\(if \: x + y + z = 0 \: then \: show \: that \: {x}^{3} + {y}^{3 } + {z}^{3} = 3xyz\)
​

The equation relating L to D is; L = 9 + D

Please find attached the graph of L = 9 + D, created with MS Excel

An equation is a statement of equivalence between two expressions, and a function maps a value in a set of input values to a value in the set of output values.

The initial length of the road = 9 miles

The length of road the construction crew is adding each day = 1 mile

The length in mile of the road after D days = L

The equation for the length is therefore;

The graph of the length of the road can therefore be obtained from the equation for the length by plotting the ordered pairs obtained from the equation.

Please find attached the graph of the equation created using MS Excel.

Learn more on writing equations here: https://brainly.com/question/29339697

#SPJ1

One angle of an isosceles triangle measures 120°. The other two possible angles are 60 degree. So the option B is correct.

One angle of an isosceles triangle measures 120°.

An isosceles triangle has two equal sides. An isosceles triangle is a triangle with two sides of equal length and two angles of equal measure. The two equal sides are usually referred to as the base and the other side is called the vertex.

As we know that in a isosceles triangle have a sum of all sides is 180 degree.

Since the ne side is 120 degree.

So the measure of other two sides = 180° - 120°

The measure of other two sides = 60°

To learn more about isosceles triangle link is here

brainly.com/question/2456591

#SPJ4

The complete question is:

One angle of an isosceles triangle measures 120°. what measures are possible for the other two angles? choose all that apply.

A. 30°

B. 60°

C. 120°

D. 180°

Answer:

For a day VFR flight in a Piper Archer, you would need a fuel reserve of approximately 5 gallons.

Step-by-step explanation:

The amount of fuel reserve that must be carried on a day VFR (Visual Flight Rules) flight, the FAA requires a minimum fuel reserve of 30 minutes at cruising speed for day VFR flights. To calculate the gallons needed for a Piper Archer, follow these steps:

1. Determine the fuel consumption rate of the Piper Archer at cruising speed, which is typically around 10 gallons per hour (GPH).
2. Divide the required fuel reserve minutes (30) by the minutes in an hour (60): 30 / 60 = 0.5 hours.
3. Multiply the fuel consumption rate (10 GPH) by the required fuel reserve time in hours (0.5 hours): 10 * 0.5 = 5 gallons.

Therefore, for a day VFR flight in a Piper Archer, you would need a fuel reserve of approximately 5 gallons.

learn more about "fuel reserve":-https://brainly.com/question/31663770

#SPJ11

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

Learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ1

Answer:

(x-12)^2+(y-2)^2=4

Step-by-step explanation:

Answer:

x=2.5

Step-by-step explanation:

a) The plane x = k will be given by the equation:

y^2 - z^2 = 9 - k^2.

b)   The graph is rotated so that its axis is the y-axis (option b). This is because the change in signs in the equation swaps the roles of x^2 and y^2, resulting in a rotation of the coordinate axes.

c)   The "+2y" term causes the shift to be in the positive y-direction by two units. The equation now represents a shifted elliptical cone.

(a) To find and identify the traces of the quadric surface x^2 + y^2 - z^2 = 9 given the plane x = k, we substitute x = k into the equation of the quadric surface:

(k)^2 + y^2 - z^2 = 9.

Simplifying this equation, we have:

k^2 + y^2 - z^2 = 9.

This equation represents a hyperbolic cylinder, where the cross-sections parallel to the yz-plane are ellipses and the cross-sections parallel to the xy-plane are hyperbolas. The traces on the plane x = k will be the intersection of this cylinder with the plane x = k. Since the equation does not involve k, it remains unchanged, and the traces on the plane x = k will be given by the equation:

y^2 - z^2 = 9 - k^2.

(b) If we change the equation in part (a) to x^2 - y^2 + z^2 = 9, the graph is affected in the following way:

The graph is rotated so that its axis is the y-axis (option b). This is because the change in signs in the equation swaps the roles of x^2 and y^2, resulting in a rotation of the coordinate axes.

(c) If we change the equation in part (a) to x^2 + y^2 + 2y - z^2 = 8, the graph is affected in the following way:

The graph is shifted one unit in the positive y-direction (option e). This is because the coefficient of y^2 is positive, indicating that the graph is shifted upward along the y-axis. The "+2y" term causes the shift to be in the positive y-direction by two units. The equation now represents a shifted elliptical cone.

Learn more about quadric here:

https://brainly.com/question/32271712

#SPJ11

The equation of the altitude from vertex A of the triangle is y = (3/2)x + 3/2.

To write an equation for the altitude from vertex A of the triangle where point A is (-1,0), point B is (8,-5), and point C is (2,-3), we need to use the slope-intercept form of an equation for the line that contains the side opposite vertex A. Here are the steps:

1. Find the slope of the line containing side BC using the slope formula: m = (yb - yc)/(xb - xc) = (-5 - (-3))/(8 - 2) = -2/3.

2. Find the equation of the line containing side BC using point-slope form: y - yb = m(x - xb). Using point B, we get: y + 5 = (-2/3)(x - 8). Simplifying, we get y = (-2/3)x + 19/3.

3. The altitude from vertex A of the triangle is perpendicular to side BC. Therefore, its slope is the negative reciprocal of the slope of side BC, which is 3/2.

4. We can find the equation of the altitude by using point-slope form again, this time using point A: y - ya = m(x - xa). Using point A and the slope 3/2, we get: y - 0 = (3/2)(x + 1). Simplifying, we get: y = (3/2)x + 3/2.

Summary: To find the equation of the altitude from vertex A of the given triangle, we first found the slope of the line containing the side opposite vertex A, which is BC. Then, we found the equation of this line using point-slope form. Next, we used the fact that the altitude is perpendicular to side BC and found its slope, which is the negative reciprocal of the slope of side BC. Finally, we used the point-slope form again to find the equation of the altitude using point A and its slope. The equation we obtained is y = (3/2)x + 3/2.

For more questions on equations

https://brainly.com/question/29174899

#SPJ8

Answer: one point only.

Step-by-step explanation:

Since the length of the sides of the square is 9 cm, taking a point outside the square which is equidistant from point B and C will never give exact 6 cm from A.

The only way to achieve this is by taking a equidistant point inside.

You can achieve exactly 6 cm from point A from point between B and C

But can only achieve a single point if it has to be equidistant from point B and C.

Answer:

2+2=4

Step-by-step explanation:

The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

You should perform x trials until you observe a success.

We have given that,

There are exactly two possible outcomes success and failure.

We have to determine the following is NOT a common characteristic of a binomial distribution.

By process of elimination:-

A binomial experiment is a statistical experiment that must meet certain requirements

All trials are independent.

There are a fixed number of n trials.

The probability of success, p, is the same for each trial.

To learn more about the probability visit:

brainly.com/question/24756209

#SPJ1

Descriptive statistics are those that involve gathering, arranging, and summarizing data.

Brief informational coefficients known as descriptive statistics are used to sum up a given data set, which may be a sample of a population or a representation of the entire population. Measures of the central tendency or measures of variability make up descriptive statistics (spread).

A descriptive statistic's main function is to summarize data. Only the data set from which they were derived are statements made by descriptive statistics; they never extend further than the data you have.

To know more about  descriptive statistics visit:

https://brainly.com/question/28352023

#SPJ4

Carl can select red marbles most likely.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given Carl is going to select 1 marble,

total marbles in bag = 12

number of red marbles = 6

probability of red marbles = 6/12

number of blue marbles = 3

probability of blue marbles = 3/12

number of green marbles = 1

probability of green marbles = 1/12

number of yellow marbles = 2

probability of yellow marbles = 2/12

since the chances of red marble is more as compared than others.

Hence there of chances of selecting red marble.

Learn more about probability;

brainly.com/question/30034780

#SPJ1

the image of bag is attached.

solving value mixture problems involves finding the amount of two or more substances mixed together to create a desired mixture. These problems can be solved using a linear equation calculator by setting up an equation based on the given information and solving for the unknown variable.

Value mixture problems involve finding the amount of two or more substances mixed together to create a desired mixture. These problems can be solved using a linear equation calculator. Here's a step-by-step explanation of how to solve a value mixture problem using a linear equation calculator:

By following these steps and using a linear equation calculator, you can solve value mixture problems efficiently and accurately.

About solving value mixture problems here:

https://brainly.com/question/29076863

#SPJ11

A value mixture problem using a linear equation calculator is solved by considering an appropriate example which is described below.

To solve a value mixture problem using a linear equation calculator,

We need to take an example as follows:

Suppose you have a 10% saline solution and a 20% saline solution,

Then how much of each should you mix to create 100 mL of a 15% saline solution?

To solve this problem using a linear calculator,

we can set up two equations:

Let x be the amount of the 10% saline solution to use, and y be the amount of the 20% saline solution to use.

The first equation represents the total volume of the mixture:

x + y = 100

The second equation represents the percentage of saline in the mixture:

0.1x + 0.2y = 0.15(100)

Simplifying the second equation, we get:

0.1x + 0.2y = 15

Now solve for one variable in terms of the other.

Solve for x in terms of y:

x = 100 - y

Substituting this into the second equation, we get:

0.1(100 - y) + 0.2y = 15

Simplifying and solving for y, we get:

y = 50 mL

Therefore, the amount of the 10% saline solution to use is:

x = 100 - y = 50 mL

So we need to mix 50 mL of the 10% saline solution with 50 mL of the 20% saline solution to create 100 mL of a 15% saline solution.

To learn more about linear equations visit:

https://brainly.com/question/32634451

#SPJ4

The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

Learn more about area of similar figures on:

https://brainly.com/question/17132861

#SPJ1

A good fitting multiple regression model should have the following characteristics:

1. High Adjusted R-squared value: The adjusted R-squared value should be high, indicating that the model accounts for a large proportion of the variation in the dependent variable that is not explained by the independent variables.

2. Low p-values: The p-values of the coefficients should be low, indicating that the independent variables are statistically significant in explaining the variation in the dependent variable.

3. Low residual standard error (RSE): The RSE should be low, indicating that the model's predictions are close to the actual values.

4. No multicollinearity: There should be no multicollinearity among the independent variables, meaning that they should not be highly correlated with each other.

5. Homoscedasticity: The residuals should be homoscedastic, meaning that they should have constant variance across all levels of the independent variables.

6. Normality of residuals: The residuals should be normally distributed, indicating that the model's predictions are unbiased.

Overall, a good fitting multiple regression model should accurately predict the dependent variable using the independent variables while satisfying the statistical assumptions of the regression model.

Learn more about multiple regression model here: brainly.com/question/25814703

#SPJ11

Answer:

A. 28.1 cm^2

Step-by-step explanation:

a = bh

a = (7.6)(3.7)

a = 28.12 cm^2

a = 28.1 cm^2

Answer:

\(\frac{3^{10} }{3^{2} }\) , \((3*3)^{4}\), \((3^{4})^{2}\)  

Step-by-step explanation:

The expressions 3¹⁰/3², (3⁴)², and (3·3)⁴ are equivalent to the given expression. which is the correct answer would be options (B), (D), and (E).

Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. To answer the exponential expressions, we may need to apply the relationship between exponents and logarithms.

As per option (B), we have

3¹⁰/3²

3¹⁰⁻²

Apply the subtraction operation in the exponent

3⁸

As per option (D), we have

(3⁴)²

3⁴ˣ²

Apply the multiplication operation in the exponent

3⁸

As per option (E), we have

(3·3)⁴

(3²)⁴

3⁴ˣ²

3⁸

Thus, the expressions 3¹⁰/3², (3⁴)², and (3·3)⁴ are equivalent to the given expression.

Hence, the correct answer would be options (B), (D), and (E).

Learn more about exponential function here:

brainly.com/question/11487261

#SPJ2

Answer:

The amount Rizzo has = x = $5.25

The amount Shonda has = y = $6.75

Step-by-step explanation:

Let us represent:

The amount Rizzo has = x

The amount Shonda has = y

Rizzo has $1.50 less in his piggy bank than his sister Shonda.

x = y - 1.50.......Equation 1

If Shonda had $9 more, she would have three times as much money as Rizzo.

y + 9 = 3(x)

y + 9 = 3x..... Equation 2

y = 3x - 9

We substitute 3x - 9 for y in Equation 1

x = y - 1.50.......Equation 1

x = 3x - 9 - 1.50

9 + 1.50 = 3x - x

10.50 = 2x

x = 10.50/2

x = $5.25

Solving for y

y = 3x - 9

y = 3(5.25) - 9

y = $6.75

Therefore:

The amount Rizzo has = x = $5.25

The amount Shonda has = y = $6.75

Answer:

root 50

Step-by-step explanation:

Root 8 = 2root 2root 18 = 3root 2root32 =4root 2common difference = 4root 2 - 3root 2=root2 next term = 5root2 = root50.

Answer:

Option B

Step-by-step explanation:

Let:

w = number of withdrawals

C = Monthly cost

For Bella:

$3 = Fixed monthly charge

$1.50 × w = Amount charged for every withdrawal she makes

∴Linear equation describing her monthly cost:

C = 3 + 1.5w

For Justin:

$0 = Fixed monthly charge

$2 × w = Amount charged for every withdrawal he makes

∴Linear equation describing his monthly cost:

C = 2w

∴System of equations:

      C = 3 + 1.5w

      C = 2w

∴Option B

Answer:

1.7 degrees fahrenheit

Step-by-step explanation:

Answer:

can you re-upload the picture its blurry

Step-by-step explanation:

Let's say we have a graph with four nodes: A, B, C, and D. The edges and their lengths are as follows:
- A to B: 3
- A to C: 1
- B to D: 2
- C to D: -5

Using this we can show that the Dijkstra's algorithm fails if negative edge lengths are allowed

If we use Dijkstra's algorithm to find the shortest path from A to D, we would start at A and initially assign a distance of 0 to it. We would then look at its neighbors, B and C, and update their distances accordingly (3 for B and 1 for C). We would then choose C as the next node to visit since it has the shortest distance so far. However, when we update the distance to D through C, we would get a distance of -4 (since -5 + 1 = -4).

This negative distance causes a problem because Dijkstra's algorithm assumes that all edge weights are non-negative. When we update the distance to D through C, it becomes shorter than the distance we assigned to it when we initially looked at it through B. This means that we would have to revisit D and potentially update its distance again, leading to an infinite loop.

Therefore, Dijkstra's algorithm fails if negative edge lengths are allowed.

To learn more about Dijkstra's algorithm visit : https://brainly.com/question/31309462

#SPJ11

The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

To learn more about constraint: https://brainly.com/question/30655935

Answer:

see image

Step-by-step explanation:

Putting the data on the line plot is not too bad. Just put an x above the number on the numberline. If a number in the data set repeats, just stack those x's up over the numberline. It seems like the hardest part is labelling the number line. Each tick mark can be 1/8. On the image I wrote all the fractions in eighths at the bottom, then to label the numberline I used the simplified fractions. For example I started with 1 3/8 because it was the smallest number in the data set. Next is 1 4/8, but simplified that is 1 1/2. So 1 1/2 is how we label the numberline.

There were 12 pieces of data, but really only six numbers because some were repeated.

Stack x's above the numberline. Done! You have a line plot. See image.

Answer:

1. 1/⅜

2. 1/⅜

3 is 2/¼

4 is 2/¼

5 is 2/¼

6 is 2/⅞

7 is 2/⅞

8 is 2/⅞

9 is 3/⅛

10 is 3/⅛

11 is 3/⅛

Step-by-step explanation:

Mixed number to Improper Fraction

1.9/4

2.13/4

3.23/8

4.25/8

5.23/8

6.25/8

7. 5/2

8.9/4

9. 23/8

10. 5/2

11. 11/8

12. 25/8

then you make it into the same denominator

1. 18/8

2. 26/8

3. 23/8

4. 25/8

5. 23/8

6. 25/8

7. 20/8

8. 18/8

9. 23/8

10. 20/8

11. 11/8

12. 25/8

then what ever numerator is smallest you put at front and it goes onto the biggest one

e.g ASCENDING ORDER

However you'll need to put it back into the normal mixed number, so all you have to do is revert let's say 25/8 into 3/⅛, and put it onto the graph

1. 1/⅜

1. 1/⅜2. 1/⅜

. 1/⅜3 is 2/¼

. 1/⅜3 is 2/¼ 4 is 2/¼

. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼

. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼6 is 2/⅞

. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼6 is 2/⅞7 is 2/⅞

8 is 2/⅞

9 is 3/⅛

9 is 3/⅛10 is 3/⅛

11 is 3/⅛

and number 12 which is the biggest and the last one the you should put(on the end of graph) is

3/¼

I did rush this so I hope this is the correct answers

The horizontal distance between the base of the ladder and the wall is approximately 16.06 feet.

To find the flat distance between the foundation of the  stool and the wall, we utilize geometry. For this situation, we can utilize the sine capability, which relates the contrary side of a right triangle to the hypotenuse and the point inverse the contrary side.

Let x be the flat distance between the foundation of the stepping stool and the wall. Then, utilizing the given point of 64 degrees, we can compose:

sin(64) = inverse/hypotenuse

where the hypotenuse is the length of the stepping stool, which is 18 feet.

Addressing for the contrary side, which is the even distance we need to find, we get:

inverse = sin(64) x hypotenuse

inverse = sin(64) x 18

inverse = 16.06 feet

Accordingly, the even distance between the foundation of the stepping stool and the wall is roughly 16.06 feet.

To learn more about Trigonometry, refer:

https://brainly.com/question/30350752

#SPJ4

Answer:

each lb of jellybeans = $1.50

each lb of almonds = $2.75

Step-by-step explanation:

let j = jellybean cost for each pound

let a = almond cost for each pound

3j + 2a = 10

5j + 6a = 24

Using elimination method:

15j + 10a =50

15j + 18a = 72

------------------------

-8a = -22

a = 2.75

using 3j + 2a = 10

3j + 2(2.75) = 10

3j + 5.5 = 10

3j = 4.5

j = 1.5

Part-A:  linear model is not reasonable which is strong

Part-B : Strong, but linear model is not reasonable

Part-C :  Strong,  linear model is reasonable

Part-D : moderate, linear model is not reasonable

Given that,

We have to find explain the strength of the relationship in the data and whether or not it would be appropriate to fit a linear model.

We know that,

There are 4 options that are:

weak relationship

moderate, linear model is reasonable

strong, linear model is reasonable

strong, but linear model is not reasonable

moderate, but linear model is not reasonable

Therefore,

Part-A:  linear model is not reasonable which is strong

Part-B : Strong, but linear model is not reasonable

Part-C :  Strong,  linear model is reasonable

Part-D : moderate, linear model is not reasonable

To learn more about linear visit: https://brainly.com/question/20286983

#SPJ4