PLEASE ANSWER ASAP For the equation y=2x2-16x+30 Identify the vertex and convert into vertex form. STEP BY STEP PLEASE EXPLAIN HOW TO GET THE VERTEX

The function \(y = (4/5) * e^x * e^{-4x}\) does not satisfy the given differential equation \(y' - 4y = 4e^x.\)

The given differential equation is y' - 4y = 4e^x. Let's first find the derivative of y with respect to x.

\(y = (4/5) * e^x * e^{-4x}\)

To differentiate y, we can use the product rule of differentiation, which states that for two functions u(x) and v(x), the derivative of their product is given by:

\((d/dx)(u(x) * v(x)) = u'(x) * v(x) + u(x) * v'(x)\)

Applying the product rule to the function y, we have:

\(dy/dx = [(4/5)' * e^x * e^{-4x}] + [4/5 * (e^x * e^{-4x})']\)

Now, substituting the values of Term 1 and Term 2 back into dy/dx, we have:

\(dy/dx = [(4/5)' * e^x * e^{-4x}] + [4/5 * (e^x * e^{-4x})'] \\\\= [0 * e^x * e^{-4x}] + [4/5 * (-3e^x * e^{-4x})] \\\\= 0 - (12/5)e^x * e^{-4x} \\\\= -(12/5)e^x * e^{-4x} \\\\= -(12/5)e^x * e^{-4x} \\\\\)

Multiplying the coefficients, we get:

\(-12e^x * e^{-4x}/5 - 16e^x * e^{-4x}/5 = 4e^x\)

Combining the terms on the left-hand side, we have:

\((-12e^x * e^{-4x} - 16e^x * e^{-4x})/5 = 4e^x\)

Using the fact that \(e^a * e^b = e^{a+b}\) we can simplify the left-hand side further:

\((-12e^{-3x} - 16e^{-3x})/5 = 4e^x\)

Combining the terms on the left-hand side, we get:

\(-12e^{-3x} - 16e^{-3x} = 20e^x\)

Adding 12e^(-3x) + 16e^(-3x) to both sides, we have:

\(0 = 20e^x + 12e^{-3x} + 16e^{-3x}\)

Now, we have arrived at an equation that does not simplify further. However, it is important to note that this equation is not true for all values of x. Therefore, the function \(y = (4/5) * e^x * e^{-4x}\) does not satisfy the given differential equation \(y' - 4y = 4e^x.\)

To know more about differential equation here

https://brainly.com/question/30074964

#SPJ4

Answer:

14

Step-by-step explanation:

))))))))((((())(((.....

Answer:

The mean is 12

Step-by-step explanation:

If you see and check its 12:)

Answer:

15. -3 1/4

16. -4 1/2 OR -4 2/4

17. 1 1/4

18. -5 3/4

19. 1/2 OR 2/4

20. -2 1/2 OR -2 2/4

Step-by-step explanation:

Answer:

15) -3.25

16) -4.5

17)1.25

18)-5.75

19).5

20)-2.5

Answer:

45 x 56=

2520 and

5 x 7=35*8=280*9=2520

2520=2520

Hope This Helps!!!

Answer:

Step-by-step explanation:

To find the length of JL in the right triangle JKL, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse (the longest side). In this case, JL is the hypotenuse and JK and KL are the two shorter sides.

Since K is a right angle in triangle JKL, we can find the lengths of JK and KL using the given information. We have KM = 6 and JM = 8, so we can use those values to find JK and KL:

JK = √(JM^2 - KM^2) = √(8^2 - 6^2) = √(64 - 36) = √(28) = 2√(7)

KL = KM = 6

Finally, to find JL, we can use the Pythagorean theorem:

JL = √(JK^2 + KL^2) = √( (2√(7))^2 + 6^2) = √(4 * 7 + 36) = √(52) = 2√(13)

So, JL = 2√(13).

The equation Y=-3x-1 represents a linear relationship between x and y, and can be used to model real-world situations such as distance vs. time or cost vs. quantity.

The equation Y=-3x-1 represents a straight line on a coordinate plane. The "slope-intercept" form of the equation is y=mx+b, where m is the slope and b is the y-intercept.

In this case, the slope is -3 and the y-intercept is -1. This means that the line goes downwards at a rate of 3 units for every 1 unit to the right, and intersects the y-axis at -1.

To find the solution to this equation, you would need to have a specific value for either x or y.

If you were given a value for x, you could plug it into the equation to find the corresponding value for y. If you were given a value for y, you could solve for x by rearranging the equation.

To learn more about : equation

https://brainly.com/question/17145398

#SPJ11

Answer:

x=8

Step-by-step explanation:

If the two rectangles have the same area, then you have to first find the area to solve the problem. To find the area, do 6(Length)x4(Width)=24. So now that we know that the area is 24, now all you have to do is divide 24 by 3 to find the missing dimension. 24÷3=8. Therefore, x=8.

The pennies placed on the squares D, E, F, G, and H will be 8, 16, 32, 64, and 128 pennies.

Given

There are 8 rows and 8 columns, which means 64 squares on a chessboard.

We are placing 1 penny on Row 1 Column A, 2 pennies on Row 1 Column B, 4 pennies on Row 1 Column C, and so on.

A matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

So, we are increasing the number of pennies twice the amount of the previous square.

So, the pennies on next squares will be,

\(\rm Column \ D = 2\times 4=8\\\\Column \ E = 2\times 9=16\\\\Column \ F= 2\times 16=32\\\\Column \ G= 2\times 32=64\\\\Column \ H = 2\times 64=128\)

Therefore, the pennies placed on the squares D, E, F, G, and H will be 8, 16, 32, 64, and 128 pennies.

For more details about the matrix refer to the link:

https://brainly.com/question/4492099

The allowable is a term used in advertising and marketing to refer to the maximum cost per acquisition (CPA) that a business can afford to pay. So, the given statement is False.

"The allowable" is a term used in advertising and marketing to refer to the maximum cost per acquisition (CPA) that a business can afford to pay to acquire a customer while still remaining profitable. It is not directly related to the conversion rate needed to break even.

To determine the conversion rate needed to break even, you would need to consider the cost of acquiring a customer, the profit margin on the product or service being sold, and the total revenue generated by each customer. This calculation can help determine the minimum conversion rate needed to achieve profitability.

Know more about allowable here:

https://brainly.com/question/29646168

#SPJ11

Option C is correct.  Less than 100  is closest to total deaths resulting from ladder misuse each year.

According to the Consumer Product Safety Commission (CPSC), on average, approximately 300 people die each year in the United States from falls involving ladders.

However, not all of these deaths are due to ladder misuse. In fact, the number of deaths resulting specifically from ladder misuse is likely to be lower. It is estimated that a significant portion of ladder-related fatalities are caused by factors such as overreaching, misusing the ladder, or failing to follow proper safety guidelines.

To reduce the number of deaths and injuries resulting from ladder misuse, it is important to follow safety guidelines and to choose the right ladder for the job, taking into consideration factors such as height, weight, and stability.

To know more about Deaths click here:

https://brainly.com/question/28187145#

#SPJ11

Answer:

Each student gets 2.25 pieces

of granola bar.

Step-by-step explanation:

i pretty much divided 9 by 4 and got 2 with a Remainder of 1 aka R.1 , depends if they want the second one though

Dilation scale factor:-

Hence he found the opposite scale factor which is for enlargement .

Answer:

D

Step-by-step explanation:

To find the scale factor of dilation, measure the distance between one of the points and the center of dilation for both the original shape and the dilated shape, then compare.

Distance from (0, 0) to point A = 9 units

Distance from (0, 0) to point A' = 2 units

Let x be the scale factor of dilation:

⇒ 9x = 2

⇒ x = 2/9

So the scale factor of dilation that reduces ΔABC to ΔA'B'C' is \(\sf \frac29\).

Therefore, the mistake the friend made was finding the scale factor that enlarges ΔA'B'C' to ΔABC

Answer:WFG=116

Step-by-step explanation:

Answer:

The probability of choosing a marble with stripes, P(stripes), would be 0.2. The complement of choosing a marble with no design, P'(no design), would also be 0.2.

Step-by-step explanation:

1. The probability of choosing a marble with stripes, P(stripes), would depend on the proportion of marbles with stripes in the overall population of marbles available to choose from.

2. If, for example, there are 20 marbles with stripes and 80 marbles without stripes in a set of 100 total marbles, the probability of choosing a marble with stripes would be 20/100, or 0.2.

3. The complement of choosing a marble with no design, P'(no design), would be the probability of choosing a marble with stripes, or P(stripes).

4. This is because the complement of an event is the probability of the event not occurring.

5. So, if the probability of choosing a marble with stripes is 0.2, the probability of not choosing a marble with stripes (i.e. choosing a marble with no design) would also be 0.2.

Answer:

answer ????

Step-by-step explanation:

x = 33°

hope that helps!!!

The square has a 48 centimeter perimeter.

To find the perimeter of the square, we need to calculate its side length. The area of a rectangle is given by its length multiplied by its width, so we can use the given measurements of the rectangle to calculate its area: 25 cm x 16 cm = 400 cm². The area of a square is given by the square of its side length, so we can use the area of the rectangle to calculate the side length of the square: √400 cm² = 20 cm.

Thus, the perimeter of the square is equal to 4 times its side length, or 4 x 20 cm = 80 cm.

Learn more about square here

https://brainly.com/question/29192128

#SPJ4

Answer:

another ratio is 3:5=6:10 or 9:15

Explanation:

3:5×2=6:10

3:5×3=9:15

Answer:

(9,15) aka C

Step-by-step explanation:

3 times 3 is 9 and so you multiply the same number to the y-coordinate. 5 times 3 is 15!

Answer:

2,-5,1

Step-by-step explanation:

Answer:

117,649

Step-by-step explanation:

Good luck! <3

Answer:

7 to the 6th power is conventionally written as 76, with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 7^6.

76 stands for the mathematical operation exponentiation of seven by the power of six.

As the exponent is a positive integer, exponentiation means a repeated multiplication:

The exponent of the number 7, 6, also called index or power, denotes how many times to multiply the base (7).

Thus, we can answer what is 7 to the 6th power as

7 to the power of 6 = 76 = 117649.

When the point N is dilated, the coordinate of N changes to N' ,the coordinate of point N is (8,12).

What is dilation?

In arithmetic, a dilation may be a perform f from a mathematical space M into itself that satisfies the identity d=rd for all points x, y \in M, wherever d is that the distance from x to y and r is a few positive imaginary number.

Main body;

How to determine the coordinate of N

The given parameters are:

N' = (10,15)

k = 5/4

To calculate the coordinate of N, we make use of:

N * k = N'

So, we have:

N * 5/4 = (10,15)

Multiply both sides by 4

N * 5 = (40,60)

Divide both sides by 5

N = (8,12)

Hence, the coordinate of point N is (8,12)

Read more about dilation at:

brainly.com/question/3457976

#SPJ1

The random variable x follows an exponential distribution with a rate parameter μ = 25, This means that the average rate at which events occur or the average time between events is 25 units (such as hours, minutes, or seconds, depending on the context).

Now, let's dive into the explanation of the exponential distribution and its parameters:

The exponential distribution is characterized by the probability density function (PDF) mentioned earlier:

f(x) = (1/μ) * exp(-x/μ)

In this formula, x represents the random variable, and exp denotes the exponential function. The rate parameter μ determines the shape of the distribution. It is the inverse of the average rate or average time between events. In other words, if μ is large, it indicates a smaller rate or longer average time between events, and vice versa.

In your example, μ is given as 25, meaning that the average time between events is 25 units. You can use this information to calculate probabilities or make predictions based on the exponential distribution.

if you want to find the probability that x is less than or equal to a certain value, let's say 50, you can integrate the PDF from 0 to 50:

P(x ≤ 50) = ∫[0 to 50] (1/25) * exp(-x/25) dx

Solving this integral will give you the probability of x being less than or equal to 50.

Similarly, you can calculate probabilities for other ranges or perform other types of analyses using the exponential distribution.

Learn more about Exponential distribution

brainly.com/question/14560314

#SPJ11

Wi represents the weight of the course, and xi represents the grade received for that course.

Care must be taken when assigning variables to weights and observations, because the average grade point average (GPA) is the average grade received for each hour of coursework taken.

Therefore, each grade must be weighed against the number of credits for that course.

For example, if two courses are worth 3 credits and one course is worth 6 credits, then the GPA would be calculated by adding the three grades together and then dividing by the sum of the credits (3+3+6=12).

In this case, a grade of A in the 6 credit course would have a greater impact on the GPA than the same grade in the 3 credit course.

To know more about grade point average click on below link:

https://brainly.com/question/29193406#

#SPJ11

If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

Learn more about confidence interval at https://brainly.com/question/15576092

#SPJ11

Answer:

265

Step-by-step explanation:

It's a cube, so all sides are the same, so 6.5 x 6.5 x 6.5

This equals 264.625. They want 3 significant figures, so u round to the nearest whole number. Significant numbers are whole numbers. This becomes, 265.

Answer:

(x^2 + 7) (x^4 - 7 x^2 + 49)

Step-by-step explanation:

Factor the following:

x^6 + 343

Hint: | Express x^6 + 343 as a sum of cubes.

x^6 + 343 = (x^2)^3 + 7^3:

(x^2)^3 + 7^3

Hint: | Factor the sum of two cubes.

Factor the sum of two cubes. (x^2)^3 + 7^3 = (x^2 + 7) ((x^2)^2 - 7 x^2 + 7^2):

(x^2 + 7) ((x^2)^2 - 7 x^2 + 7^2)

Hint: | Evaluate 7^2.

7^2 = 49:

(x^2 + 7) ((x^2)^2 - 7 x^2 + 49)

Hint: | For all positive integer exponents (a^n)^m = a^(m n). Apply this to (x^2)^2.

Multiply exponents. (x^2)^2 = x^(2×2):

(x^2 + 7) (x^4 - 7 x^2 + 49)

Hint: | Multiply 2 and 2 together.

2×2 = 4:

Answer: (x^2 + 7) (x^4 - 7 x^2 + 49)

The correct factored form of \(343 + x^6\) is :

D. \((7 + x^2)(49 - 7x^2 + x^4)\).

Here, we have to factor the expression \(343 + x^6\), we can notice that it's a sum of cubes.

In this case, 343 is the cube of 7, i.e. \((7^3)\), and \(x^6\) is the cube of \(x^2\)

(since \((x^2)^3 = x^6\)).

The sum of cubes can be factored using the formula:

\(a^3 + b^3 = (a + b)(a^2 - ab + b^2).\)

For the given expression, let's apply this formula:

\(343 + x^6 = 7^3 + (x^2)^3\\= (7 + x^2)((7)^2 - 7x^2 + (x^2)^2)\\= (7 + x^2)(49 - 7x^2 + x^4).\)

So, the correct factored form is \((7 + x^2)(49 - 7x^2 + x^4)\), which corresponds to option D.

To learn more on Expression click:

brainly.com/question/14083225

#SPJ3

Answer:

The answer is option C.

Hope this helps you

Answer:

C

Step-by-step explanation:

find slope of the two lines:

(-6,5) , (-2,7)

m=y2-y1/x2-x1

m=7-5/-2-(-6)

m=2/4=1/2 for first line

second line : (4,2) , (6,6)

m=6-2/6-4

m=4/2=2

parallel lines have same slope, perpendicular has opposite reciprocal slope

Answer:

Step-by-step explanation:

Gogli complexes packages proteins, while endoplasmic reticulums transport proteins made by the gogli complexes around the cell.