2. a) Determine an equation for the family of cubic functions with zeros - 3/2; 1, and 5/2 (2 points) b) Determine an equation, in simplified form, for the member of the family whose graph passes through the point (-1, -28). (4 points)

Answer:

7

Step-by-step explanation:

The question asks for f(3).  f(3) is the y value.  "3" is the x value.  In other words the question asks, "What is the value of y when x is 3?"

When x is 3, y=7.  

Answer:

72

Explanation:

First, we can find the top and bottom smaller squares of the rectangular prism. Since we are working with a variety of rectangles, we only need to use the equation L×W.

To start with, let's multiply 2×3, which gives us 6, the surface area of both the bottom and top rectangles, so now we need to multiply it by 2 to account for both of them. 6×2=12

Now, we'll find the surface area of the bigger rectangles in the middle, which are 6 by 3, so again we will need to multiply length times width, then by 2 to count both rectangles. 6×3=18×2=36

Finally, we can find the surface area of the smaller rectangles in the middle, which are 6 by 2. 6×2=12, then multiply by 2 since there are 2 of those rectangles, 12×2=24

Now to find the total surface area, we need to add the gathered surface area from each shape, 12+36+24=72

Answer:

I think it's B

Step-by-step explanation:

I hope you get it right

Steve runs \(\frac{3}{8}$\) of a mile each day.

For instance, traveling at 60 mph equates to traveling 60 miles per hour. There are an hour in 60 minutes, so partition the miles by that sum, and presto! One mile can be covered in one minute.

Victor runs \(\frac{1}{2}$\) of a mile each day.

Steve runs \(\frac{3}{4}$\) of the distance that Victor runs, which is \(\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$\) of a mile.

Therefore, Steve runs \(\frac{3}{8}$\) of a mile each day.

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Answer:

It's C

Step-by-step explanation:

took the test

Answer:c

Step-by-step explanation:

Answer:

(-2,8) (0,4) (2,3) (4,2)

Step-by-step explanation:

Answer:

75 dollars.

Step-by-step explanation:

Each person costs 25 dollars and p=3 we just put this into a equation.

25 × 3 = 75

C = 75

Answer:

8x^2-6a+9b+14

Step-by-step explanation:

P=(12a^2 + 5a + 9b + 16)

(4a^2 + 9a - 8)+ (2a + 2b + 10) +(x)= (12a^2 + 5a + 9b + 16)

(4a^2+11a+2)+(x)=(12a^2 + 5a + 9b + 16)

subtract (4a^2+11a+2) from both sides

x= 8x^2-6a+9b+14

Answer:

ello luv

Step-by-step explanation:

Answer:

4:1

Step-by-step explanation:

Every 4 circles there is 1 triangle.

Answer:

  50 ft by 25 ft . . . . . 50 ft parallel to the barn

Step-by-step explanation:

You want the dimensions of the largest rectangular area that can be enclosed using 100 ft of fence for three sides.

If the dimensions of the space are L feet in length and W feet in width, where L is parallel to the barn, the length of the perimeter fence is ...

  P = L +2W

Solving for W gives ...

  W = (P -L)/2

The area of the enclosed space is ...

  A = LW

  A = L(P -L)/2 . . . . . substitute for W

The area formula is the equation for a parabola that opens downward. It has zeros at L=0 and at L=P. The vertex (maximum) is found at the value of L that lies on the line of symmetry, halfway between these zeros. If we call that length M, then we have ...

  M = (0 +P)/2 = P/2

The length of enclosure that maximizes the area is 1/2 the length of the available fence.

The width is ...

  W = (P -P/2)/2 = P/4

The width of the enclosure that maximizes the area is 1/4 the length of the available fence.

Using 100 feet of fence, the dimensions are ...

__

Additional comment

Note that we have solved this in a generic way. The solution given is the general solution to the 3-sided enclosure problem.

This is a special case of the general rectangular enclosure problem which has the solution that the total cost in one direction is equal to the total cost in the orthogonal direction. This rule applies even when costs are different for the different sides or for any partitions that might divide the enclosure.

Here the "cost" is simply the length of the fence. The 50 ft of fence parallel to the barn is equal in length to the 25 +25 ft of fence perpendicular to the barn.

The dimensions that give the maximum area inside the rectangle are x = 50 feet (parallel to the barn wall) and y = 25 feet (perpendicular to the barn wall).

To maximize the area of the rectangular fence, follow these steps:

1. Let's assign variables to the dimensions: let the length of the rectangle parallel to the barn wall be x feet, and the length perpendicular to the barn wall be y feet.

2. We are given that 100 feet of fence will be used for the other three sides. This means the fencing equation is:

x + 2y = 100.

3. Solve for x:  x = 100 - 2y.

4. The area A of the rectangle is given by the product of its dimensions: A = xy.

5. Substitute the expression for x from step 3 into the area formula:  A = (100 - 2y)y.

6. Expand the expression: A = 100y - 2y^2.

7. To maximize the area, we need to find the maximum value of the quadratic function A(y). Since the coefficient of the y^2 term is negative, the graph of A(y) is a downward-opening parabola, which means it has a maximum value.

8. To find the maximum, we'll use the vertex formula for parabolas: y_vertex = -b/(2a), where a = -2 and b = 100. Plugging in these values, we get y_vertex = -100/(2 * -2) = 25.

9. Substitute the value of y_vertex back into the equation for x: x = 100 - 2(25) = 50.

10. So the dimensions that give the maximum area inside the rectangle are x = 50 feet (parallel to the barn wall) and y = 25 feet (perpendicular to the barn wall).

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Step-by-step explanation:

a slope of 0 means the slope is 0/x. in other words, y does not change at all.

and that means that the first point has the same y coordinate as the second point.

q = 2

the point is (10, 2).

According to the information we can infer that Dora's conclusion may be incorrect because the information provided only states that the number of people who spent time reading falls within specific ranges (0-2 hours, 2-4 hours, and 2-10 hours), but it does not give a specific count for those who spent at least 4 hours. Therefore, Dora's assumption that "most people spent at least 4 hours a week reading" is not supported by the given data.

The range of the time spent reading cannot be determined from the information provided because the ranges are overlapping. For example, a person who spent exactly 2 hours reading could fall into both the first range (0-2 hours) and the second range (2-4 hours). Without more specific data or non-overlapping ranges, it is not possible to determine the exact range of time spent reading.

To estimate the mean time spent reading by Dora's friends, we can calculate the midpoint of each range and use it as an approximate value. The midpoint for the first range (0-2 hours) is 1 hour, for the second range (2-4 hours) is 3 hours, and for the third range (2-10 hours) is 6 hours. We can then calculate the estimated mean by taking the weighted average of these midpoints using the respective number of people as weights.

Estimated mean = [(4 * 1) + (5 * 3) + (11 * 6)] / (4 + 5 + 11) = 4.53 hours (approximately)

So, an estimate of the mean time spent reading by Dora's friends is approximately 4.53 hours.

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Answer:

8x10x

Step-by-step explanation:

The function f(x) = 1/2(3)ˣ + 7 depicts exponential decay.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Euler’s Number ‘e’ is a numerical constant used in mathematical calculations and is an irrational number. Jacob Bernoulli discovered the mathematical constant e.

e =  \(\lim_{n \to \infty} (1 + 1/n)^{n}\)

We have the following function -

f(x) = 1/2(3)ˣ + 7

It can be seen that the graph decreases and becomes constant in the first quadrant. Therefore, the function depicts exponential decay.

Therefore, the function f(x) = 1/2(3)ˣ + 7 depicts exponential decay.

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Answer:

This is the answer to your question

Answer:

x=1

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

4x−7=−3x

Step 1: Add 3x to both sides.

4x−7+3x=−3x+3x

7x−7=0

Step 2: Add 7 to both sides.

7x−7+7=0+7

7x=7

Step 3: Divide both sides by 7.

7x

7

=

7

7

x=1

Answer: Not enough information provided, please provide any additional instructions, answers, and text which may have been included in the question.

Step-by-step explanation:

Answer:

on which days did it rain less then one-fifth of an inch

Step-by-step explanation:

The equation x^2 + 2x - 8 = 0 implies the equation x^2 + 2x + 1 = 9, and vice versa.

To solve the quadratic equation x^2 + 2x - 8 = 0, we can use the method of completing the square. Adding 9 to both sides of the equation, we get x^2 + 2x + 1 = 9. This step allows us to create a perfect square trinomial on the left side.

Next, we can rewrite the left side of the equation as (x + 1)^2 = 9, applying the binomial formula (x + a)^2 = x^2 + 2ax + a^2. In this case, we choose a = 1.

Taking the square root of both sides, we have x + 1 = ±√9, which simplifies to x + 1 = ±3. By solving for x, we find two possibilities: x = 2 and x = -4.

Therefore, the solutions to the quadratic equation x^2 + 2x - 8 = 0 are x = -4 and x = 2.

In summary, the equation x^2 + 2x - 8 = 0 implies the equation x^2 + 2x + 1 = 9, and the solutions to the original equation are x = -4 and x = 2. By completing the square, we transformed the given quadratic equation into an equivalent form that allowed us to find the solutions accurately.

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Answer:

F type connector

Step-by-step explanation:

Use an F-type connector for broadband cable connections that use coaxial cable.

The F connector is a coaxial RF connector commonly used for "over the air" terrestrial television, cable television and universally for satellite television and cable modems,

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Answer:

4(x+8)

Step-by-step explanation:

4x+32

x+8 in parentheses

and put the 4 on the outside of the parentheses

like this 4(x+8)

Answer:

4(x+8)

Step-by-step explanation:

4x + 32

Rewriting

4*x + 4*8

Factor out 4

4(x+8)

Answer:

8510

Step-by-step explanation:

By dividing the angle of rotation by the duration of one rotation, the angular velocity of the Earth around its axis can be determined. The time it takes the Earth to complete one full rotation, which is equivalent to 360 degrees or 2 radians, is roughly 24 hours.

Angle change divided by time change equals angular velocity (v), as follows:

ω = θ / t

We can substitute the following values into the equation since the Earth completes one rotation every 24 hours:2 radians each day equals.

By multiplying by 3600 (the amount of seconds in an hour), we may convert the time from hours to seconds:

2 radians are equal to (24 hours * 3600 seconds/hour)

Condensing the equation:

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Without specific details about the Tannenbaum textbook or the exact diagram you are referring to, I can only provide a general explanation of a two-tiered architecture in client-server organizations.

In a two-tiered architecture, also known as a client-server architecture, the system is divided into two main components: the client and the server.

The client refers to the end-user device or application that interacts with the server to request services or resources. It could be a desktop computer, a laptop, a mobile phone, or any other device with network connectivity.

The server, on the other hand, refers to a central computer or system that provides services or resources to the clients. It is responsible for processing client requests, performing business logic, and managing data. Servers can range from simple web servers to more complex application servers or database servers.

The communication between the client and the server typically follows a request-response model. The client sends a request to the server, specifying the desired service or resource. The server processes the request and sends back the corresponding response, which could include data, information, or the result of a specific operation.

This two-tiered architecture is commonly used in many client-server applications, such as web applications, where the client (web browser) communicates with a remote server to access web pages or retrieve data.

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The given series is 1 3 9 27 81

here, all the numbers are the multiplication of three.

it is the series of function f(x) = 3^x

substitute x= 1, 2 , 3 , 4 , 5......

Part (a)

The resultant vector is the vector formed by adding the two vectors a and b. So we effectively add the corresponding components.

You can use the parallelogram law as a visual alternative.

Adding a and b leads to

a+b = (3i-2j) + (pi-2pj)

a+b = (3i+pi) + (-2j-2pj)

a+b = (3+p)i - (2+2p)j

Define vector d to be d = a+b so we can use it later below.

Recall that parallel vectors point in the same direction. This means the ratio of their components or coordinates are equal.

We can say the following

(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)

(3+p)/(2) = (-(2+2p))/(-3)

Let's solve for p

(3+p)/(2) = (-(2+2p))/(-3)

(3+p)/(2) = (2+2p)/3

3(3+p) = 2(2+2p) .... cross multiply

9+3p = 4+4p

4p+4 = 3p+9

4p-3p = 9-4

p = 5

========================================================

Part (b)

Since p = 5, from part (a), we can determine vector b

b = pi - 2pj

b = 5i - 2*5j

b = 5i - 10j

Then add vectors a and b to get

a+b = (3i-2j) + (5i - 10j)

a+b = (3i+5i) + (-2j - 10j)

a+b = (3+5)i - (2+10)j

a+b = 8i - 12j

Or we can say

a+b = (3+p)i - (2+2p)j  .... from part (a)

a+b = (3+5)i - (2+2*5)j ... plugging in p = 5

a+b = 8i - 12j

Note the ratio of the components of vector d and vector c are such

(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)

8/2 = -12/(-3)

4 = 4

This helps confirm the answer

You could also graph the vectors c = 2i - 3j and d = 8i - 12j to note the two lines produce the same slope -3/2. We can see that -12/8 = -3/2. Lines of the same slope are parallel lines

a.

The value of p is 5

Since vector a = 3i - 2j and vector b = pi - 2pj, the resultant of vectors a and b is R = a + b

= 3i - 2j + pi - 2pj

= (3 + p)i - 2(1 + p)j

Since R is aparallel to vector c = 2i - 3j, it implies that the cross product of R and c is zero.

The cross product of two vectors a and b is a × b = absinФ where a and b are the magnitudes of a and b and Ф is the angle between them.

So, R × c = [(3 + p)i - 2(1 + p)j] × [2i - 3j]

= (3 + p)i × 2i + (3 + p)i × (-3j) + (-2(1 + p)]j × 2i + (-2(1 + p)]j×(-3j)

= 0 - 3(3 + p)k - 4(1 + p)(-k) + 0

= -3(3 + p)k + 4(1 + p)k

= [-3(3 + p) + 4(1 + p)]k

= [-9 - 3p + 4 + 4p)]k

= [-9 + 4 - 3p + 4p)]k

=  [-5 + p]k

[-5 + p]k = RcsinФ.

Since R and c are parallel, Ф = 0°

So, Rcsin0° = Rc × 0 = 0

So,   [-5 + p]k = 0

-5 + p = 0

p = 5

The value of p is 5

b.

The resultant of vectors a and b is R = 8i - 12j

Since p = 5 and the resultant of vectors a and b is R = (3 + p)i - 2(1 + p)j

Substituting the value of p = 5 into r, we have

R = (3 + p)i - 2(1 + p)j

R = (3 + 5)i - 2(1 + 5)j

R = 8i - 2(6)j

R = 8i - 12j

So, the resultant of vectors a and b is R = 8i - 12j

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If a bloodstain has measurements of 30 cm and 15 cm, the angle of impact is going to be 30 degrees.

The angle of impact can be defined as the angle formed when a blood droplet hits the surface of any object. It is usually an acute or right angle.  It is important since it becomes a useful factor in many criminal investigations.  

It is used using the formula = arcsin(w/l) (i)

Here, it has been mentioned that the width, w is = 15 cm (ii)

The length of the blood stain is = 30 cm (iii)

Using the values of (ii) and (iii) in (i), we get -

= arcsin(15/30)

= 30 degrees

Hence, using the formula we know that the angle of impact is 30 degrees.

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Answer:14

Step-by-step explanation:

Answer:

n=11/2 or 5 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distribute:

2n-12-15=-6n+18-1

Combine like terms:

2n-27=-6n+17

Put -27 on other side and -6n on other side:

8n=44

Divide:

n=5.5

Answer:

1?

Step-by-step explanation:

ya is it 1??Step-by-step explanation: