can be answered by the concept of Trigonometry.

First, let's recall the definitions of the asymptotic notations used in the question

f(n) = O(n²) means that there exists a positive constant c and a positive integer N such that f(n) <= c × n² for all n >= N.

g(n) = Theta(n²) means that there exist positive constants c1, c2, and a positive integer N such that c1 × n² <= g(n) <= c2 × n² for all n >= N.

Now, since f and g are non-decreasing positive functions, we can assume without loss of generality that N > 0 and c1 > 0. Then, for all n >= N, we have:

f(n) <= c × n² (by the definition of O notation)

c1 × n² <= g(n) <= c2 × n² (by the definition of Theta notation)

Multiplying the first inequality by c1, we get:

c1 × f(n) <= c × c1 × n²

Since c1 and n^2 are positive, we can divide both sides by n² to obtain:

c1 × (f(n) / n²) <= c × c1

Now, let's define a new function h(n) = f(n) / n². Since f(n) and n² are both non-decreasing positive functions, h(n) is also non-decreasing and positive. Moreover, for all n >= N, we have:

h(n) <= (c × c1) / c1 = c

Therefore, we have shown that there exists a positive constant c and a positive integer N such that h(n) <= c for all n >= N. This means that h(n) = O(1).

Using this result, we can conclude that:

f(n) = h(n) × n² = O(1) × n² = O(n²)

Therefore, we have:

f(n) = O(n²) and g(n) = Theta(n²) => f(n) = O(g(n))

Therefore, the answer to the question is True.

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To solve for \(\(x\) and \(y\)\), we can use the method of substitution or elimination. hus, we have successfully put the first equation in the required form. Now we need to solve this system of equations to find the value of x. Substituting the value of 2x from equation

Given equations:

Equation \((1): \(2x = 3y + 4\)\)

Let's solve it using the substitution method:

From equation (1), we can express \(x\) in terms of \(y\):

\(\(2x = 3y + 4\)\)

Dividing both sides by 2, we get:

\(\(x = \frac{3}{2}y + 2\)\)

Now, substitute this value of \(x\) into equation (2):

\(\(5x - 6y = -1\)\)

\(\(5\left(\frac{3}{2}y + 2\right) - 6y = -1\)\)

Simplifying the equation:

\(\(\frac{15}{2}y + 10 - 6y = -1\)\)

Combine like terms:

\(\(\frac{3}{2}y + 10 = -1\)\)

Subtract 10 from both sides:

\(\(\frac{3}{2}y = -11\)\)

Substitute the value of \(y\) back into equation (1):

\(\(2x = 3\left(-\frac{22}{3}\right) + 4\)\)

Therefore, the correct solution to the given system of equations is:

\(\(x = -20\) and \(y = -\frac{22}{3}\).\).

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No, we cannot draw a triangle with sides 3 cm, 3.5 cm, and 6.5 cm.

Let's understand the concept behind this:

Apply the triangle's length-of-sides property, which stipulates that the total of any two sides should be more than the value of the third side. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side.

We must determine whether the supplied side lengths constitute a triangle. We now understand that the triangle's third side should be greater than the sum of any two of its sides. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side. So, we'll try every combination and see if it meets the criteria.

Let’s assume AB = 3 cm, BC = 3.5 cm and AC = 6.5 cm.

AB + AC = 3 + 6.5 cm = 9.5 cm > 3.5 cm = BC.

AC + BC = 6.5 + 3.5 = 10 cm > 3 cm = AB.

AB + BC = 3 + 3.5 cm  = 6.5 cm = AC.

However, in this case, the length of the third side is equal to the total lengths of the other two sides, which renders the triangle's condition incorrect.

Therefore, there does not exist any triangle with sides of 3 cm, 3.5 cm, and 6.5 cm.

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Answer:

Perimeter, P = 112 meters

Step-by-step explanation:

Translating the word problem into an algebraic expression, we have;

L = 6W  ...... equation 1

Given the following data;

To find the perimeter of the rectangle;

First of all, we would determine the dimensions of the rectangle using its area.

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = LW  ..... equation 2

Substituting eqn 1 into eqn 2, we have;

384 = 6W(W)

384 = 6W²

Dividing both sides by 6, we have;

W² = 384/6

W² = 64

Taking the square root of both sides, we have;

W = √64

Width, W = 8 meters

Next, we would find the length;

L = 6W

L = 6 * 8

Length, L = 48 meters

Lastly, we would determine the perimeter of the rectangle using the above dimensions;

Mathematically, the perimeter of a rectangle is given by the formula;

Perimeter = 2(L + W)

Substituting the values into the formula, we have;

Perimeter, P = 2(48 + 8)

Perimeter, P = 2(56)

Perimeter, P = 112 meters

The conclusion regarding the publisher's claim is that it is not valid. When the testing firm rejected the null hypothesis after performing a test at the 0.05 level of significance.

Therefore, the claim that 50% of their readers own a laptop by the newsletter publisher is not true. A null hypothesis is a statement that is being tested for possible rejection under the assumption that it is true. It is often symbolized as H0. A one-tailed test examines only one side of the distribution, while a two-tailed test examines both sides.

For a one-tailed test, the null hypothesis is rejected if the sample statistic is at the extremes of the distribution (either in the upper or lower tail). On the other hand, for a two-tailed test, the null hypothesis is rejected if the sample statistic is at the extremes of both tails.The level of significance, denoted as alpha (α), is the probability of committing a Type I error. A Type I error is the rejection of a null hypothesis that is true. Alpha is typically set to 0.05 or 0.01. A p-value is a probability that is calculated from the test statistics.

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(a) There is no extreme value of A subject to the given constraint,

(b) For x = 0, y + z² ≤ 16.

y is between -4 and 4. In this case, f(y,z) = y² and the maximum value is 16.

For x = ±y, z = 4 - y².

y is between -2 and 2. In this case, f(y,z) = 2y² - y⁴ and the maximum value is 2.

When dividing by a variable, one should always keep in mind that the variable cannot be equal to zero. In other words, if the value of the variable is zero, the function or expression will not be defined or will give an undefined result. The reason is that division by zero is not defined in the set of real numbers.

Therefore, one should exclude the value of zero from the domain of the function or expression.

In part (a) of the given question, we are asked to find the global maximum and minimum of A(x,y,z) = 12 + 3x + y² - 2y subject to the constraint x + y + z = 2.

Let's find the partial derivatives of A with respect to x, y, and z.

∂A/∂x = 3

∂A/∂y = 2y - 2 = 2(y - 1)

∂A/∂z = 0

Now, we have to solve the system of equations consisting of the partial derivatives and the constraint equation.

\(3 = \lambda_1 + \lambda_2,\\2y - 2 = \lambda_1 + \lambda_2,\\\lambda_1x + \lambda_2x = 0,\\\lambda_1y + \lambda_2y - 1 = 0,\\\lambda_1z + \lambda_2z = 1.\)

Substituting the values of the partial derivatives, we get:

\(\lambda_1 + \lambda_2 = 3,\\\lambda_1 + \lambda_2 = -2,\\\lambda_1(3) + \lambda_2(0) = 0,\\\lambda_1(y - 1) + \lambda_2(y - 1) = 0,\\\lambda_1(0) + \lambda_2(1) = 1.\)

The second and third equations are contradictory. So, under the given constraint, A has no extreme value.

In part (b), we are asked to find the global maximum and minimum of A(x,y,z) = x² + y² on the closed bounded domain x² + y + z² ≤ 16.

Let's use the method of Lagrange multipliers to solve the problem. We have to find the critical points of the function f(x,y,z) = x² + y² subject to the constraint x² + y + z² = 16.

We have to solve the system of equations consisting of the partial derivatives of f, the partial derivatives of the constraint function, and the equation of the constraint function.

2x = λ(2x),

2y = λ(1),

2z = λ(2z).

Substituting the value of λ from the second equation into the first equation, we get: x = 0 or x = ±y.

Substituting the values of x and λ from the first and second equations into the third equation, we get:

z = 4 - y² or z = 0.

Since the constraint is x² + y + z² ≤ 16, we have to consider the following cases:

Case 1: x = 0, y + z² ≤ 16.

So, y is between -4 and 4. The maximum value of f(y,z)=y² is 16 in this case.

Case 2: x = ±y, z = 4 - y².

So, y is between -2 and 2. The maximum value of f(y,z) = 2y² - y⁴ is 2 in this case.

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Answer:

2a+ay+2b+by

We multiple the first number by the two numbers in the next parentheses

Answer:

\(2a+2b+ay+ab\)

Step-by-step explanation:

\((a+b)(2+y)\\(2a+ay+2b+by)\\(2a + 2b+ay+ab)\)

The polynomial function in expanded form is f(x) = x² - 3x² + 4x - 2.

A polynomial function with rational coefficients that has the given numbers as zeros, considering their conjugates . Since 1+i is a zero, its conjugate 1-i must also be a zero.

Using the zero-product property,  that if a polynomial has a zero at a given number, then the polynomial must have a factor of (x - zero). Therefore, the polynomial function with the given zeros can be written as:

f(x) = (x - (1+i))(x - (1-i))(x - 1)

Expanding this expression,

f(x) = ((x - 1) - i)((x - 1) + i)(x - 1)

= ((x - 1)² - i²)(x - 1)

= ((x - 1)² + 1)(x - 1)

= (x² - 2x + 1 + 1)(x - 1)

= (x² - 2x + 2)(x - 1)

= x² - 2x² + 2x - x² + 2x - 2

= x² - 3x²+ 4x - 2

.

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Answer:

7/12 chance

Step-by-step explanation:

(1 2 3 4 5 6)

(1 2 3 4 5 6)

All the possibilities:

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 18 odd sums.

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 3 possibilities whose sums add up to 10.

Since there are 36 total possibilities and 21 numbers that fit the rule of having an odd sum or a sum of 10. There is a 21/36 chance or simplified, 7/12 chance.

Answer:

A = 6.4

Step-by-step explanation:

A - 5.36 = 1.04

    +5.36   +5.36

A = 6.4

In a bundle of 50 kg of cloth, the weight of each material is:

Cotton: 12.5 kg

Nylon: 7.5 kg

Polyester: 20 kg

Others: 10 kg

To calculate the percentage of each material found in the cloth, we need to convert the given angles in the pie chart into percentages.

i) Calculating the percentage of each material:

Cotton: 90° / 360° * 100% = 25%

Nylon: 54° / 360° * 100% = 15%

Polyester: 144° / 360° * 100% = 40%

Others: 72° / 360° * 100% = 20%

Therefore, the percentage of each material found in the cloth is:

Cotton: 25%

Nylon: 15%

Polyester: 40%

Others: 20%

ii) To calculate the weight of each material contained in a bundle of 50 kg of cloth, we need to multiply the percentage of each material by the total weight.

Weight of Cotton = 25% * 50 kg = 0.25 * 50 kg = 12.5 kg

Weight of Nylon = 15% * 50 kg = 0.15 * 50 kg = 7.5 kg

Weight of Polyester = 40% * 50 kg = 0.40 * 50 kg = 20 kg

Weight of Others = 20% * 50 kg = 0.20 * 50 kg = 10 kg

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Answer:

so Divide or subtract 252 - 6%= 236.

Step-by-step explanation:

236.

The major benefit of enterprise application integration (EAI) is that it allows different applications and systems within an organization to seamlessly communicate and share data.

This integration eliminates data silos and enables real-time data exchange, leading to improved efficiency, productivity, and decision-making within the organization.

By implementing EAI, businesses can achieve the following benefits:

1. Enhanced Data Accuracy and Consistency: EAI ensures that data is synchronized and consistent across different systems, eliminating the need for manual data entry and reducing the risk of errors or discrepancies.

2. Increased Efficiency and Productivity: EAI automates the flow of information between applications, reducing the need for manual intervention and streamlining business processes.

This leads to improved efficiency and productivity as employees spend less time on repetitive tasks.

3. Improved Decision-Making: EAI provides a unified view of data from various systems, enabling better analysis and decision-making. Decision-makers have access to real-time and accurate information, allowing them to make informed and timely decisions.

4. Cost Savings: By integrating existing applications instead of developing new ones from scratch, EAI can help businesses save costs. It reduces the need for duplicate systems, minimizes data duplication, and optimizes IT infrastructure.

5. Scalability and Flexibility: EAI allows organizations to easily integrate new applications or systems as their needs evolve. It provides a flexible framework that can accommodate future growth and changes in business requirements.

Overall, the major benefit of enterprise application integration is the ability to achieve seamless connectivity and data exchange between systems, leading to improved efficiency, productivity, and decision-making in an organization.

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The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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The mean score on the rescored exam is 75.5 points.

To find the mean of the rescored exam, we need to add 8 points to each student's score and then find the new mean.

To do this, we can use the formula:

New Mean = (Sum of Rescored Scores) / Number of Students

We know that there are 32 students and the original mean score was 67.2 points.

So the sum of the original scores is:

Sum of Original Scores = Mean x Number of Students
= 67.2 x 32
= 2144.

To find the sum of the rescored scores, we need to add 8 points to each student's score:

Sum of Rescored Scores = Sum of Original Scores + (8 x Number of Students)
= 2144 + (8 x 32)
= 2416.

Now we can find the new mean:

New Mean = Sum of Rescored Scores / Number of Students
= 2416 / 32
= 75.5.

Therefore, the mean score on the rescored exam is 75.5 points.

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Answer:

  (c)  h(x) = 2(0. 35)^–x

Step-by-step explanation:

You want to know the function that is a reflection of f(x) = 2(0.35^x) over the y-axis.

When a point is reflected across the y-axis, the sign of its x-coordinate is changed. The y-coordinate is unchanged.

For a function y = f(x), the reflected function is y = f(-x).

For h(x) = 2(0.35^x), the reflected function is ...

  h(x) = 2(0.35^-x)

<95141404393>

Step-by-step explanation:

Hope it will help you a lot.

In the given image, the length of JI is 6

From the question, we are to solve for JI

From the given image, we can write that

JI + IH = JH

Then,

2x + 28 + 5 = x + 22

Solving for x

2x + 28 + 5 = x + 22

First, collect like terms

2x - x = 22 - 28 - 5

Simplifying

x = -11

But,

JI = 2x + 28

∴ JI = 2(-11) + 28

JI = -22 + 28

JI = 6

Hence, the length of JI is 6

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