solves the equation
8x-2 =3(x-9)

Answer:

(0,0) is a saddle point

(-4,4) is a local maximum

Step-by-step explanation:

\(\displaystyle z=3x^3-36xy-3y^3\\\\\frac{\partial z}{\partial x}=9x^2-36y\\\\\frac{\partial z}{\partial y}=-36x-9y^2\)

Determine critical points

\(9x^2-36y=0\\9x^2=36y\\\frac{x^2}{4}=y\)

\(-36x-9y^2=0\\-36x-9(\frac{x^2}{4})^2=0\\-36x-\frac{9}{16}x^4=0\\x(-36-\frac{9}{16}x^3)=0\\\\x=0\\\\-36-\frac{9}{16}x^3=0\\-36=\frac{9}{16}x^3\\-64=x^3\\-4=x\)

When x=0

\(9x^2-36y=0\\9(0)^2-36y=0\\-36y=0\\y=0\)

When x=-4

\(9x^2-36y=0\\9(-4)^2-36y=0\\9(16)-36y=0\\144-36y=0\\144=36y\\4=y\)

So, we need to check what kinds of points (0,0) and (-4,4) are.

For (0,0)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(0))(-18(0))-(-36)^2\\\\H=-1296 < 0\)

Therefore, (0,0) is a saddle point since \(H < 0\).

For (-4,4)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(-4))(-18(4))-(-36)^2\\\\H=(-72)(-72)-1296\\\\H=5184-1296\\\\H=3888 > 0\)

Because \(H > 0\) and since \(\frac{\partial^2z}{\partial x^2}=-72 < 0\), then (-4,4) is a local maximum

Answer:

um whats the question....

Step-by-step explanation:

there was 12 left? 88% of the milk cartons were purchased? idek what ur looking for in an answer

Answer:

well if ur talking about 100-88 it's 12... but u didn't ask for a specific question so

The equation could be used to solve for charles' rate if it is represented by x is 2x=54.

In the given question wehave to find the equation could be used to solve for charles' rate if it is represented by x.

Bill riding a bicycle at an average rate of 9 mph.

Charles' rate is x.

So the relative rate = x−9 mph

Distance traveled by Bill in 4 hours = 9*4 =36 mph

Charles' overtook Bill in 2 hours. So

Relative Rate = Distance/Time

x−9=36/2

Multiply by 2 on both side. We get

2(x−9)=36

Simplifying

2x−18=36

Add 18 on both side, we get

2x=36+18

2x=54

Hence, the equation could be used to solve for charles' rate if it is represented by x is 2x=54.

To learn more about speed formula link is here

brainly.com/question/7359669

#SPJ4

The integral method for calculating ksn was chosen for the main analysis due to its reduced vulnerability to uncertainty.

In our study, we opted to utilize the integral method for determining the ksn (a parameter) in our main analysis. The selection of this method was primarily based on its ability to mitigate the impact of uncertainty. The integral method offers several advantages over alternative approaches when dealing with uncertainty.

Firstly, it incorporates a broader range of data points by integrating over a continuous range of values, resulting in a more comprehensive assessment. This helps to minimize the influence of outliers or errors in individual data points, leading to a more robust estimation of ksn.

Additionally, the integral method accounts for the distribution of uncertainty across the entire range of values, providing a more representative characterization of the parameter. By considering these factors, we can enhance the reliability and accuracy of our analysis, making the integral method a suitable choice for our main analysis.

Learn more about integral here:

https://brainly.com/question/31433890

#SPJ11

Selecting KSN calculated using the integral method for your main analysis due to its lower susceptibility to uncertainty suggests that you have found this particular approach to be more reliable or robust when dealing with uncertain data compared to other methods.

The integral method in KSN refers to the incorporation of information from integrals or cumulative distribution functions (CDFs) in the estimation process, which can help in reducing the impact of uncertainty in the data.

By choosing KSN with the integral method, it implies that you believe this approach provides more accurate or stable results in the presence of uncertainty. This could be due to the specific properties of the integral method in KSN, such as its ability to incorporate information from distribution functions or handle non-stationary data.

It's important to note that the suitability of any method depends on the specific characteristics of your data, the nature of the problem, and the goals of your analysis. Different interpolation methods have their strengths and weaknesses, and it's crucial to evaluate them based on the specific requirements of your study.

Learn more about cumulative distribution functions here:

https://brainly.com/question/30985385

#SPJ11

we selected ksn calculated using the integral method for our main analysis due to its lower susceptibility to uncertainty. What does it suggests?

Answer:

Siiiiii

Step-by-step explanation:

To determine the number of miles you and your friend need to drive for the cost to be the same between the SUV dealership and the Acura dealership, we can set up an equation using the given information and solve for the miles.

Let's assume the number of miles driven is represented by 'x'. For the SUV dealership, the total cost would be $30 (flat rate) plus 10 cents per mile, which can be expressed as $0.10x. Therefore, the total cost for the SUV dealership is given by the equation: 30 + 0.10x.

For the Acura dealership, the total cost would be $40 (flat rate) plus 5 cents per mile, which can be expressed as $0.05x. Hence, the total cost for the Acura dealership is given by the equation: 40 + 0.05x.

To find the mileage where the costs are equal, we set the two equations equal to each other and solve for 'x':

30 + 0.10x = 40 + 0.05x.

Simplifying this equation, we subtract 0.05x from both sides to get:

0.10x - 0.05x = 40 - 30.

This reduces to 0.05x = 10.

To isolate 'x', we divide both sides by 0.05:

x = 10 / 0.05 = 200.

Therefore, you and your friend would need to drive 200 miles for the cost to be the same between renting a car from the SUV dealership and renting a car from the Acura dealership.

To learn more about SUV - brainly.com/question/1030535

#SPJ11

[11] B. 6

1 * 3 = 3, so 2 * 3 = 6

[12] A. 3

20 / 5 = 4, so 15 / 5 = 3

[13] B. 7

2 * 2 = 4, so 7 * 2 = 14,

[14] A. direct proportion

We can figure this out using 150:2 = x:3, which is a direct proportion because y is constant directly with x

-> Not 100% sure on this one

[15] C. partitive proportion

A proportion such as 1:2:3 is more specifically known as a partitive proportion, so this answers the question

[16] B. inverse proportion

As more painters are added, the time that is taken to paint the house decreases, so this is an inverse proportion

-> Not 100% sure on this one

[17] C. 1400 cupcakes

-> 2 weeks = 14 days

-> solve with 200:2 = x:14

-> 2*7 = 14, so 20 * 7 = 1,400

[18] D. 153

-> Putting it simpler, 2:3:3 = Grade 4: Grade 5: Grade 6

-> We are looking for Grade 6

-> 2x + 3x + 3x = 408

-> 8x = 408

-> x = 51

-> 3x = 3(51) = 153

[19] C. 16 hours

-> We can solve with 6:10 = 10:x

-> 10/6 = \(\frac{5}{3}\), so 10 * \(\frac{5}{3}\) = 16.666666, or for here 16 hours

[20] D. Php 750

-> Put simpler, Mark:Justin:David = 4:5:6

-> 4:5:6 = 4x:5x:6x

-> 5x = 250 which becomes 250 / 5 = 50

-> 4*50 = 200 & 6*50 = 300

-> 200 + 300 + 250 = Php 750

Have a nice day! - Note: not exactly sure on the wording for 14 & 16

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

10

Step-by-step explanation:

as you want to find the square root of 100, by using a calculator you will find out that it is 10, also in other way you can check whether it is true by multiply 10 with 10, which you will get 100. in other way, square root of 100 means what value times with what value will get 100

Hey there!

First of all, what is this "√" sign?

It means "square root"

Wow, numbers have square roots? Yes.

The square root of a number is the opposite of squaring a number.

Squaring a number simply means multiplying it times itself.

So taking the square root of a number is the opposite of squaring a number.

So, we have

\(\bold{\sqrt{100} }\)

What is the square root of 100? in other words, what number times itself equals 100?

That's right, 10.

Hence, the answer is:

\(\boxed{\boxed{\bold{10}}}\)

Hope everything is clear.

Let me know if you have any other questions; if you do, please comment.

#LearningDoesn'tEnd

\(\rule{200}{2}\)

Step-by-step explanation:

x²y = k, where k is a real constant.

When x = 3.5, y = 8.

=> (3.5)²(8) = k, k = 98.

When y = 8/9,

we have x²(8/9) = (98).

=> x² = 110.25

=> x = 10.5 or x = -10.5.

Since we want the negative value,

the answer is x = -10.5.

The required negative value of variable x when y = 8/9 is -10.5. To understand the calculations, check below.

Important information:

Using the given inverse proportional statement, we get

\(y\propto \dfrac{1}{x^2}\)

\(y=\dfrac{k}{x^2}\)     ...(i)

Substitute \(x=3.5,y=8\).

\(8=\dfrac{k}{3.5^2}\)

\(8=\dfrac{k}{12.25}\)

\(8\times 12.25=k\)

\(98=k\)

Substitute \(k=98\) in (i).

\(y=\dfrac{98}{x^2}\)

Substitute \(y=\dfrac{8}{9}\).

\(\dfrac{8}{9}=\dfrac{98}{x^2}\)

\(x^2=98\times \dfrac{9}{8}\)

\(x^2=110.25\)

\(x=\pm \sqrt{110.25}\)

\(x=\pm 10.5\)

We need only negative value.

\(x=-10.5\)

Therefore, the required value of variable x is -10.5.

Find out more about 'Proportion' here:

https://brainly.com/question/15179946

Answer:

I think it's A or B

Step-by-step explanation:

1. The  probability of landing on red is 7/20.

2. I will predict 25 to be white.

3. I will predict 48 to be blue.

4. It will most likely land on red.

Probability deals with the study of random events. It involves determining the likelihood or chance of an event occurring, based on the information available.

The basic formula for probability is:

P(event) = number of favorable outcomes / number of possible outcomes

number of possible outcomes = 7 + 5 + 4 + 4 = 20

1) P(red) = number of red / number of possible outcomes

P(red) = 7/20

2) when spun 100 times:

number of white = P(white) * 100

number of white = 5/20 * 100 = 25

3) when spun 240 times:

number of blue = P(blue) * 100

number of blue = 4/20 * 240 = 48

4) That will be the color with highest probability. That is color red with probability of 7/20.

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ1

30 boxes of popcorn and 20 free DVD rentals were given away.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

let a variable represent the number of the highest-cost item (boxes of popcorn). If that is p, then the number of DVD rentals is (53-p) and the total cost is ...

 2p +(50 -p) = 80

 p = 80 -50 = 30 . . . . . . . boxes of popcorn

50-p= (50 -30) = 20 . . . DVD rentals

To learn more about the solution of an equation from the given link

https://brainly.com/question/22688504

#SPJ1

It is correct to say that measurements are affected by both bias and chance error, as these factors contribute to the overall uncertainty and variability in the measurement process.

Measurements are typically affected by both bias and chance error. Bias refers to a systematic error or tendency for measurements to consistently deviate from the true value in the same direction. It can be caused by various factors such as calibration issues, instrument inaccuracies, or human error. Bias affects the accuracy of measurements by introducing a consistent deviation from the true value.

On the other hand, chance error, also known as random error, is the variability or inconsistency in measurements that occurs due to unpredictable factors. These factors can include environmental conditions, variations in measurement techniques, or inherent limitations of the measuring instruments. Chance error leads to fluctuations in measurement values around the true value and affects the precision of measurements.

Therefore, it is correct to say that measurements are affected by both bias and chance error, as these factors contribute to the overall uncertainty and variability in the measurement process.

Learn more about measurements here:

brainly.com/question/28913275

#SPJ11

a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

Learn more about homeostasis at: https://brainly.com/question/3888340

#SPJ4

Answer:

10p

Step-by-step explanation:

have a good day :)

The present value of the payments is smaller than the amount of the loan, so you will not be able to pay off the loan.

The present value of the payments refers to the current value of the future payments, considering the time value of money. In this case, the payments are made over a period of 8 months, and each payment is listed. To determine if the payments will be enough to pay off the credit card, we need to calculate the present value of these payments and compare it to the initial loan amount of $5,000.

Since the interest rate on the credit card is 1.5% per month, we need to discount each payment back to its present value. By discounting the payments, we can see the equivalent value of these payments in today's dollars. If the present value of the payments is equal to or greater than $5,000, it would be enough to pay off the loan. However, if the present value is smaller than $5,000, it means the payments will not be sufficient to pay off the loan.

In this case, without specific information about the discount rate used to calculate the present value, we cannot make an exact determination. However, based on the given information, which states that the present value of the payments is smaller than the amount of the loan, it suggests that the payments will not be enough to pay off the credit card debt.

Learn more about discount here: brainly.com/question/31746893

#SPJ11

Answer:

Step-by-step explanation:

ED :  DL = FD : DM

or

ED / DL = FD / DM

FD = ED·DM / DL

FD = 88 ·  84  / 48 = 154

Answer:

the 7th

0.007805 or  59 / 756

Step-by-step explanation:

To determine the Friday that he needed more pounds, determine the number of pounds he needed per dog for each Friday.

to do this, divide the total pounds by the number of dogs

on the 14th

3/8 ÷ 35 =

3/8 x 1/35 = 3/280

on the 7th

1/2 ÷ 27 =

1/2 x 1/27 = 1/54

to determine which fraction is larger multiply each by 100 to determine its percent

3/280 x 100 = 1.071

1/54 x 100 = 1.852

1/54 is larger. Thus, more pounds was needed on Friday the 7th

the difference between these fractions should be determined  

\(\frac{1}{54}\) - \(\frac{3}{280}\)

\(\frac{280 - 162}{1512}\) = \(\frac{118}{1512}\) = 59 / 756

The container whose sugar water mixture is a darker shade of red is: A. the small bowl's mixture is a darker shade of red.

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this scenario, the ratio of the sugar water mixture in the small bowl (S) to the sugar water mixture in the large bucket (L) can be represented by this mathematical expression:

S:L = 1:3

Also, when red coloring is added to both containers, we have:

S:L = 1r:3r

In this context, we can reasonably and logically deduce that the mixture in the small bowl would have a darker shade of red because it is less diluted in comparison with the sugar water mixture in the large bucket.

Read more on ratio here: https://brainly.com/question/28083504

#SPJ1

Complete Question:

For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?

answer choices

The small bowl's mixture is a darker shade of red.

The large bucket's mixture is a darker shade of red.

Neither. The mixtures are the same shade of red.

Answer:

-2x+8y-3 if im not wrong

The value of x and y in the algebra (3x - y, 2) = (2, x + y) ​ are 1 and 1 respectively.

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Given the algebra:

(3x - y, 2) = (2, x + y) ​

Therefore, equation:

3x - y = 2        (1)

Also:

x + y = 2        (2)

From both equations, solving simultaneously:

x = 1, y = 1

The value of x and y are 1 and 1 respectively.

Find out more on equation at: https://brainly.com/question/29174899

#SPJ1

The function for the value of the motorcycle after x years are;

y = 8000 - 500x

y = -500x + 8000

A function is a relationship between inputs where each input is related to exactly one output.

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have given that new motorcycle has a value of $8,000. Every year its value decreases by $500.

Now, we have y = amount of the motorcycle

x = number of years

The function for the value of the motorcycle after x years.

y = 8000 - 500x

y = -500x + 8000

Thus,

y = 8000 - 500x

y = -500x + 8000

Learn more about functions here:

brainly.com/question/28533782

#SPJ3

Value of b would be \(\sqrt{c^{2}-a^{2} }\).

Pythagoras' theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right-angled triangle. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In mathematical terms, the theorem can be expressed as:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the two shorter sides of the right-angled triangle, and c is the length of the hypotenuse.

This theorem has important applications in many fields, including engineering, physics, and architecture. It is also used in many geometric proofs, and is considered one of the most important and well-known results in mathematics.

Now given equation is

\(a^2 + b^2 = c^2\)

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

To know more about Pythagoras visit:

https://brainly.com/question/1527521

#SPJ1

Answer:

Step-by-step explanation:

6(x-3)=6(x)+6(-3)=6x-18

Answer: the answer is 6x-18 i believe its B

How?

All you have to do is distribute so:

6*X= 6x and 6*-3= -18 put them together and you get 6x-18

The \(x^{th}\) number in the sequence will be   \(F[x]=\dfrac{5}{2} F[x]\)

The given function is

\(F[x]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1}\)

Now at  \(x=x+1\) for the function

\(F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x+1-1}\)

\(F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x }\)

Now we can write

\(F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1} \dfrac{5}{2}^1\)

Since     \(F[x]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1}\)

so

\(F[x]=\dfrac{5}{2} F[x]\)

Thus the \(x^{th}\) number in the sequence will be   \(F[x]=\dfrac{5}{2} F[x]\)

To know more about Functions follow

https://brainly.com/question/24748644

Answer:

A

Step-by-step explanation:

Took exam and got 100

Given:

The expression is:

\(0.0004\times 0.02\)

To find:

The value of the given expression.

Solution:

We have,

\(0.0004\times 0.02\)

It can be written as:

\(=\dfrac{4}{10000}\times \dfrac{2}{100}\)

\(=\dfrac{8}{1000000}\)

\(=0.000008\)

Therefore, the value of the given expression is 0.000008.