Please show that V1,f V1,i and Vz,f Vz,i satisfies both Eqs. (5) and (6) and explain why it is not regarded as a physical solution to an elastic collision problem:'

Answer:

y=-1 and x=-4

Step-by-step explanation:

2x+y=-9

and

2x-5y=-3

Multiply the second equation by -1, now we have

2x+y=-9

and

-2x+5y=3

Now you can add both sides of the equations and the x values will cancel, because they are opposites (2x and -2x)

2x+y-2x+5y=-9+3

6y=-6

y=-1

We now know y is -1, so we can substitute back into one of our original equations

2x+y=-9

2x+(-1)=-9

2x=-8

x=-4

y is -1 and x is -4

When someone just starts a company and adds $60,000 cash to start, it will be considered beginning cash for the cash flow statement. The cash flow statement presents an overview of the cash that comes in and goes out of a company. It categorizes the cash flows into three main categories:

operating activities, investing activities, and financing activities. The cash flow statement provides information regarding the amount of cash that is flowing in and out of the company. The statement of cash flows is used to determine a company's liquidity and the ability to meet short-term obligations.The cash flow statement's beginning cash balance should be the amount of cash that the company had at the beginning of the reporting period. In this case, the $60,000 would be the beginning cash balance for the cash flow statement.

When someone just starts a company and adds $60,000 cash to start, it will be considered beginning cash for the cash flow statement. The cash flow statement is a critical financial statement that presents an overview of the cash that comes in and goes out of a company. It categorizes the cash flows into three main categories: operating activities, investing activities, and financing activities. The cash flow statement provides information regarding the amount of cash that is flowing in and out of the company. The statement of cash flows is used to determine a company's liquidity and the ability to meet short-term obligations.The cash flow statement's beginning cash balance should be the amount of cash that the company had at the beginning of the reporting period. In this case, the $60,000 would be the beginning cash balance for the cash flow statement. The beginning cash balance is important because it sets the stage for the cash flows that will be presented in the statement. The cash flow statement's beginning cash balance is calculated by taking the previous reporting period's ending cash balance. The ending cash balance from the previous reporting period would be $0 since the company did not exist yet. The $60,000 would, therefore, be the beginning cash balance for the cash flow statement.

To summarize, when someone starts a new company and adds $60,000 cash to start, the $60,000 will be considered beginning cash for the cash flow statement. The cash flow statement is a critical financial statement that provides information on the cash that comes in and goes out of a company. The beginning cash balance for the cash flow statement is the amount of cash that the company had at the beginning of the reporting period. Since the company did not exist in the previous reporting period, the $60,000 will be the beginning cash balance for the cash flow statement.

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The correct deductions for Larren Buffett's paycheck are as follows: Social Security taxes: $317.68, Medicare taxes: $59.45, and Federal Income Tax withholding: $475.90.

Larren Buffett, who is paid a weekly salary of $4,100, is concerned about the accuracy of her deductions for Social Security, Medicare, and Federal Income Tax withholding (FIT). To determine the correct deductions, we need to consider her marital status, number of claimed deductions, and prior earnings. According to the information provided, Larren claims 3 deductions and has total earnings of $128,245. For Social Security, the rate of 6.2% applies to a maximum of $128,400, resulting in a deduction of $317.68. Medicare tax, calculated at 1.45%, amounts to $59.45. As for FIT, further details are not provided, so we cannot determine the exact amount without additional information.

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Answer:

Step-by-step explanation:

Do you know how to use the quadratic formula?

\(x = \frac{-b +/- \sqrt{b^2 - 4*a*c} }{2*a}\)

a = 5

b = -1    

c = 3

\(x = \frac{1 +/- \sqrt{1 - 4*1*3} }{2}\\x= \frac{1 +\sqrt{-11} }{2}\\x = \frac{1 +/- i\sqrt{11} }{2}\)

Answer:

9x+6

Step-by-step explanation:

Answer:

\(\fbox{3\sqrt{2}}\)\(3\sqrt2\)

Step-by-step explanation:

Step 1:

Let us figure out the measurements of all the angles first. We are given one angle of 45º, and another of 90º. The angles of a triangle must add up to 180º, hence we can use basic addition and subtraction to find the last angle.

\(\angle=180-90-45\\\angle=45\)

Great our angle is 45º! Notice something...?

Step 2:

We now have two 45º angles in our triangle. This means we have an isosceles triangle.

According to BATh (base angle theorem), in an isosceles triangle, the angles opposite the congruent sides are congruent. Thus, y is congruent to the given side of \(3\sqrt2\).

y=\(\fbox{3\sqrt{2}}\)\(3\sqrt2\)

I hope this helps! Let me know if you have any questions :)

The probability to get a 3 or 4 in the third toss and 6 in the fourth toss is 1/18.

The sample space for a six-sided die is

{1, 2, 3, 4, 5, 6}

Hence the total number of possibilities = 6

The rolling of a die is IID that is Independently and Identically distributed.

Hence,

the result of one toss will not affect the result of the successive tosses.

Probability

= n(E)/n

= no of favorable outcomes for any event /total no. of outcomes

Here,

n = 6

Let A be the event of getting a 3 or 4 in the third toss

Let B be the event of getting 6 on the fourth toss

E(A) = {3,4}

n(A) = 2

Hence,

P(A) = 2/6

= 1/3

B = {6}

n(B) = 1

P(B) = 1/6

Since these are IID,

P(A and B) = P(A) X (B) [Property of independent events]

Hence P(A∩B) = 1/3 X 1/6

= 1/18

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Answer:

Step-by-step explanation: 122x2=144

Answer: x = 12, - 12

Step-by-step explanation:

True. A piece-wise function is composed of different functions that are joined together at certain points and each of these functions will either have an x-intercept or a y-intercept.

Yes, a piece-wise function will always have at least one x-intercept or at least one y-intercept. A piece-wise function is composed of different functions that are joined together at certain points. Each of these individual functions can either be linear, quadratic, or any other type of function, and each of these functions will either have an x-intercept or a y-intercept. For example, if a piece-wise function contains two linear equations, each of them will have one x-intercept and one y-intercept. The same is true for quadratic equations, and for any other type of equation. Therefore, since a piece-wise function is composed of these individual functions, it will always have at least one x-intercept or at least one y-intercept.

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Answer:

Step-by-step explanation:

Answer:

8.7

Step-by-step explanation:

hypotenuse= 14 =c

a=11

b=x

a²+b²=c²

b²=c²-a²

b²=14²-11²

b²= 196-121

b²=75

b=√75=5√3=8.7 rounded to the nearest tenth

Final Answer:

x = 8.66

Step-by-step explanation:

formula: \(b=\sqrt{c^2-a^2}\)

a = 11

b = x

c = 14

\(b=\sqrt{14^2-11^2}\)

\(b=\sqrt{196-121}\)

\(b=\sqrt{75}\)

b = 8.66025

x = 8.66

rounded off to the nearest hundredths: 8.66

The polynomial (4x + 4)(x + 1) is factored completely into the product of two linear binomials: 4(x + 1)(x + 1).

To factor the polynomial (4x + 4)(x + 1) completely, we can use the distributive property. We start by multiplying the terms in the first binomial (4x + 4) by each term in the second binomial (x + 1).

(4x + 4)(x + 1) can be expanded as follows:

= 4x(x + 1) + 4(x + 1)

Using the distributive property, we multiply 4x by each term in (x + 1) and then multiply 4 by each term in (x + 1):

= 4x^2 + 4x + 4x + 4

Simplifying further, we combine like terms:

= 4x^2 + 8x + 4

Now we can see that the polynomial (4x + 4)(x + 1) has been fully expanded. However, to factor it completely, we look for common factors in the terms.

In this case, we can factor out a common factor of 4 from all the terms:

= 4(x^2 + 2x + 1)

Now, we observe that the expression inside the parentheses (x^2 + 2x + 1) is a perfect square trinomial, which can be factored as follows:

= 4(x + 1)(x + 1)

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The total derivative of a function is not necessarily one-to-one. The total derivative represents the change in a function with respect to all of its input variables.

If a function has multiple input variables, the total derivative is a matrix, called the Jacobian matrix, whose entries represent the partial derivatives of the function with respect to each input variable.

A function with a non-invertible Jacobian matrix is not one-to-one, since multiple input values can result in the same output value. For example, consider the function f(x,y) = (x^2, y^2). The total derivative of f is given by the Jacobian matrix:

| 2x 0 |

| 0 2y|

This matrix is non-invertible when x=0 or y=0, since it has a determinant of zero. Thus, the function f is not one-to-one when x=0 or y=0.

In terms of polynomials, the total derivative is important for determining whether a polynomial has multiple roots. A root of a polynomial is a value of the input variable that causes the polynomial to equal zero. If a polynomial has multiple roots, it is not one-to-one, since different input values can result in the same output value.

The total derivative of a polynomial can be computed using the power rule of differentiation. For example, consider the polynomial p(x) = x^3 - 6x^2 + 11x - 6. The total derivative of p with respect to x is:

p'(x) = 3x^2 - 12x + 11

If p'(x) has multiple roots, then p(x) has multiple roots as well. In this case, p'(x) has roots at x=1 and x=11/3, so p(x) has multiple roots at x=1 and x=3. Thus, the total derivative is useful for identifying when a polynomial is not one-to-one.

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Is total derivative  is one-to-one? explain the significance of this result in terms of the derivative on polynomials.

Answer:

y = 6

Step-by-step explanation:

24/12 = 2  

2*3 = 6

Answer:

y=6 if x=24 hope this helps

Step-by-step explanation:

Hey there!

Simply use the formula for midpoint to solve it.

Here, The given points are (6,5) and (-4,12).

Using midpoint formulae,

\((x,y) = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )\)

Put all values.

\((x,y) = ( \frac{6 - 4}{2} , \frac{5 + 12}{2} )\)

Simplify them to get answer.

\((x,y) = ( 1, \frac{17}{2} )\)

Therefore the midpoint is (1,17/2).

Hope it helps...

Answer: 2 hours 15 minutes

Step-by-step explanation:

3/4 of an hour times 3 will be 9/4; each fourth is 15 minutes. 9 times 15 is 135 minutes, which is 2 hours and 15 minutes

Answer:

2.25 hours

Step-by-step explanation:

The man traveled 1/3 of the distance in 3/4 of an hour.

This means that he needs to travel for 3 times as long to travel the entire distance.

3 * 3/4 = 9/4 = 2.25

2.25 hours.

Or, 2 hours and 15 minutes (as 0.25 = 1/4).

Answer: 0.9

Step-by-step explanation:

Sqrt 81 is 9

over 10 is 9/10

which is 0.9

Answer:

-15.1

Step-by-step explanation:

Two negative numbers add the same way as positive numbers, so it is -(7.5 + 7.6) or -15.1.

The number of game disks that must be produced for the average cost to be $4.70 is 2600.

Given:

The average cost of producing x game disks for a computer is given by the function C(x) = 2.6+5460/x

To determine the number of game disks that must be produced for the average cost to be $4.70.

Substitute the average cost in the equation and solve to find the value of x i.e. number of disks,

4.70 = 2.6 + 5460/x

4.70 - 2.6 = 5460/x

2.1x = 5460

x = 5460/2.1

x = 2600

Therefore, the number of game disks that must be produced for the average cost to be $4.70 is 2600.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

Step-by-step explanation:

1/6  is the probability that in seven rolls of a six-sided die, the result of 2 appears exactly 4 times

Define Probability

Probability can be defined as the likelihood or chance of an event occurring.

Probability is a branch of Mathematics that deals with the calculation on the chances of happening of a particular event.

The probability of getting some number in a cube corresponds to 1/6, the cube has six sides.

P(1) =1/6

P(2) =1/6

P(3)=1/6

P(4)= 1/6

P(5)=1/6

P(6)= 1/6

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Answer:

answer

Step-by-step explanation:

the answer is 8

first we add 4 and 6

then we subtract 2

Answer:

3x+2>0

Step-by-step explanation:

the 3x is there because its 3 times an unknown # and add 2, its also > sign because its greater than 0

its not rlly paragraph form but i hope it helps :)

Step-by-step explanation:

5²=4²+x²

25=16+x²

25-16=x²

9=x²

√9=√x²

3=x

A

The soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day for the soft drink vendor, we need to use the formula P(x) = 0.001x^2 + 3x + 1800, where x is the number of cans of soda pop sold in one day.

To find the maximum profit, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex is given by -b/2a, where a = 0.001 and b = 3. Plugging in these values, we get x = -3/(2*0.001) = -1500.

Since the soft drink vendor cannot sell a negative number of cans, we know that the maximum profit occurs at the closest whole number to x = -1500, which is x = 1500.

To find the maximum profit per day, we can plug in x = 1500 into the profit function:

P(1500) = 0.001(1500)^2 + 3(1500) + 1800 = $5250

Therefore, the soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day and the number of cans needed to reach that profit, we'll first need to find the critical point of the given quadratic profit function, P(x) = -0.001x^2 + 3x - 1800.

Step 1: Find the derivative of P(x) with respect to x. This will give us the rate of change of profit as the number of cans sold changes.

P'(x) = -0.002x + 3

Step 2: Set the derivative equal to zero and solve for x. This will give us the critical point where the maximum profit occurs.

-0.002x + 3 = 0

x = 1500 cans

Step 3: Substitute the critical point (x = 1500) back into the profit function P(x) to find the maximum profit.

P(1500) = -0.001(1500)^2 + 3(1500) - 1800

P(1500) = $600

So, the maximum profit per day is $600, and the soft drink vendor must sell 1500 cans to reach the maximum profit.

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The maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

The profit function for the soft drink vendor is given by:

P(x) = \(0.001x^2 + 3x + 1800\)

To find the maximum profit, we need to find the vertex of the parabola represented by this function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

where a = 0.001 and b = 3. Substituting these values, we get:

x = -3 / (2 * 0.001) = -1500

Since the value of x cannot be negative in this context, we know that the maximum profit occurs at x = 1500. To find the maximum profit, we substitute this value of x into the profit function:

P(1500) =\(0.001(1500)^2 + 3(1500) + 1800 = $4800\)

Therefore, the maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

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Answer:

D

Step-by-step explanation:

The answer is D because the pattern adds one angle every one shape. Ex. Triangle, Rectangle, Pentagon, Hexagon