f(x)=−(x−7)^2+6. What is the domain and range?

Answer:

5n + 3

Step-by-step explanation:

8 , 13 , 18

difference = 5

8 - 5(1) = 3

therefore nth term = 5n + 3

proof:

5(2) + 3 = 13

5(3) + 3 = 18

Step-by-step explanation:

Hey there!

The sequences are; 8,13,18,23.....

Common difference (d)= 5

Use formula: tn = t1+(n-1)d

Where d is the common difference and t1 is first sequence.

Or, tn = 8 + (n-1)5

= 8+5n -5

= 5n +3.

Therefore the required nth term is; tn = 5n+3.

Check;

1st term (t1) = 8 = 5×1+3=8 (true)

2nd term (t2) = 13 = 5×2+3=13 (true)

3rd term (t3)= 18 = 5×3+3=18 (true)

4th term (t4) = 23 = 5×4+3=23 (true).

Hope it helps..

The amount of total cost at q* is 1.

To determine the production level that minimizes total cost, we need to find the value of q (production level) at which the derivative of the total cost function TC(q) is equal to zero. Let's begin by finding the derivative of TC(q):

TC(q) = 10 - 6q + q^2

To find the minimum point, we differentiate TC(q) with respect to q:

d(TC(q))/dq = -6 + 2q

Setting the derivative equal to zero and solving for q:

-6 + 2q = 0

2q = 6

q = 3

So the production level q* that minimizes the total cost is 3.

To find the amount of total cost at q*, we substitute q = 3 into the total cost function TC(q):

TC(q*) = 10 - 6(3) + (3)^2

TC(q*) = 10 - 18 + 9

TC(q*) = 1

Therefore, the amount of total cost at q* is 1.

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The solution of each of the quadratic equations are:

5) x = +3, -3

6) x = +3/2, -3/2

7) x = -4, 1/3

8) x = +9, -9

The general form of a quadratic equation is:

ax² + bx + c = 0

The quadratic formula to find the roots is:

x = [-b ± √(b² - 4ac)]/2a

5) The quadratic equation is given as 4x² - 36.

Thus:

x = [-0 ± √(0² - 4(4 * -36))]/2(4)

x = ±√4(4 * 36))/8

x = ±24/8

x = +3, -3

6) The quadratic equation is given as 64x² - 144

Thus:

x = [-0 ± √(0² - 4(64 * -144))]/2(64)

x = ±(√36864)/8

x = ±192/128

x = ±3/2

x = +3/2, -3/2

7) The quadratic equation is given as 3x² + 11x - 4

Thus:

x = [-11 ± √(11² - 4(3 * -4))]/2(3)

x = [-11 ± (√169)]/6

x = (-11 ± 13)/6

x = -4, 1/3

8) The quadratic equation is given as x² - 81

Thus:

x = [-0 ± √(0² - 4(1 * -81))]/2(1)

x = ±(√324)/2

x = ±18/2

x = ±9

x = +9, -9

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Answer:

x=10

Step-by-step explanation:

8x+10=6x+30

8x-6x=30-10

2x=20

x=10

To find the values of x for which the two trinomials are equal, we need to set them equal to each other and solve for x.

For the trinomials 3x^2 - 4x + 3 and x^2 + x + 1:

3x^2 - 4x + 3 = x^2 + x + 1

By rearranging the equation and combining like terms, we get:

2x^2 - 5x + 2 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, the equation can be factored as:

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

Setting each factor equal to zero, we have:

2x - 1 = 0   -->   2x = 1   -->   x = 1/2

x - 2 = 0   -->   x = 2

Therefore, the values of x for which the two trinomials are equal are x = 1/2 and x = 2.

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Answer:

225%

Step-by-step explanation:

250*.1 = 25

250-25=225$

Answer:

slope is -3

y-intercept is -2

Step-by-step explanation:

Answer:

[tex]-3x+y=10[/tex]

Step-by-step explanation:

To write this equation we first need to know what the standard form is. Standard form of a line is written as [tex]Ax + By = C[/tex]. To get this, we first need to put the equation into point slope form or [tex]y-y1 = m(x-x1)[/tex] where [tex]m[/tex] is slope and [tex](x1,y1)[/tex] is a point on the graph. Using the information we know we can make the equation [tex]y+2=4(x+3)[/tex].

Now that we have point slope form we need to convert it. To do this we need to first get rid of the parenthesis by distribution. This will give us [tex]y+2=3x+12[/tex]

Next, we know we need to get [tex]x[/tex] and [tex]y[/tex] on the same side of the equal sign. We do this by subtracting 3x on both sides to get [tex]-3x+y+2=12[/tex]

Finally, we can subtract 2 on both sides to put the equation into standard form. This will give us [tex]-3x+y=10[/tex]

The two smallest positive solutions for x in the equation 12cos(2π/5x) + 10 = 16 are x = 5/6 and x = 17/6. Therefore, the correct option is B) 5/6, 25/6.

To find the two smallest positive solutions for x in the equation 12cos(2π/5x) + 10 = 16, we need to solve the equation for x.

Let's start by isolating the cosine term:

12cos(2π/5x) = 16 - 10

12cos(2π/5x) = 6

Next, divide both sides of the equation by 12:

cos(2π/5x) = 6/12

cos(2π/5x) = 1/2

To find the values of x that satisfy this equation, we can take the inverse cosine (arccos) of both sides:

2π/5x = arccos(1/2)

To determine the two smallest positive solutions, we need to find the values of x that correspond to the acute angles whose cosine is 1/2.

The arccosine of 1/2 is π/3, so:2π/5x = π/3

Next, solve for x:

x = (π/3)(5/2π)

x = 5/6

Therefore, the first solution for x is 5/6.

To find the second solution, we can add 2π to the right-hand side of the equation:

x = (π/3)(5/2π) + 2π

x = 5/6 + 12π/6

x = 5/6 + 2

x = 5/6 + 12/6

x = 17/6

Therefore, the second solution for x is 17/6.

Option b

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Answer:

x = -2, 7

Step-by-step explanation:

1.Single out 6x^2 to x^2 by dividing 6 on both sides

= x^2-5x-14=0

2.Write -5x as a difference in order to factor

= x^2+2x-7x-14=0

3. Factor.

= (x+2)(x-7)

4. Set equal to 0

x+2=0

x=-2

x-7=0

x=7

The solution of the equation 6x² – 30x – 84 = 0 from least to greatest will be  –2 and 7.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

6x² – 30x – 84 = 0

Then the factor of the equation will be

        x² – 5x – 14 = 0

x² – 7x + 2x – 14 = 0

x(x – 7) + 2(x – 7) = 0

       (x + 2)(x – 7) = 0

Then the solution will be

x = –2, 7

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Answer:

it's B

Step-by-step explanation:

14

Answer: B

11 - (-3) = 14.

-3 + 3 = 0.

11 + 3 = 14.

The answer is B, 14.

Hope it helps!

Answer:

Ok I will help because i'm the nicest person you'll ever meet lol Ok anyway

there will be no step by step explanation

Direction variation:   and Not direction variation:

y= 3x

X= -1

and

Y= 4

now for the other one the non-direction---------------------> Y = (2/7)x

------------------------------------------------------------------------------> -0.5x = Y

------------------------------------------------------------------------------> Y= 2.2x + 7

TADA I'm finished and your welcome!!! :D

A.  Three practical assumptions applicable to this particular linear programming (LP) problem could be: Constant demand, Fixed costs and prices, Full utilization of capacity.

B. LP Model: Decision Variables, Objective Function, Constraints.

C. set up the LP model in Excel and run Solver to obtain the answer and sensitivity reports.

D. it would not be feasible to deploy buses to Malacca.

E. The revenue would decrease due to the lower number of passengers, while the cost may remain relatively fixed (assuming the breakdowns do not incur additional repair costs).

(a) Three practical assumptions applicable to this particular linear programming (LP) problem could be: Constant demand, Fixed costs and prices, Full utilization of capacity.

Constant demand: The LP model assumes that the demand for Merlion's point-to-point coach services remains constant throughout the planning period. This means that the number of passengers traveling between Singapore and Malaysia is assumed to be consistent.

Fixed costs and prices: The LP model assumes that the costs associated with operating the buses, such as fuel, maintenance, and driver salaries, remain fixed. It also assumes that the ticket prices charged to passengers are constant and do not change based on factors like demand or competition.

Full utilization of capacity: The LP model assumes that all available seats on each bus will be filled by passengers. It does not account for scenarios where there might be empty seats due to insufficient demand or other factors.

(b) LP Model: Decision Variables, Objective Function, Constraints.

Decision Variables:

Let X i represent the number of buses deployed to city i, where i can take values 1 to n (n being the total number of cities in Malaysia).

Objective Function:

Maximize daily profit:

Maximize Profit = ∑(Revenue - Cost)

Constraints:

Capacity constraint for each city:

∑(X i * Seats per Bus) ≤ Total Available Seats

Demand constraint for each city:

X i ≥ Minimum Demand i

Non-negativity constraint:

X i ≥ 0 for all i

(c) Solution using Excel Solver:

Please provide the following information:

Total available seats

Seats per bus

Minimum demand for each city

Revenue and cost data

With the given input, I can help you set up the LP model in Excel and run Solver to obtain the answer and sensitivity reports.

(d) To determine the profit per passenger required for buses to be deployed to Malacca, we need to consider the revenue and cost associated with each passenger. Let's assume the revenue per passenger is R and the cost per passenger is C.

The profit per passenger can be calculated as follows:

Profit per Passenger = Revenue per Passenger - Cost per Passenger

To deploy buses to Malacca, the profit per passenger should be at least equal to zero or positive. If the profit per passenger is negative, it means that the cost per passenger is higher than the revenue per passenger, resulting in a loss for each passenger. In such a case, it would not be feasible to deploy buses to Malacca.

(e) If two buses were to break down on a given day, it would impact Merlion's profit because there would be a reduction in the number of available buses to transport passengers. This could result in a lower revenue as fewer passengers can be accommodated.

To analyze the impact on profit, you would need to consider the revenue and cost implications of operating with reduced capacity. The revenue would decrease due to the lower number of passengers, while the cost may remain relatively fixed (assuming the breakdowns do not incur additional repair costs).

By estimating the revenue and cost changes based on the reduced capacity, you can compare the new profit with the original profit to determine the impact.

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Answer:

The one at the top because the expression would be 6.23x10x10x10x10x10x10x10x10x10x10x10x10= 6,230,000,000,000

Step-by-step explanation:

Answer:

I believe it is the first one because it equals 6230000000000

Step-by-step explanation:

Answer:

P(x) = (-0.2x² + 480x - 24480)

Step-by-step explanation:

1). Expression representing the "Cost" to produce the shirts is,

  C(x) = 160x + 24480

  Where 'x' represents the number of shirts.

  Cost to produce 900 printed shirts will be,

   C(900) = 160×900 + 24480

                = 144000 + 24480

                = Php 168480

2). Revenue generated by selling 900 shirts is,

   R(x) = 640x - 0.2x²

   For x = 900,

   R(x) = 640(900) - 0.2(900)²

          = 576000 - 162000

          = Php 414000

3). Expression for profit:

   Since, Profit = Revenue generated - Cost for production

   P(x) = R(x) - C(x)

          = (640x - 0.2x²) - (160x + 24480)

          = (640x - 160x) - 0.2x² - 24480

          = 480x - 0.2x² - 24480

  P(x) = (-0.2x² + 480x - 24480)

Wayne's rectangular patio is adjacent to his house, and he wants to hang a string of lights around three sides of the patio, which is 86 feet long in total. The length of the patio, which is the side along the house, is 6 feet longer than twice its width. In this problem, we need to find the length and width of the patio.

Let's assume the width of the patio is 'w' feet. According to the given information, the length of the patio is 6 feet longer than twice its width, which can be expressed as 2w + 6 feet.

The total length of the three sides of the patio is given as 86 feet. Since we have two sides of equal length (width) and one side of length (length), we can set up the following equation:

2w + 6 + 2w + 2w = 86

Simplifying the equation, we have:

6w + 6 = 86

Subtracting 6 from both sides:

6w = 80

Dividing both sides by 6:

w = 80/6

w ≈ 13.33 feet (rounded to two decimal places)

Therefore, the width of the patio is approximately 13.33 feet. To find the length, we substitute the value of 'w' back into the equations for the length:

Length = 2w + 6

Length = 2(13.33) + 6

Length ≈ 32.67 feet (rounded to two decimal places)

Thus, the length of the patio is approximately 32.67 feet.

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the expected total number of orange candies and the standard deviation for the total number of orange candies in the two samples, respectively, are 13.75 and 3.033. Option E is correct.

We are given that Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange.

Two independent random samples, each of size 25, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies and we are asked to find the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples.

To solve this problem, we will use the formula for mean and variance of a binomial distribution.

Mean or Expected Value E(X) = np

Variance V(X) = np(1-p)The formula for standard deviation is as follows;

Standard deviation of X, σ(X) = √np(1 - p)The number of orange candies in each sample of size 25 is expected to be:

For Dynamite Mints: np = 25 × 0.1 = 2.5For Holiday Mints: np = 25 × 0.45 = 11.25Therefore, the expected total number of orange candies in the two samples is: 2.5 + 11.25 = 13.75The variance for Dynamite Mints is:

V(X) = np(1 - p) = 25 × 0.1 × (1 - 0.1) = 2.25The variance for Holiday Mints is:

V(X) = np(1 - p) = 25 × 0.45 × (1 - 0.45) = 6.9375Therefore, the total variance for the two samples is:

V(X1 + X2) = V(X1) + V(X2) = 2.25 + 6.9375 = 9.1875The standard deviation for the two samples is:

σ(X1 + X2) = √V(X1 + X2) = √9.1875 = 3.033

So, the expected total number of orange candies and the standard deviation for the total number of orange candies in the two samples, respectively, are 13.75 and 3.033. Option E is correct.

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Answer:

Step-by-step explanation:

Solving for variables

1.......................................

2.......................................

3.......................................

4.......................................

here are your answer

d = 2/3

c = 3/2

y = 2/3

x = 4 2/19

have a good day

Answer:

2(x+5)

Step-by-step explanation:

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

ill help

Step-by-step explanation:

Answer:

x = 32/3

Step-by-step explanation:

Step 1: Write equation

x/6 = 16/9

Step 2: Solve for x

The minimum amount of emergency savings you should have is $130.

To determine the minimum amount of emergency savings you should have, we need to consider the essential expenses.

In this case, the gasoline expense and the credit card payment are marked as essential expenses.

Let's calculate the minimum amount of emergency savings required to cover these essential expenses.

Essential expenses:

Gasoline (essential) = $100

Credit card payment (essential) = $30

To calculate the minimum emergency savings required, we add up the essential expenses:

Minimum emergency savings = Gasoline (essential) + Credit card payment (essential)

Minimum emergency savings = $100 + $30

Minimum emergency savings = $130

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Sides of a square are all the same.

4(x-2) = (5x-20)

Distribute the left side:

4x -8 = 5x-20

Subtract 4x from both sides:

-8 = x -20

Add 20 to both sides:

X = 12

Now replace x with 12 and solve for the length:

5(12) -20 = 60-20 = 40

The sides are 40 cm long.

Answer:

34

Step-by-step explanation:

The probability that either event will occur is approximately 0.4028.

To find the probability that either event will occur, we need to add the probabilities of A and B and subtract the probability of their intersection (i.e., the probability that both A and B occur).

Let P(A) be the probability of event A occurring, P(B) be the probability of event B occurring, and P(A ∩ B) be the probability of their intersection (i.e., the probability that both A and B occur).

Then the probability that either event will occur is given by:P(A ∪ B) = P(A) + P(B) - P(A ∩ B)Let n(S) be the number of ways the experiment can be conducted. Then:1. P(A) = 29/180,

since there are 29 words containing A and there are a total of 180 words.2. P(B) = 14/180,

since there are 14 words containing B and there are a total of 180 words.3. P(A ∩ B) = P(A) × P(B) = (29/180) × (14/180) = 203/32400.4. P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 29/180 + 14/180 - 203/32400 = 217/540 ≈ 0.4028.

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Answer: 14

Step-by-step explanation: An integer is any number that is not either a decimal or a fraction.

Hope this helps :)

Answer:

the answer is A.6(x + 3)

a) [tex]\(T(I) = B^{-1}IB = B^{-1}B = I\), \(T(B) = B^{-1}BB = B^{-1}B = I\)[/tex]

b) T is a linear transformation as it satisfies the properties of additivity and homogeneity.

c)[tex]\(\text{ker}(T) = \{0\}\), \(\text{nullity}(T) = 0\)\\[/tex], [tex]\(CE \in M_{an}\) implies \(C \in \text{ker}(T)\)[/tex]

a) [tex]\(T(I) = B^{-1}IB = B^{-1}B = I\)[/tex], [tex]\(T(B) = B^{-1}BB = B^{-1}B = I\)[/tex].

b) T is a linear transformation as it preserves addition and scalar multiplication:[tex]\(T(A+C) = T(A) + T(C)\)[/tex] and[tex]\(T(A+C) = T(A) + T(C)\)[/tex].

c) The kernel of T, [tex]\(T(A+C) = T(A) + T(C)\)[/tex], consists only of the zero matrix:[tex]\(T(A+C) = T(A) + T(C)\)[/tex].

d) The nullity of T, [tex]\(\text{nullity}(T)\)[/tex], is 0 since the kernel contains only the zero matrix.

e) If C is invertible and A is in [tex]\(\text{nullity}(T)\)[/tex], then CA is also in[tex]\(M_{an}\)[/tex].

Therefore, if [tex]\(\text{nullity}(T)\)[/tex] then[tex]\(\text{nullity}(T)\)[/tex]

T and TB both equal . T is a linear transformation preserving addition and scalar multiplication. The kernel of T is 0 with nullity 0. If [tex]\(\text{nullity}(T)\)[/tex], the[tex]\(\text{nullity}(T)\)[/tex]

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The linear transformation T(A) = B^(-1)AB, where B is a fixed n x n invertible matrix, is analyzed. It is found that T(I) = I and T(B) = B, demonstrating the behavior of T on the identity matrix and the matrix B itself. The linearity of T is proven by showing that it satisfies the properties of additivity and scalar multiplication. The kernel of T is shown to be {0}, indicating that the only matrix mapped to the zero matrix under T is the zero matrix itself. The nullity of T is determined to be 0, meaning T is injective or one-to-one. Lastly, it is demonstrated that if C is an eigenvector of B, then C is also an eigenvector of T.

For T(I), substituting I into the expression T(A) = B^(-1)AB yields T(I) = B^(-1)IB = B^(-1)B = I, where I is the identity matrix. This shows that the identity matrix remains unchanged under the transformation T.
Similarly, for T(B), substituting B into the expression T(A) = B^(-1)AB gives T(B) = B^(-1)BB = B^(-1)B^2 = B. This indicates that the matrix B itself is mapped to B under T.
To prove the linearity of T, let A and C be two matrices, and let k be a scalar. By substituting kA and A + C into the expression for T(A), we can demonstrate additivity and scalar multiplication. T(kA) = B^(-1)(kA)B = kB^(-1)AB = kT(A), showing scalar multiplication. T(A + C) = B^(-1)(A + C)B = B^(-1)AB + B^(-1)CB = T(A) + T(C), demonstrating additivity.
The kernel of T, denoted ker(T), is the set of matrices A for which T(A) = 0. Since T(A) = B^(-1)AB, the only matrix that satisfies this condition is A = 0, resulting in ker(T) = {0}.
The nullity of T, denoted nullity(T), is the dimension of the kernel of T. Since ker(T) = {0}, which contains only the zero matrix, nullity(T) = 0. This implies that T is injective or one-to-one.
Lastly, if C is an eigenvector of B, then B^(-1)CB = λC, where λ is the corresponding eigenvalue. Substituting this into the expression for T(A), we find T(C) = B^(-1)CB = λC. Thus, if C is an eigenvector of B, it is also an eigenvector of T with the same eigenvalue λ.


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the complete question is:

  Let B be a fixed n x n invertible matrix. Define T:Mnn →Mnn by T (A) = B-¹AB. Find T (I) and T(B). i) ii) Show that T is a linear transformation. iii) Show that ker(T) = (0). What ia nullity(7)? Show that if CE Man, then CER(T). iv)Show that if CE Man, then CE R(T).GENERATE THE ANSWER IN 150 WORDS IT WILL BE DIVIDED INTO TWO PARAGRAPHS THE FIRST PARA WILL BE THE SUMMARY OF THE ANSWER in 2 lines, AND SECOND PARA WILL BE THE EXPLANATION OF THE ANSWER