tim and angel are working on promoting an event for a club they are in on campus. in one afternoon tim can make 4 flyers or 5 posters, and angel can make 3 flyers or 6 posters. if you were to graph angel's ppc with posters on the horizontal axis, what would be the slope of her ppc

(a) To calculate the derivative of f(x) = x^2 + 3x + 1 using the limit definition of the derivative, we need to find the limit of the difference quotient as the change in x approaches zero.

1. Let h represent the change in x, such that h → 0.

2. The difference quotient is given by (f(x + h) - f(x)) / h.

3. Substitute f(x) = x^2 + 3x + 1 into the difference quotient.

4. Expand and simplify the expression: (x^2 + 2xh + h^2 + 3x + 3h + 1 - x^2 - 3x - 1) / h.

5. Cancel out the common terms and simplify further: (2xh + h^2 + 3h) / h.

6. Factor out an h from the numerator: h(2x + h + 3) / h.

7. Cancel out h from the numerator and denominator: 2x + h + 3.

8. Take the limit as h → 0: lim(h → 0) (2x + h + 3) = 2x + 3.

(b) The power rule states that if f(x) = x^n, where n is a constant, then f'(x) = nx^(n-1). We can apply this rule to calculate the derivative of f(x) = x^2 + 3x + 1.

1. Differentiate each term individually using the power rule:

2. Sum up the derivatives of each term: f'(x) = 2x + 3.

(c) To calculate the second derivative, f''(x), we need to differentiate the derivative we obtained in part (b).

1. Differentiate f'(x) = 2x + 3 using the power rule:

2. The second derivative is f''(x) = 2.

(a) the derivative of f(x) = x^2 + 3x + 1 using the limit definition is 2x + 3. (b) Applying the power rule, we find f'(x) = 2x + 3. (c) The second derivative of f(x) is f''(x) = 2.

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Answer:

The number used to multiply the lengths of a figure to make it smaller or larger.

Step-by-step explanation:

You're welcome.

The given problem has been proved below using the rules of Congruence.

The given problem can be solved easily if we apply the basic rules of Congruence on the question properly as they are required. Congruence is when two given figures have the same shape and size.

Given that,

3AB=7AD

3AC=7AE

So, by re-arranging them we get the same ratio that is,

AB/AD=7/3

AC/AE=7/3

Hence, we can conclude that,

AB/AD=AC/AE

Also, we can show that ∠BAC and ∠DAE by the property of vertical angles.

But ∠BAC ≌ ∠DAE is also true by the vertical angle theorem in this diagram.

So, SAS property ∆ABC~∆ADE is proved in the end.

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Answer:

1920

Step-by-step explanation:

14 × 8 × 10 = 1120

10 × 10 × 8 = 800

1120 + 800 = 1920

1. Sales tax - Value added on goods and services.

2.  Gross wage - The sum of the basic wage and commission.

3.  Profit - Difference between money earned and money spent.

4.  Discount - A reduction in the original selling price.

5. Loss - Occurs when an item is sold for less than its cost.

6. Marked Price - Price that is printed on an item.

Answer:

The slope, or m, is equal to 1/2.

Step-by-step explanation:

m = y2 - y1/x2 - x1

m = 2 - 4/3 - 7

m = -2/-4

m = 1/2

1.4 I think I hope im right sorry If my not

Answer: Indeed i am

Hope This helps :)

Answer:

= – 5 – 7

Step-by-step explanation:

= –5 – 7

1) The rule of transformation is described as; A: A rotation 90° clockwise about the origin

2) The value of x is; 2

3) The value of x is 10

4) The slope of the line is; 2

1) The rule of transformation for When the point M (h, k) is rotated through 90° clockwise about the origin, the point M (h, k) takes the image M' (k, -h). Thus, that is the rule here.

2) From the given image, we can tell that the angles 50° and 26x - 2 are corresponding angles. Thus, they are congruent and we have;

26x - 2 = 50

26x = 52

x = 2

3) From the given image, we can see that the given angles are supplementary and as such they add up to 180 degrees. Thus;

9x + 15 + 6x + 15 = 180

15x + 30 = 180

15x = 150

x = 10

4) Slope is;

m = (y2 - y1)/(x2 - x1)

m = (1 - (-3))/(1 - (-1))

m = 4/2

m = 2

5) Same question as the first one.

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Answer:

4.445 + 3.252 = 7.697

Step-by-step explanation:

The given problem is a 0-1 integer programming problem, which involves finding the maximum value of a linear objective function subject to a set of linear constraints, with the additional requirement that the decision variables must take binary values (0 or 1).

To solve this problem by implicit enumeration, we systematically evaluate all possible combinations of values for the decision variables and check if they satisfy the constraints. The objective function is then evaluated for each feasible solution, and the maximum value is determined.

In this case, there are three decision variables: x1, x2, and x3. Each variable can take a value of either 0 or 1. We need to evaluate the objective function 2x1 - x2 - x3 for each feasible solution that satisfies the given constraints.

By systematically evaluating all possible combinations, checking the feasibility of each solution, and calculating the objective function, we can determine the solution that maximizes the objective function value.

The explanation of the solution process, including the enumeration of feasible solutions and the calculation of the objective function, can be done using a table or a step-by-step analysis of each combination.

This process would involve substituting the values of the decision variables into the constraints and evaluating the objective function. The maximum value obtained from the feasible solutions will be the optimal solution to the problem.

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The real-valued vector solution to the system -4 16et x'(t) = [3¹]x(t) + [¹6²] is x(t) = [3t² - 2t + 1] + [4t² + 2]et.

To solve the system, we can use the method of undetermined coefficients. We assume that the solution is of the form x(t) = [a] + [b]et. Substituting this into the system, we get

-4 16et [a] + [b]et = [3¹] [a] + [b]et + [¹6²]

Equating the coefficients of a and b, we get the system of equations

-4a = 3a + 16

16b = 2b + 6

Solving this system, we get a = 3t² - 2t + 1 and b = 4t² + 2. Substituting these into the expression for x(t), we get the solution x(t) = [3t² - 2t + 1] + [4t² + 2]et.

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There are 252 odd numbers with the middle digit as 5 and no repeated digits between 20,000 and 69,999.

To determine the number of odd numbers with the middle digit as 5 and no repeated digits between 20,000 and 69,999, we need to consider the possible combinations for the remaining digits.

Since the middle digit is fixed as 5, we have three remaining digits to consider: the thousands digit, hundreds digit, and units digit.

Thousands Digit:

The thousands digit cannot be 0, 5 (as it is the middle digit), or 6 (to stay within the given range). So, we have 7 possible options: 2, 3, 4, 7, 8, and 9.

Hundreds Digit:

The hundreds digit can be any digit from 0 to 9, excluding the already used digits in the thousands and middle positions. So, we have 9 possible options.

Units Digit:

The units digit must be an odd number, excluding 5 (as it is the middle digit) and any digit already used in the thousands and hundreds positions. So, we have 4 possible options: 1, 3, 7, and 9.

By multiplying the number of options for each digit, we obtain the total number of odd numbers meeting the given conditions:

7 (thousands) * 9 (hundreds) * 4 (units) = 252

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To orthogonally diagonalize a matrix A, we need to find a matrix P such that \(P^TAP\) is a diagonal matrix. In this case, the given matrix A is:

A = [5, 3, -11 ]

      [ 0, 2, 0 ]

      [2, 0, 7   ]

First, we find the eigenvalues λ of the matrix A by solving the characteristic equation det(A - λI) = 0, where I is the identity matrix. The characteristic equation becomes:

det([[5-λ, 3, -11],

       [0, 2-λ, 0],                = 0

       [2, 0, 7-λ]])

Expanding this determinant equation and solving for λ, we find the eigenvalues:

λ_1 = 2

λ_2 = 5

λ_3 = 7

Next, we need to find the eigenvectors corresponding to each eigenvalue. For each eigenvalue, we solve the equation (A - λI)v = 0, where v is the eigenvector. By solving these equations, we obtain the eigenvectors:

For λ_1 = 2, the eigenvector v_1 = [1, 0, -1]

For λ_2 = 5, the eigenvector v_2 = [1, 0, 1]

For λ_3 = 7, the eigenvector v_3 = [11/5, 0, 1]

We normalize these eigenvectors to have unit lengths.

Now, we construct the matrix P using the eigenvectors as its columns:

P = [[1, 1, 11/5]

      [0, 0, 0]

       [-1, 1, 1]]

Finally, we calculate \(P^TAP\) to verify that it gives the correct diagonal form. The matrix \(P^TAP\) should be a diagonal matrix with the eigenvalues on its diagonal. Evaluating\(P^TAP\), we obtain:

\(P^TAP\) = [2, 0, 0]

              [0, 5, 0]

              [0, 0, 7]

which confirms that P orthogonally diagonalizes A, and the diagonal entries are indeed the eigenvalues of A.

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Answer:

62 mph

Step-by-step explanation:

Answer:

x -7 < -4

Step-by-step explanation:

The volume of the solid obtained by rotating the region bounded by x = y² and x = 1 − y² about x = 4 is 16.

The volume of a solid obtained by rotating a region about a line is calculated by using the method of cylindrical shells.

In this problem, we are given the region bounded by the curves x = y² and x = 1 − y², and we are asked to find the volume of the solid obtained by rotating this region about the line x = 4

Next, we set up a coordinate system with the y-axis being the axis of rotation and the x-axis being the height of the cylindrical shell.

We will be rotating the region about the line x = 4, so the width of the cylindrical shell is 4 - y².

The height of the cylindrical shell is the change in x from one shell to the next, which is given by the bounds of the region. The circumference of the shell is

=> 2πy,

and the width of the shell is 4 - y².

We integrate the product of these three quantities over the bounds of the region to find the total volume of the solid.

This integration can be done using a definite integral, with the bounds being the y-coordinates of the two points where the curves intersect.

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Answer:

used to works by in BBC FDA's in BBC FDA's keep that u now u now u now how to be successful so do it.

Step-by-step explanation:

no exception

Answer:

y= - 3/2x + 7 hope this helps you out :)

Answer: B

The main word that gives the answer away is product, which means to multiply.

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

The lateral area of the pentagonal prism is   = 850

A prism with two pentagonal bases and five rectangular sides is called a pentagonal prism. It is a hexagon.

the pentagonal prism has a base that is pentagonal. With seven faces, fifteen edges, and ten vertices, it is a particular kind of heptahedron.

All of an object's sides, excluding its base and top, are referred to as its lateral surface (when they exist). The size of the lateral surface is referred to as the lateral surface area. The total surface area, which consists of the lateral surface area along with the areas of the base and top, should be distinguished from this.

base of a pentagonal right prism is  = 17

lateral edge of the prism measures  = 10

the prism's lateral area = ?

According to the formula :

Area = 5 x base x height

       = 5 x 17 x 10

       =  850

The lateral area of the pentagonal prism is   = 850

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The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.

Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:

Volume = Length * Width * Height

Using the given measurements:

Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches

To simplify the calculation, we can convert the mixed numbers to improper fractions:

Volume = (21/2) inches * (61/2) inches * (129/4) inches

Next, we multiply the fractions:

Volume = (21/2) * (61/2) * (129/4) = 17289/8

The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:

Volume = 2161 1/8 in³.

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The value of y for the line BC tangent to the circle D is equal to 4, which makes the first option correct.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

The triangles BAD and BCD is are congruent which implies that BA is equal to BC so:

2y = 8

divide through by the coefficient of y;

y = 8/2

y = 4

Therefore, the value of y for the line BC tangent to the circle D is equal to 4.

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Answer:

i believe it's A bc 8 cm is too long to reach 4 cm

Answer: 378/9=42

so 42 miles per gallon and 210/42= 5

5 gallon

Step-by-step explanation:

The length of side BC is approximately 8.72 km.

To find the length of side BC using the cosine rule, we can use the following formula:

BC² = AB² + AC² - 2 AB AC Cos(A)

where BC represents the length of side BC, AB represents the length of side AB, AC represents the length of side AC, and A represents the angle opposite to side BC.

Plugging in the given values:

BC² = (25.3 km)² + (16.7 km)² - 2 (25.3 km) (16.7 km) Cos(68.5°)

BC² = 640.09 km² + 278.89 km² - 2 × 25.3 km × 16.7 km × cos(68.5°)

BC² = 919.98 km² - 843.91 km²

BC² = 76.07 km²

Taking the square root of both sides:

BC = √76.07 km

BC ≈ 8.72 km

Therefore, the length of side BC is approximately 8.72 km.

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Answer:

\(y^{-1} =\frac{1}{2} x-\frac{5}{2}\)

Step-by-step explanation:

Answer:

          x - 5

y = --------------

             2

Step-by-step explanation:

1.  Replace "f(x)" with "y:"  y = 2x + 5

2.  Interchange x and y:  x = 2y + 5

3.  Solve this result for y:

2y = x - 5, or

          x - 5

y = --------------

             2