Use the distance formula to find the length of AB. Give your answer as a radical and rounded to the nearest tenth.

To solve the problem we will calculate the amount of food consumed by Deon's dog in 2.5 weeks.

The new bag of food will last for 2.5 weeks.

Given to us

To know the amount of food consumed by Deon dog in 2.5 weeks, we will multiply the food consumed by Deon dog in 1-week by the Number of weeks for which food is been consumed.

Food consumed by Deon dog in 2.5 weeks

= Food consumed by Deon dog in 1-week x Number of weeks

= 62 cups of dog food x 2.5

= 155 cups of dog food

Thus, the food consumed by Deon's Dog is 155 cups.

As we can see the Dog will consume 155 cups of dog food in 2.5 weeks, therefore, the new bag of food will last for 2.5 weeks.

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The optimal feasible solution is x1 = 1, x2 = 0.4, and the problem is a regular linear programming problem.

To solve the given linear programming problem, let's define the decision variables and formulate the objective function and constraints:

Decision Variables:

x1, x2

Objective Function:

Maximize: 2x1 + 6x2

Constraints:

2x1 + 5x2 ≤ 4

4x1 + x2 ≤ 6

x1, x2 > 0

To find the optimal feasible solution, we can use a linear programming solver. Here is the optimal solution for the given problem:

Optimal Solution:

x1 = 1

x2 = 0.4

The maximum value of the objective function is obtained when x1 = 1 and x2 = 0.4. The maximum value is 2(1) + 6(0.4) = 4.8.

Now let's analyze if the solution is a special case of linear programming.

This problem falls under the category of Linear Programming (LP) problems. However, it does not represent any specific special case of LP such as degeneracy, unboundedness, or infeasibility. The given problem has a feasible solution, and the objective function is maximized within the given constraints. Hence, it is a regular LP problem without any special case conditions.

Note: Since the solution is text-based, there is no need to scan or provide a separate file.

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The transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we have

f(x) = x²

The translation 6 units left and 4 units up means that

g(x) = f(x + 6) + 4

So, we have

g(x) = (x + 6)² + 4

This means that the transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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Answer:

The Number is 11

Step-by-step explanation:

by first condition

we got it is an odd number

second condition

number less then12

third condition

between 10 to 14

Now,

odd number between 10 to 14

is 11 and 13

13 is greater then 12

therefore 11 is your answer

Answer:

180

Step-by-step explanation:

A 3-digit number cannot start with 0, so the leftmost digit is a choice of 6 digits out of the 7. The middle digit can be chosen from all 7 digits minus the one already used, so there are 6 choices. The right digit can be chosen from 5.

6 × 6 × 5 = .180

The number of three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 is 180.

This can be calculated by finding the number of element availabe at first place which is 6 excluding 0 than for second position 6 as first number is excluded and 0 is added and for the last positon the number of possibe combination is 5 as 2 digits are already used.

The final answer is 6*6*5 = 180

so count of 3 digit numbers that can be formed by the given set of digit without repetetion allowed is  180

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Answer:

15,90

Step-by-step explanation:

it goes by 6

(14 x 6=84) and so on and so forth

let y1 and y2 have the joint probability density function given by f(y1, y2) = 4y1y2, 0 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1, 0, The main answer is that the covariance between y1 and y2 is zero, cov(y1, y2) = 0.

To compute the covariance, we first need to calculate the expected values of y1 and y2. Then we can use the formula for covariance:

1. Expected value of y1 (E(y1)):

  E(y1) = ∫[0,1] ∫[0,1] y1 * f(y1, y2) dy1 dy2

        = ∫[0,1] ∫[0,1] y1 * 4y1y2 dy1 dy2

        = 4 ∫[0,1] y1^2 ∫[0,1] y2 dy1 dy2

        = 4 ∫[0,1] y1^2 * [y2^2/2] |[0,1] dy1 dy2

        = 4 ∫[0,1] y1^2 * 1/2 dy1

        = 2/3

2. Expected value of y2 (E(y2)):

  E(y2) = ∫[0,1] ∫[0,1] y2 * f(y1, y2) dy1 dy2

        = ∫[0,1] ∫[0,1] y2 * 4y1y2 dy1 dy2

        = 4 ∫[0,1] y2^2 ∫[0,1] y1 dy1 dy2

        = 4 ∫[0,1] y2^2 * [y1/2] |[0,1] dy1 dy2

        = 4 ∫[0,1] y2^2 * 1/2 dy2

        = 1/3

3. Covariance of y1 and y2 (cov(y1, y2)):

  cov(y1, y2) = E(y1 * y2) - E(y1) * E(y2)

              = ∫[0,1] ∫[0,1] y1 * y2 * f(y1, y2) dy1 dy2 - (2/3) * (1/3)

              = ∫[0,1] ∫[0,1] y1 * y2 * 4y1y2 dy1 dy2 - 2/9

              = 4 ∫[0,1] y1^2 ∫[0,1] y2^2 dy1 dy2 - 2/9

              = 4 * (1/3) * (1/3) - 2/9

              = 4/9 - 2/9

              = 2/9 - 2/9

              = 0

Therefore, the covariance between y1 and y2 is zero, indicating that the variables are uncorrelated in this case.

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Answer:

D

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

we can use point-slope form to find this answer.

first, make this equation

y-y 1=m(x-x1)

y-4=-6(x-1)

m=-6 because you can use slope intercept form to find the slope (as the name states lol)

then just distribute!!

y-4=-6x+6

add four to both sides

y=-6x+10

whoops, i did a little too much the answer is in bold!!!

good luck!! hope this helped! <3

the required area of the region is 207/2 square units.

Given,

x = (66 + 3)y²/2y

Area of the region bounded by the curve x = (66 + 3)y²/2y,

the y-axis and abscissa y = 1 and y = 4 is to be found.

To find the area of the given region, integrate x with respect to y.

∫x dy [lower limit = 1, upper limit = 4] ⇒ ∫(66 + 3)y dy [lower limit = 1, upper limit = 4]

The antiderivative of 66 is 66y and of 3y is 3y²/2.

Therefore, the antiderivative of the entire integrand becomes (66 + 3)y²/2.

Then the integral becomes,⇒ ∫(66 + 3)y dy [lower limit = 1, upper limit = 4]⇒ [(66 + 3)y²/2] [lower limit = 1, upper limit = 4]

Putting the limits, we get the area of the region bounded by the curve x = (66 + 3)y²/2y,

the y-axis and abscissa y = 1 and y = 4,Area = [(66 + 3)(4²) / 2] - [(66 + 3)(1²) / 2]= [69 × 8] / 2 - [69 × 1] / 2= 276/2 - 69/2= 207/2 square units

Hence, the required area of the region is 207/2 square units.

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Step-by-step explanation:

x2+1/x2=27

x2+1=27x2

1=26x2

x2 = 1/26

x = √(1/26)

x3+1/x3 = (√(1/26))^3 + 1 / (√(1/26))^3

x3+1/x3 = 134

Please find attached photograph for your answer

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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The area enclosed by the two curves y=2-x2 and y= -x is 6 square units.

To find the area enclosed by the two curves y=2-x2 and y= -x, we need to first find the points of intersection of the two curves. This can be done by setting the two equations equal to each other and solving for x.

2-x2 = -x

x2 - x - 2 = 0

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

x = 2 or x = -1

Now we can use these points of intersection to find the area enclosed by the two curves. This can be done by integrating the difference between the two curves from the leftmost point of intersection to the rightmost point of intersection.

∫[-1, 2] (2-x2) - (-x) dx

= ∫[-1, 2] (2-x2 + x) dx

= ∫[-1, 2] (3-x2) dx

= [3x - (x3/3)] from -1 to 2

= [(3(2) - (23/3)) - (3(-1) - ((-1)3/3))]

= [(6 - (8/3)) - (-3 - (-1/3))]

= [(18/3 - 8/3) - (-9/3 - (-1/3))]

= [(10/3) - (-8/3)]

= 18/3

= 6

Therefore, the area enclosed by the two curves y=2-x2 and y= -x is 6 square units.

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By analizying the zeros on the graph, we conclude that the equation that could represent the graph is:

y = (x  + 5)²*(x - 3)²

On the graph, we have a polynomial.

Remember that the degree of the polynomial is related to the zeros of the polynomial. Here we can see that we have two double zeros, one at x = -5 and other at x = 3

We know that are double zeros because the curvature of the polynomial changes there.

Then the equation will be something like:

y = (x  + 5)²*(x - 3)²

So that is the correct option, top right.

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Answer:

Take 20% of 35000 and add it

Step-by-step explanation:

20% of 35000 is 7000 so we take 35000 + 7000 which would be 42000

The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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Answer: Domain: {-5,-1,3} and Range: {3,0,-4,2}

The coordinates of the point on the directed line segment from (-8,8) to (7,-7) that partitions the segment into a ratio of 3 to 2 are (1, 2.2).

Coordinates are a set of numbers that specify the position or location of a point in a geometric space. In two-dimensional space, coordinates are typically represented as a pair of numbers (x, y), where x represents the horizontal distance from a reference point (usually the origin) to the point, and y represents the vertical distance from the reference point to the point.

In the given question,

To find the coordinates of the point on the directed line segment from (-8,8) to (7,-7) that partitions the segment into a ratio of 3 to 2, we can use the following formula:

P = (2A + 3B) / 5

where P is the coordinates of the partition point, A is the coordinates of the starting point (-8, 8), and B is the coordinates of the ending point (7, -7).

Substituting the given values into the formula, we get:

P = (2(-8, 8) + 3(7, -7)) / 5

P = (-16/5, 32/5) + (21/5, -21/5)

P = (5/5, 11/5)

P = (1, 2.2)

Therefore, the coordinates of the point on the directed line segment from (-8,8) to (7,-7) that partitions the segment into a ratio of 3 to 2 are (1, 2.2).

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Answer:

r = 4

a8 = 114,688

Step-by-step explanation:

a1=7

a11 = 7340032

a11 = a1*r^10

7340032 = 7 * r^10

7340032 = 7r^10

r^10 = 7340032/7

r^10 = 1,048,576

Find the 10th root of both sides

10√r^10 = 10√1,048,576

r = 4

a8 = a1 * r^7

= 7 * 4^7

= 7 * 16,384

= 114,688

a8 = 114,688

Given the figure, we can deduce the following information:

1. The lines intersect at point (-2,-2).

To determine which quadrant is the answer to the given system of equations, we note the quadrants as shown below:

Based on the given graph, we can notice that the lines intersect at point (-2,-2) which is located at Quadrant 3.

Therefore, the answer is C. Quadrant 3.

Answer:

It's D, E, and F

Step-by-step explanation:

The first five terms of the sequence: an = 2an – 1 – an – 2; a1 = 4; a2 = 3. the correct option is B. {4, 3, 2, 1, 0}.

Given a recursive sequence an = 2an – 1 – an – 2 with a1 = 4, a2 = 3. We need to find the first five terms of the sequence.

To find the first five terms of the sequence, we can use the formula: an = 2an – 1 – an – 2. Using the formula, we havea3 = 2a2 – a1 = 2(3) – 4 = 2a4 = 2a3 – a2 = 2(2) – 3 = 1a5 = 2a4 – a3 = 2(1) – 2 = 0

Therefore, the first five terms of the sequence are {4, 3, 2, 1, 0}.

Hence, the correct option is B. {4, 3, 2, 1, 0}.Option A is incorrect since the fourth and fifth terms are not equal to 2.Option C is incorrect since it has random numbers. Option D is incorrect since it has an increasing sequence.

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The error that the student made was that he forgot to square.

The conversion rate of converting meter to feet (linear measurement) is given as:

1 meter = 3.28 feet.

The measures given is in area, therefore, we would need to square when doing our conversion. To convert 3.5 square meter to square feet, do the following:

3.5 m² × (3.28 ft/1 m)² (this is where the student made an error by omitting or forgetting to square)

= 3.5 × 10.8

= 37.8 square feet

Therefore, we can conclude that the error that the student made was that he forgot to square.

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Answer:

The Quotient Property of Square Roots states that the square root of a quotient is equal to the quotient of the square roots of the dividend and divisor

Step-by-step explanation:

Answer: y+6x = -34

Step-by-step explanation:

y-2= -6(x+6)                              (Ax+By=C is the goal)

y-2= -6x-36  (-6) x & (-6) 6

y=-6x-34 (Add 2 to both sides)

y+6x = -34   [Add 6x to both sides]

Answer:

8

Step-by-step explanation:

it would be 8 as 17 is on the y axis and then you go along the corridor and down the stairs and the dot is on 8

Answer:

8

Step-by-step explanation:

scale goes up in 2s

read from X axis

Answer:

3x + 4 ≤ 13

Step-by-step explanation:

Step-by-step explanation:

y = 200  - 3 *x  has slope = -3   this is downward sloping from L to R

Answer:downward sloping

Step-by-step explanation:

negative slope