travis purchased a car for 25,000.​

Therefore, the minimum value of the function is -10.

To find the minimum value of the function \(f(x, y, z) = x^2 - 4x + y^2 - 6y + z^2 - 2z + 5\), subject to the constraint x + y + z = 3 using Lagrange multipliers, we set up the following system of equations:

∇f = λ∇g

g = x + y + z - 3

Taking the partial derivatives of f with respect to x, y, and z:

∂f/∂x = 2x - 4

∂f/∂y = 2y - 6

∂f/∂z = 2z - 2

And the partial derivatives of g with respect to x, y, and z:

∂g/∂x = 1

∂g/∂y = 1

∂g/∂z = 1

Setting up the equations:

2x - 4 = λ

2y - 6 = λ

2z - 2 = λ

x + y + z = 3

From the first three equations, we can solve for x, y, z in terms of λ:

x = (λ + 4)/2

y = (λ + 6)/2

z = (λ + 2)/2

Substituting these expressions into the fourth equation:

(λ + 4)/2 + (λ + 6)/2 + (λ + 2)/2 = 3

Simplifying the equation:

3λ + 12 = 6

Solving for λ:

λ = -2

Substituting λ = -2 back into the expressions for x, y, and z:

x = (λ + 4)/2

= ( -2 + 4)/2

= 1

y = (λ + 6)/2

= ( -2 + 6)/2

= 2

z = (λ + 2)/2

= ( -2 + 2)/2

= 0

Thus, the minimum value of f(x, y, z) subject to the constraint x + y + z = 3 is \(f(1, 2, 0) = 1^2 - 4(1) + 2^2 - 6(2) + 0^2 - 2(0) + 5 = -10.\)

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This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Solving for the area and scale factor we have:

L= 5 units

W = 2 units

A = (5 x 2)

A = 10 square units.

A= (Scale factor of  L * W)*  L * W

= (2 x 2 x 5 x 2)

A = 40 square units.

A= (Scale factor of  L * W)*  L * W

= (3 x 3 x 5 x 2)

A= 90 square units

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Answer:

Yeah he call me patty cake cause the way that ace shake

Step-by-step explanation:

Step-by-step explanation:

number = 15/2 or 7.5

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you.

The 90% confidence interval is: (2.51, 3.22)

It is a boundary of values which is eventually to comprise a population value with a certain degree of confidence. It is usually shown as a percentage whereby a population means lies within the upper and lower limit of the provided confidence interval.

We have the following information :

The level of significance is calculated as:

\(\alpha =1-c\\\\\alpha =1-0.90\\\\\alpha =0.10\)

The degrees of freedom for the case is:

df = n - 1

df = 15 - 1

df = 14

The 90% confidence interval is calculated as:

=x(bar) ±\(t_\frac{\alpha }{2}\), df \(\frac{s}{\sqrt{n} }\)

= 2.86 ±\(t_\frac{0.10 }{2}\), 14 \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 1.761 × \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 0.3547

= (2.51, 3.22)

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Answer:

100n² - 1

Simplifying we get

(10n)² - 1

Hope this helps.

Answer:

(10n)² - 1²

Step-by-step explanation:

100 n² − 1= (10n)² - 1²

Answer: 625 meters

Step-by-step explanation: Five hundred meters of pipe would require twenty men working for ten days.

First, we have to find the rate of work for one man. This is calculated thus:

(500m) ÷ (20men × 10 days) = 500 ÷ 200 = (5/2) = 2.5 meters per day

From the rate of work of one man, we can then calculate the length in meters that fifty men can lay in five days. This is calculated thus:

50 men × (5/2) × 5 days = 50 × 2.5 × 5 = 625 meters.

Therefore, fifty men working together would lay six hundred and twenty five (625) meters of pipe in five days.

Answer:

B=12/13

Step-by-step explanation:

Not positive, but i believe you are trying to find the angle measure using inverse sin or whatever its called and then reducing the fraction. SOHCAHTOA

Answer:

x = 0

Step-by-step explanation:

\(\frac{1}{3} (6x-5)-x=\frac{1}{3} -2(x+1)\)

We will be using the Distributive Property shown below:

5(x+1) = 5x+5

Distribute 1/3 and -2:

\(\frac{6}{3} x-\frac{5}{3}-x=\frac{1}{3} -2x-2\):

Combine Like Terms:

\(x-\frac{5}{3} =-2x-\frac{5}{3}\)

Add 2x to both sides:

\(3x-\frac{5}{3} =-\frac{5}{3}\)

Add 5/3 to both sides:

\(3x=0\)

Divide both sides by 3:

\(x=0\)

A term is a constant, a variable, or a product of numbers and variables.

A symbol (typically a letter) used in algebra to represent an unknowable numerical value in an equation or algebraic expression. A variable can be defined as a quantity that is changeable and not fixed. A variable in mathematics is an alphabet or term that stands in for an unknowable quantity, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are used. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

Here,

A term can be a number, a constant, a variable, or the product of a number and a variable.

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Answer:

Step-by-step explanation:

then simplify

Answer:

Step-by-step explanation:

a) Reflection over the x axis then a translation directly to the right

b) All the figures are conrguent since only rigid motions were used.

Answer:

whats the question?

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Remark

You must do the changes in order. Add 1 then multiply by 2

Answer: 7 14 15 30

Answer:

d. variables A and B are unrelated

(make sure that these were the only options, it could happen that two variables that might have a correlation coefficient might be totally unrelated)

Step-by-step explanation:

Since the variables A and B are already correlated, then they cannot be unrelated

The total number of band members and dancers in the halftime show in all rows were 276.

A row is an arrangement of things in a straight line next to each other.

if there are n rows and each row has m members then total number of members = m* n

Given that marching band was in 3 sections and each section has 8 rows of  8 players , then players in each section of marching band  = 8 *8 = 64

As, there are 3 such sections then total number of marching band players =3*(players in each section) = 3* 64 = 192

Given that there are 2 sections of dancers and each section has 6 rows of 7 dancers.

Then, dancers in each section of  dancers = 6*7 =42

As there are two such sections, then the total dancers = 2* 42 = 84

total no of band members and dancers = 192+84 = 276

Therefore, The total number of band members and dancers in the halftime show were 276.

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Final Answer: \(x = 3 + \sqrt{2}, 3 - \sqrt{2}\)

Steps/Reasons/Explanation:

Question: Solve by using the quadratic formula:  \(x^{2} - 6x + 7 = 0\).

Step 1: Use the Quadratic Formula.

\(x = \frac{6 + \sqrt[2]{2} }{2}, \frac{6 - \sqrt[2]{2} }{2}\)

Step 2: Simplify solutions.

\(x = 3 + \sqrt{2}, 3 - \sqrt{2}\)

~I hope I helped you :)~ The quadratic formulaic is attached in an image.

Answer:

75 squared feet

Step-by-step explanation:

Area=1/2×base ×height

Answer:

The base of the triangle is 10 ft

the height of the triangle is 15 ft

the area of the triangle is 75 square feet

Step-by-step explanation:

Solving a linear equation we will see that the measures of the angles are:

∠1 = = 6°

∠2  = 84°

We can see that we have a right angle (this is a 90° angle) and it is divided in the angles ∠1 and ∠2.

Then we can write:

∠1 + ∠2 = 90°

And we know that:

∠1 = x - 8

∠2 =  6x

Then we can write the linear equation:

x - 8 + 6x = 90

We can solve that for x toget:

x - 8 + 6x = 90

7x = 90 + 8

x = 98/7 = 14

Then the measures of the angles are:

∠1 = x - 8 = 14 - 8 = 6°

∠2 =  6x = 6*14 = 84°

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Answer:

I am assuming the 8:15 was a typo and was actually supposed to be a 8:14. Anyways, they are equivalent because they all make 4:7 when simplified.

Step-by-step explanation:

4:7 = itself at this point, as they don't have numbers that can simplify each other on both sides, unless you are looking for a decimal answer.

8:14 = 4:7 <- You can divide the 8 and 14 by two. 8 divided by 2 is four, and 14 divided by 2 is 7.

16:28 = 4:7 <- You can divide the 16 and the 28 by four. 16 divided by 4 is 4, and 28 divided by 4 is 7.

20:35 = 4:7 <- You can divide both sides by 5. 20 divided by 5 is 4, and 35 divided by 5 is 7.

Answer:

Q1 = 6.45f/s

Q2 = 0.633 times

Q3 = 0.107 miles

Step-by-step explanation:

Q1: Since

4.4 miles = 1 hour

and

1 mile = 5,280 feet

1 hour = 3600 seconds

Then 4.4 miles

= 5,280 feet × 4.4

= 23,232 feet / 3600 seconds

= 6.453f/s

= 6.45f/s

Q2: Wing beat per minute

= 38 ÷ 60

= 0.633 times

Q3: Miles per minute

Since 6.4 miles = 1 hour,

6.4 miles = 1 × 60

6.4 miles = 60 minutes

x miles = 1 minute

= 6.4/60

= 0.107 miles

Answer:

6

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

The volume of the different shapes have been calculated in the space below

Volume of rectangular prism = lwh

where we define the variables as :

l = length

w = width

h = height

then when we multiply, we will have

= 4 x 10 x 6

= 240

Volume of triangular pyramid = 1 / 3 b x h

where b = base

h = height

1 / 3 x 1.5 x 2

= 1

Volume of rectangular pyramid = lwh / 3

= 7.5 x 4.5 x 5 / 3

= 56.25

= 1/2 x b x h x l

= 1/2 x 3 x 8.5 x 7

= 89.25

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From the analysis of the above math, the amount she invested in the CD account is 5,000. See the analysis below.

Let A be the amount invested in the CD.

Let B be the amount invested in the savings bond.

A + B = 15, 000

.04A + .07B = 900

Multiply the first equation by -.04 and add it to the second equation to get rid of the A term.

-.04A-.04B = -600  add this equation to the second equation.

.03B = 300  multiplying by 100.  3B = 30,000

dividing by 3 on both sides: B = 10,000.  So A = 5,000

So she invested 5,000 in the CD account

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This process reflects the graph across the line y = x. Inverse functions can be thought of as "undoing" the operations of the original function. In this activity, we will apply these principles to plot the inverse function for the given graphs.

This reflection across the line y = x is a result of interchanging the roles of the independent and dependent variables. Let's consider an example to illustrate this. Suppose the original function f(x) is represented by a graph that starts at the point (2, 4) and passes through other points such as (3, 6) and (4, 8). To plot the inverse function, we swap the x and y coordinates of these points.

So, the point (2, 4) becomes (4, 2) on the inverse graph, (3, 6) becomes (6, 3), and (4, 8) becomes (8, 4).By repeating this process for all the points on the original graph, we can obtain the graph of the inverse function. It is important to note that not all functions have an inverse function. For a function to have an inverse, it must pass the horizontal line test, meaning that no horizontal line intersects the graph at more than one point .

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The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Answer:

Step-by-step explanation:

(5). ( \(x_{1}\) , \(y_{1}\) )  

y - \(y_{1}\) = m( x - \(x_{1}\) )

~~~~~~~~~~~~~~~~~

( 4 , 8 )

y = \(\frac{1}{7}\) x - 5 ; slope m = \(\frac{1}{7}\)

Slope of line ⊥ to the given line is opposite reciprocal to \(\frac{1}{7}\) and equal to ( - 7)

y - 8 = - 7( x - 4 )

(6).  

( \(x_{1}\) , \(y_{1}\) )

( \(x_{2}\) , \(y_{2}\) )

m = \(\frac{ y_{2} -y_{1} }{ x_{2} -x_{1} }\)

y = mx + b

~~~~~~~~~~~~

( 4 , 3 )

( 5 , 1 )

m = \(\frac{1-3}{5-4}\) = - 2

y - 3 = - 2( x - 4 )

y = - 2x + 11

(7). y = - \(\frac{1}{2}\) x + 2

The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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