why does x^2 = 64 have two solutions but x^3 = 64 only has one?

Answer:

-3×+5

Step-by-step explanation:

y=mx+b

m= y2-y1÷x2-x1

= -10+1÷5-2

= -9÷3

= -3

now,

y= -3×+b

-10 = -3(5)+b

-10 = -15+b

-10+15 = b

b= 5

therefore, y= -3×+5

The equation of the line passing through the points (2, -1) and (5, -10) in slope-intercept form is y= -3x+ 5.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have the points as (5, -10) and (2, -1).

So, the slope of line

slope = (-1 + 10) / (2 -5)

slope = 9/ (-3)

Slope= -3

Now, using the slope intercept form

y= mx+ b

y= -3x + b

and, the line passes through (2, -1)

-1 = -3(2) + b

-1 + 6 = b

b= 5

Then, the equation of line is

y= -3x + 5

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Answer:

x = 70

Step-by-step explanation:

The angles are same side interior angles and when the lines are parallel same side interior angles are supplementary

45+ (2x-5) = 180

Combine like terms

2x +40 = 180

Subtract 40 from each side

2x+40-40 =180-40

2x = 140

Divide by 2

2x/2 = 140/2

x = 70

x = 70

The implicit solution to the given differential equation Dx/dt = 4x² + (9t/√(6²+x²)) / (4tx) using the method for solving homogeneous equations is F(t,x) = C, where C is an arbitrary constant.

To solve the given differential equation, we can separate the variables and integrate both sides. Rearranging the equation, we have:

(4tx) Dx = (4x² + (9t/√(6²+x²))) dt. Next, we integrate both sides. Integrating the left side with respect to x and the right side with respect to t, we get:

∫(4tx) Dx = ∫(4x² + (9t/√(6²+x²))) dt. Integrating both sides will result in a function F(t,x) on the left side and the integral on the right side. Since we are looking for an implicit solution in the form F(t,x) = C, we can write the equation as:

F(t,x) = C. cccThis represents the general solution to the given differential equation, where C is an arbitrary constant. The specific form of the function F(t,x) will depend on the integration process and the initial conditions, if provided.

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The fencing that will be required for the rectangular plot is: 162 m

The formula to find the perimeter of a rectangle is:

Perimeter = 2(Length + Width)

Now, we are told that each of the three rectangular plots measure 20m by 11m and as such, if we have 3 meters between each plot and also the boundary of the plot, then we can say that:

Length of Plot = 3 + 11 + 3 + 11 + 3 + 11 + 3 = 45 m

Width of plot = 20 + 3 + 3 = 26 m

Thus:

Fencing required = 2(45 + 36)

Fencing required = 2 * 81

Fencing required =  162 m

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The upper bound of the 90% confidence interval for the recovery time is approximately 23.696 days.

It takes more than approximately 21.257 minutes to find a parking space 90% of the time.

To find the probability that it will take more than 11 days to recover from the surgical procedure, we need to calculate the area under the normal distribution curve to the right of 11 days.

Mean (μ) = 7 days

Standard deviation (σ) = 7.92 days

We can standardize the value of 11 days using the z-score formula:

z = (x - μ) / σ

z = (11 - 7) / 7.92

z = 0.506

Using a standard normal distribution table or a calculator, we can find the probability corresponding to the z-score of 0.506. The probability is approximately 0.3051.

Therefore, the probability that it will take more than 11 days to recover is approximately 0.3051 or 30.51%.

Question 8:

To find the upper bound of the 90% confidence interval for the number of days needed to recover from the surgical procedure, we need to calculate the z-score corresponding to the desired confidence level and then find the corresponding value using the standard deviation.

Given:

Mean (μ) = 20 days

Standard deviation (σ) = 2.24 days

For a 90% confidence interval, the z-score corresponding to the upper tail probability of 0.10 (1 - 0.90) is approximately 1.645.

Using the formula for the upper bound of the confidence interval:

Upper bound = μ + (z * σ)

Upper bound = 20 + (1.645 * 2.24)

Upper bound ≈ 23.696

Therefore, the upper bound of the 90% confidence interval for the recovery time is approximately 23.696 days.

Question 9:

To find the time it takes more than 90% of the time to find a parking space, we need to calculate the z-score corresponding to the desired upper tail probability and then find the corresponding value using the standard deviation.

Mean (μ) = 15 minutes

Standard deviation (σ) = 4.89 minutes

For a probability of 90%, the upper tail probability is 1 - 0.90 = 0.10.

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to the upper tail probability of 0.10, which is approximately 1.282.

Using the formula for the upper bound:

Upper bound = μ + (z * σ)

Upper bound = 15 + (1.282 * 4.89)

Upper bound ≈ 21.257

Therefore, it takes more than approximately 21.257 minutes to find a parking space 90% of the time.

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a. To calculate the Euclidean distances between the three pairs of facilities, we use the formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Calculating the Euclidean distances:

dAB = sqrt((51 - 26)^2 + (59 - 16)^2) ≈ 47.39 miles

dBC = sqrt((36 - 51)^2 + (41 - 59)^2) ≈ 23.53 miles

dAC = sqrt((36 - 26)^2 + (41 - 16)^2) ≈ 25.00 miles

b. To calculate the rectilinear distances, we use the formula:

d = |x2 - x1| + |y2 - y1|

Calculating the rectilinear distances:

dAB = |51 - 26| + |59 - 16| = 25 + 43 = 68 miles

dBC = |36 - 51| + |41 - 59| = 15 + 18 = 33 miles

dAC = |36 - 26| + |41 - 16| = 10 + 25 = 35 miles

Therefore, the Euclidean distances are approximately dAB = 47.39 miles, dBC = 23.53 miles, and dAC = 25.00 miles. The rectilinear distances are dAB = 68 miles, dBC = 33 miles, and dAC = 35 miles.

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Answer:

k=1/2

Step-by-step explanation:

A direct variation equation has the form

The non-dimensional surface temperature of a sphere with a Biot number of 8 and a non-dimensional centerline temperature of 0.29 is approximately 2.32.

The non-dimensional surface temperature of a sphere can be determined using the Biot number and the non-dimensional centerline temperature. The Biot number is a dimensionless quantity that represents the ratio of internal thermal resistance to external thermal resistance.

The relationship between the non-dimensional surface temperature (θ) and the Biot number (Bi) is given by the following equation:

θ = θ_s/ θ_c

Given that the Biot number (Bi) is 8 and the non-dimensional centerline temperature (θ_c) is 0.29, we can rearrange the equation to solve for the non-dimensional surface temperature (θ).

θ = Bi × θ_c

θ = 8 × 0.29

θ ≅ 2.32

Therefore, the non-dimensional surface temperature of a sphere with a Biot number of 8 and a non-dimensional centerline temperature of 0.29 is approximately 2.32.

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Express a vector A = [24, -15] as a linear combination of vectors in S, we solve the system of equations formed by equating A to the linear combination of S's vectors and find the coefficients.

i) To show that S = {[8, 2, 5], [H, H², H³]} is linearly independent, we set up the equation:

a * [8, 2, 5] + b * [H, H², H³] = [0, 0, 0]

Expanding this equation gives us the following system of equations:

8a + bH = 0

2a + bH² = 0

5a + bH³ = 0

To prove that S is linearly independent, we need to show that the only solution to this system is a = b = 0. Solving these equations will confirm the linear independence of S.

ii) Since S is linearly independent and contains two vectors, it forms a basis for a two-dimensional space, which we'll denote as Maz.

iii) To express vector A = [24, -15] as a linear combination of the vectors in S, we set up the equation:

[24, -15] = c * [8, 2, 5] + d * [H, H², H³]

Expanding this equation gives us the following system of equations:

8c + dH = 24

2c + dH² = -15

5c + dH³ = 0

By solving this system, we find the coefficients c and d that represent the linear combination of vectors in S that equals A.

Finally, substituting the values of c and d, we obtain the vector (4)s.

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Answer:

x² - 5x + c = 0

x = (5 + √(25 - 4c))/2

difference of roots = √(25 - 4c) = 1/4

25 - 4c = 1/16

-4c = -399/16

c = 399/64

Answer:the sector is 280°

Step-by-step explanation:

Answer:

g=-3

Step-by-step explanation:

7+3(2g-6)=-29

7+6g-18=-29

6g=-29+18-7

6g=-18

g=-3

I think this is the right answer :D hope this helps ;)

Answer:

Step-by-step explanation:

[tex]7+3(2g-6)= -29\\\\\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}\\\\7+3\left(2g-6\right)-7=-29-7\\\\Simplify\\\\3\left(2g-6\right)=-36\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3\left(2g-6\right)}{3}=\frac{-36}{3}\\\\Simplify\\\\2g-6=-12\\\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}\\\\2g-6+6=-12+6\\\\Simplify\\\\2g =-6\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2g}{2}=\frac{-6}{2}\\\\Simplify\\\\g =-3[/tex]

Answer:

D

Step-by-step explanation:

Answer:

$85.50 dollars

Step-by-step explanation:

Becky bought a $14.50 and $20 dress, and a $8.25 pair of flipflops. That is $42.75 . Barbara bought differernt things but still spent the same amount of $42.75 . So if you add those up, it would be $85.50 that they have spent together. Hope this helps :)

Answer:

its a :)

Step-by-step explanation:

have a good day!!

Answer:

-123

Step-by-step explanation:

Answer:

-123

Step-by-step explanation:

-(29+1+4+89)

-(30+4+89)

-(34+89)

-123

hope this helps good luck at school :))

It is indeed possible for it to take more than k pivots to find a "real" BFS when using the Big M method, where k is the number of artificial variables introduced.

If the reduced cost of all non-basic variables is strictly ≥0, it does not necessarily mean that the current basic feasible solution (BFS) is optimal. The reduced cost of a variable represents the amount by which the objective function value would improve if that variable were included in the current BFS. When the reduced cost is ≥0 for all non-basic variables, it indicates that there is no incentive to include any of those variables in the current BFS as they would not contribute to improving the objective function.

However, it is still possible that the current BFS is not optimal. There could be other feasible solutions that have a lower objective function value, and these solutions might involve changing the current set of basic variables. To determine optimality, additional criteria need to be considered, such as the feasibility of the solution and the optimality conditions of the linear programming problem.

When using the Big M method to find an initial basic feasible solution (BFS), it is possible that it may take more than k pivots to find a "real" basic feasible solution that includes only the variables in the original problem.

The Big M method introduces artificial variables with a large coefficient (M) in the objective function to enforce constraints during the initial phase of solving a linear programming problem. These artificial variables ensure that all constraints are satisfied and provide a starting BFS. However, these artificial variables are not part of the original problem and need to be removed to obtain a "real" BFS.

The number of pivots required to find a "real" BFS depends on the particular problem and the choice of artificial variables. It is possible that additional pivots are needed to eliminate the artificial variables and identify a feasible solution that includes only the original variables.

Therefore, it is indeed possible for it to take more than k pivots to find a "real" BFS when using the Big M method, where k is the number of artificial variables introduced.

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Step-by-step explanation:

Let the two numbers be X and Y respectively.

We know that :

(a) X = 6Y + 5

(b) X + Y = 75

7Y + 5 = 75

X = 65

Y = 10

Answer:

y= 10         x = 65

Step-by-step explanation

did the same assignment lol

- mark me brainliest !

Answer: F(2)=20 means the total cost or the amount if money you spent at the movies after buying a ticket and buying 2 items at the concession stand.

Explanation: One ticket is $12 and if each item is $4, then in order to get to a total of $20, then you would need 2 items, since 2 x $4 = $8, and that plus $12 is $20.

I hope this helps!

Answer:

gsugaqsgsuguwsqsw

Step-by-step explanation:

wshwsbgshswswswsw f word you

Answer:

x = 10

Step-by-step explanation

The exterior angle = the sum of the 2 interior angles (which is the other way to solve the other problem you just posted.)

-10 + 14x = 60 + 7x            Add 10 to both sides

-10+10+14x =60+10+7x     Combine

14x = 70 + 7x                     Subtract 7x from both sides

14x-7x = 70+7x-7x             Combine

7x = 70                              Divide by 7

7x/7 = 70/7

x = 10

The reflective properties of conic sections can be exploited in various applications, such as focusing light or radio waves, enhancing signal reception, and designing optical systems. Each conic section exhibits unique reflective characteristics based on the arrangement of its foci and the shape of the curve.

Let's discuss the reflective properties of the three conic sections: parabola, ellipse, and hyperbola.

Parabola:

Reflective Property: A parabola has a single focus point, located either above or below the vertex. Any ray of light parallel to the axis of symmetry of the parabola will reflect off the curve and pass through the focus point.

Application: This property of the parabola makes it useful in designing reflective surfaces, such as satellite dishes or car headlights, where incoming parallel light rays are focused at a single point.

Ellipse:

Reflective Property: An ellipse has two foci, located at the two foci points on the major axis. When a ray of light enters the ellipse, it reflects off the inner surface of the curve, obeying the law of reflection. The angle of incidence is equal to the angle of reflection.

Application: The reflective property of the ellipse is utilized in applications such as astronomy, where elliptical mirrors are used in telescopes to focus light from distant celestial objects onto a focal point.

Hyperbola:

Reflective Property: A hyperbola has two foci, one on each branch of the curve. When a ray of light enters one branch of the hyperbola, it reflects off the inner surface of the curve, obeying the law of reflection. The angle of incidence is equal to the angle of reflection.

Application: The reflective property of the hyperbola finds applications in antenna design, specifically in satellite dishes and radio telescopes. The hyperbolic shape allows incoming waves to be focused or directed towards a specific point or receiver.

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s = (-38 ± √(-6556)) / 32

Since the term inside the square root is negative, the equation has no real solutions. This means that the ball will not hit the ground.

To determine how long it will take for the ball to hit the ground, we need to find the value of s when the height h(s) equals zero. In other words, we need to solve the equation:

16s^2 + 38s + 1250 = 0

We can use the quadratic formula to solve this equation. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 16, b = 38, and c = 1250. Plugging these values into the quadratic formula, we have:

s = (-38 ± √(38^2 - 4(16)(1250))) / (2(16))

Simplifying further, we get:

s = (-38 ± √(1444 - 8000)) / 32

s = (-38 ± √(-6556)) / 32

Since the term inside the square root is negative, the equation has no real solutions. This means that the ball will not hit the ground.

This result does not reflect reality. In reality, the ball would eventually hit the ground due to factors such as air resistance. The given equation does not take these factors into account.

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Answer:

= -1031/8

Step-by-step explanation:

Hope I get brainliest

The equation is 4 meatballs for every adult and 3 for every child. Replace a and c and solve:

M = 4(20) + 2(8)

M = 80 + 16

M = 96

They need 96 meatballs.

Answer:

The cost of one pecan cheesecake is $12 and

the cost of 1 chocolate marble cheesecake is 13$

Step-by-step explanation:

Let the cost of one pecan cheesecake be x

And the cost of one chocolate marble cheesecake be y

Now, James sold 12 pecan cheesecakes and 1 chocolate marble cheesecake for $157, we represent this as,

12x + y = 157 (i)

And, Amanda sold 3 pecan cheesecakes and 5 chocolate marble cheesecake for $101, we represent this as,

3x + 5y = 101  (ii)

now, we just need to solve these two equations to get the amounts,

since 12x + y = 157

y = 157 - 12x

putting value of y in (ii)

3x + 5(157-12x) = 101

3x +785 - 60x = 101

-57x + 628 = 101

-57x = 101 - 785

-57x = -684

multiplying by -1 on both sides,

57x = 684

x = 684/57

x = 12

Now, finding y using, y = 157 - 12x

since x = 12,

y = 157 - (12)(12)

y = 157 - 144

y = 13

So, the cost of one pecan cheesecake is $12 and the cost of 1 chocolate marble cheesecake is 13$

The minimum time for completing the project, based on the critical path analysis, is 18 weeks. The critical path, which consists of activities with zero slack time, includes activities A, B, C, F, G, and H. By summing up the durations of these critical activities, we find that the minimum time for completing the project is 18 weeks.


To calculate the minimum time for completing the project, we need to identify the critical path, which consists of activities with zero slack time. Here are the step-by-step calculations:

1. Assign forward and backward pass values:

  Start by assigning the project start time as Early Start (ES) = 0 for Activity A. Then, calculate the Early Finish (EF) for each activity by adding the duration to the ES. The backward pass starts from the project completion time, which is the Late Finish (LF) for Activity I, initially set at 26 weeks. Calculate the Late Start (LS) for each activity by subtracting the duration from the LF.

  Activity A: ES = 0, EF = ES + 4 = 4, LS = LF - 4 = 26 - 4 = 22, LF = 26

  Activity B: ES = 4, EF = ES + 3 = 4 + 3 = 7, LS = LF - 3 = 26 - 3 = 23, LF = 26

  Activity C: ES = 7, EF = ES + 2 = 7 + 2 = 9, LS = LF - 2 = 26 - 2 = 24, LF = 26

  Activity D: ES = 7, EF = ES + 6 = 7 + 6 = 13, LS = LF - 6 = 26 - 6 = 20, LF = 26

  Activity E: ES = 13, EF = ES + 5 = 13 + 5 = 18, LS = LF - 5 = 26 - 5 = 21, LF = 26

  Activity F: ES = 13, EF = ES + 4 = 13 + 4 = 17, LS = LF - 4 = 26 - 4 = 22, LF = 26

  Activity G: ES = 18, EF = ES + 2 = 18 + 2 = 20, LS = LF - 2 = 26 - 2 = 24, LF = 26

  Activity H: ES = 20, EF = ES + 3 = 20 + 3 = 23, LS = LF - 3 = 26 - 3 = 23, LF = 26

  Activity I: ES = 9, EF = ES + 5 = 9 + 5 = 14, LS = LF - 5 = 26 - 5 = 21, LF = 26

2. Calculate slack time:

  Slack time (ST) can be calculated by subtracting the EF from the LS or the ES from the LF for each activity.

  Activity A: ST = LS - EF = 22 - 4 = 18

  Activity B: ST = LS - EF = 23 - 7 = 16

  Activity C: ST = LS - EF = 24 - 9 = 15

  Activity D: ST = LS - EF = 20 - 13 = 7

  Activity E: ST = LS - EF = 21 - 18 = 3

  Activity F: ST = LS - EF = 22 - 17 = 5

  Activity G: ST = LS - EF = 24 - 20 = 4

  Activity H: ST = LS - EF = 23 - 23 = 0

  Activity I: ST = LS - EF = 21 - 14 = 7

3. Identify the critical path:

  The critical path consists of activities with zero slack time. In this case, the critical path includes activities A, B, C, F, G, and H.

4. Calculate the minimum project completion time:

  Sum up the durations of the activities on the critical path to find the minimum time for completing the project.

 Minimum Time = Duration of Activity A + Duration of Activity B + Duration of Activity C + Duration of Activity F + Duration of Activity G + Duration of Activity H

              = 4 + 3 + 2 + 4 + 2 + 3

              = 18 weeks

Therefore, the minimum time for completing the project is 18 weeks.

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Q9.1: To justify the proposal, we need to compare the benefits of the road expansion (in terms of reduced travel time) with its costs. The value of time represents the monetary value individuals place on their time spent traveling. In this case, the value of time is $1.5 per minute.

First, let's calculate the reduction in travel time resulting from the road expansion. We compare the two road performance functions: t1​ = 30 + 6×10−6q and t2​ = 20 + 3×10−6q. By subtracting t2​ from t1​, we can determine the time savings: Δt = t1​ - t2​ = (30 + 6×10−6q) - (20 + 3×10−6q)    = 10 + 3×10−6q Next, we multiply the time savings by the number of trips (q) to obtain the total time savings: Total Time Savings = Δt × q = (10 + 3×10−6q) × q Now, we can determine the monetary value of the time savings by multiplying the total time savings by the value of time ($1.5 per minute): Monetary Value of Time Savings = Total Time Savings × Value of Time                             

= (10 + 3×10−6q) × q × $1.5  If the monetary value of the time savings exceeds the construction cost of $9.6×107, then the proposal is justified. Q9.2: To determine the construction cost at which the proposal becomes justified, we set the monetary value of the time savings equal to the construction cost and solve for q: (10 + 3×10−6q) × q × $1.5 = $9.6×107 By solving this equation for q, we can find the corresponding construction cost at which the proposal becomes justified.

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