Find the solution of xy" (x) - (x - 2)y(x) = 0 in the form y(x) = aoyo(x) + a1y1 (x) in powers of x – 2 up to the term (x - 2)^4. What are the values of of ao and a1 if y(2) = 1 and y'(2) = 0.

Answer:

b

Step-by-step explanation:

Answer:

-3/8b + 25/24

Step-by-step explanation:

-1/4b + 1/2 - 1/8b + 13/24

We can write as

-2/8b + 12/24 - 1/8b + 13/24

-3/8b + 25/24

Answer:

All of them except the squiggly one and the vertical one

Step-by-step explanation:

The rest are functions, two of them are lines, and the curved swoop is a parabola, which is also a function

Function is a set of relation without same or repetitive domain. Because we are checking if the following graphs are function or not. It is easier to do line test.

How to check if the graphs are function.

Overall, the graphs that are not function are the vertical line and the vertical curve graph.

Feel free to ask if you are confused.

209952 is the value of 432x486

Multiplication is a method of finding the product of two or more numbers

We need to multiply 432 and 486

Steps to follow to find this

1. Line up both your numbers with one on top of the other.

2.Make sure that the places match up for the ones, tens, and hundreds

3. Multiply the top number by the last digit of the second number – the 'ones' unit.

     432

   ×486

___________

     2592

    3456+

   1728++

_____________

   209952

Hence, 209952 is the value of 432x486

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Answer:

2(6+1)

Step-by-step explanation:

its so easy because in sec..134 there is a • like this and look

2(6+1)

2 of 7

2×7

14,,,

and

24-5×2=14,,, is the answer,,,

The correct answer is option (b) No, the statement does not represent an exponential function, h(t) = -4.9t² + 18t + 40 is a quadratic function and not an exponential function.

An exponential function is a mathematical function in which the variable is in the exponent. Exponential functions follow the form f(x) = a^x, where a is the base and x is the exponent.

The given statement is h(t) = -4.9t² + 18t + 40, which does not represent an exponential function. The value of t is not in the exponent in this case. Instead, it's a quadratic equation, which is in the form of h(t) = at² + bt + c.

Therefore, the correct answer is option (b) No, the statement does not represent an exponential function.

Explanation:

An exponential function can also be represented by the general form y = ab^x, where b > 0 and b ≠ 1. When plotted on a graph, the curve of an exponential function rises or falls at an increasing rate, depending on whether b is greater than or less than 1, respectively.

A quadratic equation is an equation of the form ax² + bx + c = 0, where a ≠ 0, and x represents a variable. Quadratic equations are second-degree equations, which means the highest exponent of the variable is two.

Therefore, h(t) = -4.9t² + 18t + 40 is a quadratic function and not an exponential function.

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Answer:

4 and 0

Step-by-step explanation:

I hope this helps

The first number is 4 and the second number is 4.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A number minus twice another number is 4.

Three times the first number plus two times the second number is 12.

Let numbers are n and m.

According to the question;

n- 2m = 4      equation 1

3n + 2m = 12      equation 2

Now, we have the system of equation.

To solve the equation,

Add both of the equation,

4n = 16

n = 4

Then m = 0

Therefore, 0 and 4 are the numbers.

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Answer:

(3x+1)(x+5)

Step-by-step explanation:

Sorry for my handwriting lol hope this makes sense

Hi! I hope you're enjoying your day!

The common factor of 10x and 5 is

5.

What is a factor?

It's a number that a number is evenly divisible by.

Example: 2 is a factor of 10, because 10 is evenly divisible by 2.

Also, it may be tempting to say, "Well, 2 is the common factor!"

And that's not true in this case, because 5 isn't divisible by 2.

x is also not a common factor; 5 is a constant, it doesn't have any variables next to it.

Hence, the factor is

\(\boxed{\boxed{\bold{5}}}\)

Hope everything is clear.

If you have any questions, please comment.

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The continuous growth rate of City A was -0.06% per year between 1965 and 1974. This means that the population decreased by an average of 6% each year during this period.

To calculate the growth rate of City A between 1965 and 1974, we first need to determine the difference in population between the two years. The population in 1965 was 85,000, and the population in 1974 was 72,000. Thus, the difference in population is -13,000. Next, we need to calculate the growth rate, which is equal to the difference in population divided by the initial population, multiplied by 100. Therefore, the growth rate of City A between 1965 and 1974 is -13,000 ÷ 85,000 x 100 = -0.06. This means that the population of City A decreased by an average of 6% each year during this period.

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Answer:

What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.

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The company's profit if there are no price increases is $120.

We have,

The problem provides a function P(x) that models the profit of a natural sponge company.

The function takes as input the number of $0.15 increases in the price of each sponge, denoted by x.

When the value of x is 0, it means that there are no price increases, and therefore the initial price of each sponge is unchanged.

Now,

If there are no price increases, then the value of x in the function P(x) is 0, since x represents the number of price increases.

Substituting x = 0 into the function, we get.

P(0) = -0.1(0)^2 + 15(0) + 120 = 120

Therefore,

The company's profit if there are no price increases is $120.

We can also see this from the graph of the function, which starts at (0, 120) and represents the profit when there are no price increases.

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Answer:

6/5 is the slope, so x=6/5+2.5y

Step-by-step explanation:

I think

Answer:

Step-by-step explanation:

I had this exact question and I figured it out.

the answer is: P(police officer and chooses car)

In order to get this answer I did the P(police officer) X P(choosing car)

It ended up being 36/45 X 15/45. Which is equal to around .2666667.

Now you take the Intersection of police officer and chooses car and you divide it by 45. That value on the chart is 12.

lucky enough, the product of 36/45 and 15/45 is equal to 12/45.

So 0.8 X 0.33 = .26

.26 = .26

Answer:

answer is P(police officer and chooses car)

Step-by-step explanation:

the probability of P(policer officer) and P(choose a car) are independent probabilities ( they are not overlapping probabilities)

Correct Question:

He counts 18 female students, 16 male students, and 6 teachers. There are

720 people in the auditorium. Consider the probability of selecting one person

at random from the auditorium.

Which of these statements are true?

Choose all that apply.

A:  The probability of selecting a teacher is 6%.

B : The probability of selecting a student is 85%.

C : The probability of selecting a male student is 32%.

D : The probability of selecting a female student is 45%.

Step-by-step explanation:

Option B  and D are correct because

The total number of people in one cross section = 18 + 16 + 6 = 40.

A = The probability of selecting a teacher is = (6/40)x100 = 15 % not equal to 6 %

B = The probability of selecting a male student is = (34/40)x100 = 85%

C = The probability of selecting a male student is = (16/40)x100 = 40 % not equal to 32 %

D : The probability of selecting a female student is = (18/40)x100= 45%

-3, -1, 3

X-intercepts are also known as the roots or zeros of a function.

Finding Intercepts From Graphs

In the problem, we are given a basic polynomial graph. The x-intercepts are where the graphs intersect with the x-axis. Remember that the x-axis is the horizontal axis. Finding x-intercepts when given a graph is as simple as just looking to see where the line crosses over. We can see that the graph crosses the axis in three points. The x-intercepts are x = -3, -1, and 3.

Finding Intercepts From Equations

In this question, we are not given an equation, but if we were there is another possible way to solve it. The x-intercepts occur when y = 0. So, to find x-intercepts from an equation, all you need to do is plug 0 in for y and solve.

The translation rule is (x, y) → (x + (-2) , y + 4)

We have,

From the figure,

We see the coordinates of Figure I.

(4, -5), (2, 1), and (-3, -3) _____(1)

We see that the coordinates of Figure Ii.

(2, -1), (0, 5), and (-5, 1) _____(2)

Now,

From (1) and (2),

Taking the corresponding coordinates.

(4, -5) and (2, -1)

(2, 1) and (0, 5)

(-3, -3) and (-5, 1)

We see that,

x coordinates is substrated by 2 and y coordinate is added by 4.

So,

The translation rule is (x, y) → (x + (-2) , y + 4)

Thus,

The translation rule is (x, y) → (x + (-2) , y + 4)

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Answer:

can u give the prices for the tickets?

An adult ticket costs $2 more than a child ticket

Let x and (x + $2)represent the cost of the child and adult ticket respectively

2(x+ $2) + 3x = $34

now solving for x

2x+ $4 + 3x = $34

5x = $30

 x = $6 , the cost of the child ticket.

the cost of adult ticket $6+2=$8

Step-by-step explanation:

Answer:

3.6 miles

Step-by-step explanation:

Set up an equation. Start with the total goal of 21.4 on one side, then think about what goes on the other. He's already ridden 7 miles, and this is going to be the same as the 21.4, so start with a 7. Then, in addition to those 7, he'll need to ride some amount on average for 4 more days, so that would be + 4x. This equation its 21.4 = 7 + 4x, and now just solve for x.

21.4 = 7 + 4x

14.4 = 4x

3.6 = x

Don't forget your units! (: Also, let me know if any part of this needs a more in-depth explanation.

Answer:

10 gallons

Step-by-step explanation:

1/3 x 30/1 =  30/3  =10

The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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Answer:

I hope that is useful for you :)

Answer: y=12

Step-by-step explanation:

Distribute

Add 10 to both sides

Simplify.

Answer: y = 12

Step-by-step explanation:

2 ( \(y\\\) - 5 ) = 14

2\(y\\\) - 2 · 5 = 14

2\(y\\\) - 10 = 14

(2\(y\\\) - 10) + 10 = 14 + 10

2\(y\\\) = 24

\(\frac{2y}{2} = \frac{24}{2}\)

The given sequence has a general term of an = 3n + 7. We need to find the 5th term of the sequence.

Step-by-step solution:

Given, the general term of a sequence, an = 3n + 7

Here, we have to find the 5th term of the given sequence.

To find the 5th term, substitute n = 5 in the general term equation of the given sequence.

So, the 5th term of the sequence is:

a5 = 3(5) + 7= 15 + 7= 22

Therefore, the 5th term of the sequence whose general term is an = 3n + 7 is 22.

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Answer:

m=0

Step-by-step explanation:

the slope (m) can be calculated from two points with the formula (y2-y1)/(x2-x1)

we are given the points (-2,1) and (7,1)

label the points:

x1=-2

y1=1

x2=7

y2=1

now substitute into the equation

m=(1-1)/(7--2)

m=0/9

m=0

the slope of the line is 0

Hope this helps!

(i) The graph is attached below. (ii) the minimum value of the function is h = 30, when x = 5. (iii) the horizontal distance traveled by the rider between the two splashes is 2 × 9 m = 18 m.

Acceleration is a physical quantity that measures the rate at which the velocity of an object changes over time. It is a vector quantity, meaning that it has both magnitude and direction.

Acceleration is defined as the change in velocity of an object divided by the time interval over which the change occurred. It is typically measured in meters per second squared (m/s²) in the metric system, or in feet per second squared (ft/s²) in the imperial system.

If the velocity of an object is increasing, its acceleration is said to be positive. If the velocity is decreasing, the acceleration is said to be negative or deceleration. If the velocity is constant, there is no acceleration.

(i) Using the given scale, we can plot the graph of h = 1.2x² - 12x + 30 for 0 ≤ x ≤ 10 as follows:

Parabolic graph is attached below.

(ii) The constant term 30 in the equation represents the minimum height of the pirate ship ride above ground level. This is because the equation is in the form of a quadratic function in standard form, y = ax² + bx + c, where the vertex of the parabola is at the point (-b/2a, c - b²/4a). In this case, the vertex is at (5, 0), which means that the minimum value of the function is h = 30, when x = 5.

(iii) We are given that a rider is 19.2 m above ground level, which means that h = 19.2. We can substitute this value into the equation and solve for x:

19.2 = 1.2x² - 12x + 30

1.2x² - 12x + 10.8 = 0

x² - 10x + 9 = 0

(x - 1)(x - 9) = 0

Therefore, the rider is at a height of 19.2 m when he is either 1 m or 9 m away from the starting point. Since the rider swings back and forth, the distance between the two splashes is twice the distance from the starting point to either splash. Therefore, the horizontal distance traveled by the rider between the two splashes is:

2 × 9 m = 18 m

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Answer:

Step-by-step explanation:

To get 4 bottles of juice and 7 bottles of soda, it would cost:

4 bottles of juice * $1.40/bottle = $5.60

7 bottles of soda * $1.20/bottle = $8.40

The total cost would be $5.60 + $8.40 = $14.00

For xx bottles of juice and y bottles of soda, it would cost:

xx bottles of juice * $1.40/bottle = $1.40 * xx

y bottles of soda * $1.20/bottle = $1.20 * y

The total cost would be $1.40 * xx + $1.20 * y.