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Consider the quadratic function y = 0.3 (x-4)2 - 2.5
Determine the axis of symmetry, x =

Answers

Answer 1
Answer:

Answer:

x=4

Step-by-step explanation:

We have the quadratic function:

\displaystyle y=0.3(x-4)^2-2.5

And we want to determine its axis of symmetry.

Notice that this is in vertex form:

y=a(x-h)^2+k

Where (h, k) is the vertex of the parabola.

From our function, we can see that h = 4 and k = -2.5. Hence, our vertex is the point (4, -2.5).

The axis of symmetry is equivalent to the x-coordinate of the vertex.

The x-coordinate of the vertex is 4.

Therefore, the axis of symmetry is x = 4.

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Unit 4 linear equations homework 12

Answers

Answer:

There's no questions or worksheet attached.

Final answer:

This question pertains to linear equations, a topic in high school level algebra. Linear equations produce a straight line when graphed and can be solved using algebraic methods. Completing the homework might involve solving for variables, graphing the equations, or interpreting the graphs.

Explanation:

The subject of this question is about Unit 4 Linear Equations Homework 12 which falls within the scope of Mathematics, specifically in the field of algebra. A linear equation is an equation between two variables that produces a straight line when graphed out. Solving such equations involves procedures such as simplification, addition, subtraction, multiplication and division.

As for homework, it might involve solving for variables, graphing the linear equations, or interpreting such graph. For example, the equation of a line could be form such as 'y=mx+b', where 'm' is the slope of the line and 'b' is the y-intercept. One might be asked to determine the slope and y-intercept from a given equation or to write an equation given certain information.

When tackling this kind of homework, one should carefully review his/her class materials and notes. Once the concept and the procedure is clear, practice with some example problems is a great way to increase confidence and proficiency in solving linear equations.

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suzi starts her hike at a elevation if -225 below sea level. When she reaches the end of the hike, she is still nelow sea level at -127 feet. What was the vhange in elevation from the beginning of Suzi's hike to the end of the hike?

Answers

The change is elevation is 98 feet.

There are a couple different ways to get this answer. You could:
A. Subtract 127 from (positive) 225, to get the height difference. Or...
B. Subtract the starting height from the ending height (-127 - (-225)) which would also give you the height difference.

I hope this helps!

B is the midpoint of AC, D is the midpoint of CE , and AE = 23. Find BD.12.5
46
11.5
23

Answers

11.5 is the length of bd

Can someone help me with this

Answers

Answer: The answer is (19, 17), (20, 18), (21, 19), (22, 20), and (23, 21).

Step-by-step explanation:

A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 64 per hour, and this rate is Poisson-distributed.

Answers

For a vending machine having Service time is 20 seconds per cup and customers arrive at a mean rate of 64 per hour, then average number of customers waiting in a line is 0.10

Number of customer in a queue means those who are waiting for a server.

Given the following information:

Mean arrival rate of customer, μ=64 customers per hour

Service time is 20 seconds per cup that is 1 customer per 20 seconds

λ=180 customers per hour

Average number of customers waiting in a line, L_q=(\lambda ^2)/(2\mu (\mu -\lambda))

On substituting the values,

L_q=(60^2)/(2* 180(180-64))\nL_q=0.098\approx 0.10

Thus, average number of customers waiting in a line is 0.10

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Complete question:

A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 64 per hour, and this rate is Poisson-distributed. Determine the average number of customers waiting in line.

Final answer:

This problem engages queueing theory in mathematics, specifically it involves a vending machine with constant service time and Poisson-distributed customer arrival rate. The system is analyzed to be stable as the service rate surpasses the arrival rate.

Explanation:

This problem is a classic case of queueing theory in mathematics, particularly relevant in Probability and Statistics. Our case involves a vending machine that has a constant service time of 20 seconds per cup of hot chocolate or coffee. The mean customer arrival rate is presented as 64 per hour, described as being Poisson-distributed.

To start, consider the service rate. With the service time being a constant 20 seconds per cup, this translates to 3 cups being served per minute or 180 cups per hour. This value becomes our service rate µ. For the arrival rate or lambda (λ), the rate was given as 64 customers per hour.

In this particular queuing system, the service rate is higher than the arrival rate. This means that the system is stable, and queues are not expected to be overly long because customers are being served at a faster rate than they are arriving.

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lim x rightarrow 0 1 - cos ( x2 ) / 1 - cosx The limit has to be evaluated without using l'Hospital'sRule.

Answers

Answer with Step-by-step explanation:

Given

f(x)=(1-cos(2x))/(1-cos(x))\n\n\lim_(x \rightarrow 0)f(x)=\lim_(x\rightarrow 0)(\frac{1-(cos^2{x}-sin^2{x})}{1-cos(x)})\n\n(\because cos(2x)=cos^2x-sin^2x)\n\n\lim_(x \rightarrow 0)f(x)=\lim_(x\rightarrow 0)((1-cos^2x)/(1-cos(x))+(sin^2x)/(1-cosx))\n\n=\lim_(x\rightarrow 0)(((1-cosx)(1+cosx))/(1-cosx)+(sin^2x)/(1-cosx))\n\n=\lim_(x\rightarrow 0)((1+cosx)+(sin^2x)/(1-cosx))\n\n\therefore \lim_(x \rightarrow 0)f(x)=1
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