What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?

The section formula provides a way to check if three points in 3D space are collinear by verifying that the equation (x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0 is satisfied when their coordinates are substituted.

To prove three points are collinear in 3D using the section formula, first determine the coordinates of the three points. Then, substitute the coordinates into the section formula equation, (x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0. Finally, calculate the equation and if it is equal to 0, the three points are collinear.

For example, if the coordinates of three points are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3), then the three points are collinear if the following equation is satisfied:

(x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0

If the equation is not equal to 0, the points are not collinear. To illustrate, if the coordinates of three points are

(x1, y1, z1), (x2, y2, z2) and (x3, y3, z3),

then the three points are collinear if the following equation is satisfied: (x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0.

If this equation is not equal to 0, then the three points are not collinear. To check if the points are collinear, one must calculate the equation and determine if the equation is equal to 0. If so, the three points are collinear.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The coordinate of the point reflection across the x-axis will be (3, -6). Then the correct option is A.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The reflection does not change the shape and size of the geometry. But flipped the image.

The quadrilateral ABCD is shown. The coordinate of point B is (3, 6).

If the quadrilateral ABCD is reflected across the x-axis. Then the coordinates of B' will be given as,

B' = (3, -6)

The coordinate of the point reflection across the x-axis will be (3, -6). Then the correct option is A.

More about the transformation of a point link is given below.

https://brainly.com/question/27224339

#SPJ1

The equation of the temperature at midnight is written as 3y + 5 = -7

The temperature at the midnight is calculated to be -4 degrees

The equation for the temperature at midnight is following the information given in the problem tripled and increased by 5

Assuming the temperature at midnight is y. For the temperature to triple we have

3y

For the temperature to rise 5 degrees will result to

3y + 5 = -7

solving for y

3y + 5 = -7

3y = -7 - 5

3y = -12

y = -4

At midnight the temperature was -4 degrees

Learn more about linear functions at:

https://brainly.com/question/29225098

#SPJ1

Mrs. Moore class has the smaller interquartile range

From the question, we have the following parameters that can be used in our computation:

Dot plots

On the dotplots, we have the following readings

           Mr Kim:       Mrs. Moore

Q1        64                   62

Q3       69                   66

The difference between Q3 and Q1 is the IQR

So, we have

           Mr Kim:       Mrs. Moore

Q1        64                   62

Q3       69                   66

IQR       5                     4

4 is less than 5

Hence, Mrs Moore class has smaller IQR

Read more about interquartile range at

https://brainly.com/question/15696302

#SPJ1

Answer:

Which of the following is a solution of the equation 2x + 3y = 6 ? * *1 pointa. (1 , 2 )b. ( 1 , 1 )c. ( -3 , 4 )d. ( 3 , 1 ). the answer is question b

Answer:I don’t know I just need points

Step-by-step explanation:

Solve one of the equations for one of the variables as the first step in substitution method.

In order to write one of the equations as x = or y =, we must first determine which variable in the two equations is the simplest to solve for. The other equation will then have either the x or the y replaced appropriately. The outcome will be a single-unknown equation that we can solve. Isolating a variable whose coefficient is 1 or -1 is useful.

Step 1: Solve one of the equations for one of the variables.

Step 2: Enter the expression as a replacement in the remaining equation. The outcome will be a single-variable linear equation that can be solved.

Step 3: Resolve the last equation.

Step 4: To find the value of the other variable, substitute the result into the other equation.

Step 5: The intersection of the two equations, which represents the coordinates of the ordered pair, is the system's solution.

To learn more about substitution method link is here

brainly.com/question/14619835

#SPJ4

The law of cosines serves as a generalization of the Pythagorean formula, which is applicable to all triangles.

Compare the total of the squares on the two smaller sides to the square on the largest side to determine if the triangle is acute, right, or obtuse. Because of the larger sum, the triangle is sharp.

The Pythagorean formula applies to all triangles and is generalised by the law of cosines. The square of one side of the triangle, c², is said to be equal to a² + b², the sum of the squares of the other two sides, minus 2ab cos C, which is the product of the two squares times the cosine of the opposite angle.

Three closed sides make up a triangle. The Pythagoras theorem and the Heron's formula are two significant formulas that pertain to triangles.

To learn more about triangles refer to:

https://brainly.com/question/1058720

#SPJ4

Answer:

Step-by-step explanation:

(3^1)^4

By using the numbers 3, 1, and 4, you are able to get the answer 81

The number 437.184 can be rounded or estimated as  437 if estimated to the tenths.

In mathematics, estimation implies approximating or rounding numbers. This is commonly used to make calculations simpler or to apply maths to real life. For example, 8 oranges divided by 6 people is equal to 1.33; however as calculating 0.33 when cutting oranges might be quite difficult it is better to estimate it as 1.

The general rule is that if a number is above five you should estimate it to the next unit, but if the number is below 5 you should estimate it to 0. Here is an example:

Learn more about numbers in: https://brainly.com/question/17429689

#SPJ1

Christine has 262 pieces of bread, 336 lice of patrami, and 302 lice of cheese, so she can make a maximum of 131 hero sandwiches if each sandwich consist of two pieces of bread, two slices of patrami, and two slices of cheese.

Therefore the answer is 131.

Christine is making hero sandwiches, each of which consist of two pieces of bread, two slices of patrami, and two slices of cheese. To find the greatest number of heroes he can make, we need to divide the total number of each ingredient by the number of that ingredient used in each sandwich.

The number of heroes Christine can make with the bread is:

262 pieces of bread / 2 pieces of bread per hero = 131 heroes

The number of heroes Christine can make with the patrami is:

336 slices of patrami / 2 slices of patrami per hero = 168 heroes

The number of heroes Christine can make with the cheese is:

302 slices of cheese / 2 slices of cheese per hero = 151 heroes

To find the greatest number of heroes Christine can make, we need to take the smallest of these three values, which is 131 heroes. This means that Christine can make a maximum of 131 heroes with the ingredients he has on hand.

To know more on highest common factor

https://brainly.com/question/802960

#SPJ4

The missing values from Ariel’s bank account are;

3. -$155.15

4. -$223.75

5. -$1.40

6. -$7.2

Week 1:

Account balance = $360.00

Change from previous week = nil (this is because the previous week account balance is not given)

Week 2:

Account balance = $337.50

Change from previous week = $337.50 - $337.50

= -$22.50

Week 3:

Account balance = $182.35

Change from previous week = $182.35 - $337.50

= -$155.15

Week 4:

Account balance = -$41.40

Change from previous week = -$41.40 - $182.35

= -$223.75

Week 5:

Account balance = -$1.40

Change from previous week = -$1.40 - (-$41.40)

= $40.00

Week 6:

Account balance = -$5.80

Change from previous week = -$5.80 - (-$1.40)

= -$7.2

Therefore, the change in Ariel's bank account from previous week can be calculated by finding the difference between the present and previous week account balance.

Read more on account balance:

https://brainly.com/question/15525383

#SPJ1

Volume of a cube = a3

here a = 4

  then = a3 = 4^3 =64

The rectangular prism shows 12 cubes: 3 rows and 4 columns.

The volume of a prism is the area of the base times the height,

The volume of a rectangular prism is the length times width times height,

The volume of a cube is the length of one side cubed,

Volume of a rectangular prism = (length x width x height) cubic units.

V = (l x w x h) cubic units

To learn more about rectangular prism refer to:

brainly.com/question/30231571

#SPJ1

We can see here that the text features that could support the ideas in the passage are :

Definition: "A satellite is an object that orbits a planet."

Examples: "Manmade satellites orbit Earth and serve many purposes. Satellites send phone calls, radio signals, and television signals from one place to another. NASA uses satellites to take pictures."

Cause and effect: "The pictures help scientists learn about conditions on Earth and other planets."

A text is a written or spoken piece of information or communication. It can take many forms such as a book, article, poem, speech, or conversation. It can contain a variety of content such as stories, information, instructions, or arguments. The purpose of a text can vary widely depending on the context in which it is created, including entertainment, education, persuasion, or documentation.

We see here that the text features likely to be seen in the passage has been identified as seen above.

Learn more about text on https://brainly.com/question/1119015

#SPJ1

Then the two solutions are: x = (4 + 5.66) / 8 = 11.2075  and x = (4 - 5.66) / 8 = -0.2075

The sine approximation formula of Bhaskara I is a rational equation in one variable for computing the approximations of the trigonometric sines found by Bhaskara I (c. 600–c. 680), an Indian mathematician of the seventh century.

Indian astronomer and mathematician Bhaskara II lived in the 12th century. He created a number of the same foundations and findings that are entirely attributable to Europeans and are still very helpful in modern science and forecasts, such as a basic form of calculus.

Here we have the equation:

y = 4 × x² - 4 × x - 1

And the graph should be available (you can see it below this answer)

Now, we're seeking answers to:

4 × x²- 4 × x - 1 = 0

The two x values at which the graph of our function intersects the y = 0 line, or the x-axis, will be these solutions.

The next step is to identify the two x values where our graph crosses the x-axis.

We can estimate the solutions in the graph as follows:

x = -0.2

x = 1.2

The Bhaskara's equation can be used to determine the precise solutions, and we will discover that the solutions are provided by:

[tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4 * 4 *(-1)}}{2 * 4}=\frac{4+-\sqrt{32}}{8}=\frac{4+-5.66}{8}[/tex]

Then the two solutions are:

x = (4 + 5.66) / 8 = 11.2075

x = (4 - 5.66) / 8 = -0.2075

To learn more about Bhaskara's equation, refer to:

https://brainly.com/question/24334139

#SPJ1

Answer:

400 m³

Step-by-step explanation:

The tent consists of a cylinder at the bottom and the roof of the tent is a cone

The height of the cone = 2h - h = h which is the same as the height of the cylindrical part

Volume of a cylinder = πr²h where r = radius, h- height

We are given this volume = 300 m³

The volume of a cone is (1/3)πr²h

If the heights and radius are the same, the volume of the cone is 1/3 the volume of the cylinder

Volume of conical part of tent = 1/3 x volume of cylindrical part

= 1/3 x 300 = 100 m³

Total volume of the tent and therefore the volume of air

= 300 + 100 = 400 m³

Case 1: The linear equations has infinite solutions.

Case 2: The linear equations has no solution.

In this problem we find two cases of systems of two linear equations with two variables, which are described by a system of the form:

a · x + b · y = c

d · x + e · y = f

Where:

The solution of this kind of systems can be found graphically on Cartesian plane, whose procedure is described briefly:

Now we proceed to find the solution for each case:

Case 1

Line 1: y = 0.5 · x + 1

y-Intercept

y = 0.5 · 0 + 1

y = 1

(x, y) = (0, 1)

x-Intercept

0 = 0.5 · x + 1

0.5 · x = - 1

x = - 2

(x, y) = (- 2, 0)

Line 2: - 2 · x + 4 · y =  4

y-Intercept

- 2 · 0 + 4 · y = 4

4 · y = 4

y = 1

(x, y) = (0, 1)

x-Intercept

- 2 · x + 4 · 0 = 4

- 2 · x = 4

x = - 2

(x, y) = (- 2, 0)

Since the two lines have the same intercepts, then there are infinite solutions.

Case 2

Line 1: y = - x - 3

y-Intercept

y = - 0 - 3

y = - 3

(x, y) = (0, - 3)

x-Intercept

0 = - x - 3

x = - 3

(x, y) = (- 3, 0)

Line 2: y + x = 2

y-Intercept

y + 0 = 2

y = 2

(x, y) = (0, 2)

x-Intercept

0 + x = 2

x = 2

(x, y) = (2, 0)

The system of linear equations has no solution as both lines are parallel.

To learn more on systems of linear equations: https://brainly.com/question/20379472?referrer=searchResults

#SPJ1

Answer:  In triangle AGH, we can use the Law of Sines. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

so, a/sin(A) = b/sin(B) = c/sin(C) = 2R where R is the circumradius of the triangle.

Given, g = 9.6 inches, m/I = 80° and m/G = 15°

AG = h, angle A = (180 - 80) = 100, angle G = (180-15) = 165

So we can use the Law of Sines to find the h,

h/sin(100) = g/sin(165) = 9.6 / sin(165) = 9.6 / sin(165) = 9.6 / 0.9659 = 9.98 inch.

Rounded to the nearest 10th of an inch, h = 9.98 inches.

Step-by-step explanation:

Answer: 85

Step-by-step explanation:

Value of f[g(x-1)] is 2x^2-4x+9. The solution has been obtained by applying the multiplication operation on functions and substituting the functions.

Just like we add, subtract, multiply and divide the terms in a function, the functions can also be added, subtracted, multiplied or divided in a similar way.

Suppose there are two functions f(x) and g(x). The notations are as follows:

For Addition: (f+g)(x) = f(x) + g(x)

For Subtraction: (f-g)(x) = f(x) - g(x)

For Multiplication: (f×g)(x) = f(x) × g(x)

For Division: (f/g)(x) = (f(x))/(g(x))

When we substitute one function into another, a function is generated in which one function is considered to be a part of another function.

Now, f(g) = 2g-3

We are given g = x^2+5

So, g(x-1) = (x-1)^2+5

Substituting the value of g(x-1) in f(g), we get

f(g(x-1)) = 2((x-1)^2+5)-3

= 2x^2-4x+9

Hence, the value of f[g(x-1)] is 2x^2-4x+9.

To know more about operations on functions visit:

brainly.com/question/27063976

#SPJ1

The methods of solving a quadratic equation are: Factoring, Quadratic Formula, Completing the Square, and Graphing.

There are several methods for solving a quadratic equation of the form ax² + bx + c = 0. The most common methods are:

1. Factoring: Factor the equation into the form (ax + b)(cx + d) = 0 and set each factor equal to zero. This will give you the solutions for x.

2. Quadratic Formula: Use the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a to find the solutions for x.

3. Completing the Square: Rewrite the equation in the form a(x + b/2a)^2 + c = 0 and then solve for x.

4. Graphing: Plot the equation on a coordinate plane and find the x-coordinates of the points where the graph crosses the x-axis (the solutions for x).

It is important to note that not all the methods are always applicable for all types of the quadratic equations.

Learn more about quadratic equation here: https://brainly.com/question/1214333

#SPJ4

The correlation coefficient r = +0.9 indicates a strong positive correlation as a strong positive (negative) linear relationship is shown by values between 0.7 and 1.0 (or -0.7 and -1.0).

What is corelation coefficient?

A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.

The following points are the accepted guidelines for interpreting the correlation coefficient  -

1. Zero means there is no linear relationship.

2. A perfect positive linear relationship, or one with a value of 1, means that as one variable rises in value, the other variable rises in value according to an exact linear law.

3. A perfect negative linear relationship is represented by a value of 1; as one variable's values rise, the other variable's values fall according to an exact linear law.

4. Values between 0 and 0.3 (0 and -0.3) denote a wobbly linear rule with a weak positive (negative) linear relationship.

5. A fuzzy-firm linear rule indicates a somewhat positive (negative) linear relationship for values between 0.3 and 0.7 (-0.3 and -0.7).

6. A strong positive (negative) linear relationship is shown by values between 0.7 and 1.0 (or 0.7 and 1.0) by a strict linear rule.

Therefore,  r = +0.9 indicates a strong positive correlation.

To learn more about corelation coefficient from the given link

https://brainly.com/question/4219149

#SPJ1

Answer:

y = 15.4

Step-by-step explanation:

the outer and inner triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{y}{11}[/tex] = [tex]\frac{8+3.2}{8}[/tex] = [tex]\frac{11.2}{8}[/tex] ( cross- multiply )

8y = 11 × 11.2 = 123.2 ( divide both sides by 8 )

y = 15.4

There are 180 degrees of longitude, which is divided into 360 lines of longitude (meridians).

Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is measured in degrees, with a full circle consisting of 360 degrees. The Prime Meridian is located at 0 degrees longitude, and each degree is further divided into 60 minutes and each minute is divided into 60 seconds. Therefore, there are 180 degrees of longitude east of the Prime Meridian and 180 degrees of longitude west of the Prime Meridian.

There are 180 degrees of longitude, which is divided into 360 lines of longitude (meridians).

learn more about longitude here

https://brainly.com/question/4749704

#SPJ4

So, 175 children's tickets were sold, and 100 adult tickets were sold.

We can start solving the problem by using a system of equations. Let x be the number of children's tickets and y be the number of adult tickets. We know that:

x + y = 275 (the total number of tickets sold)

3x + 5y = 1025 (the total value of the tickets sold)

To find the number of each type of ticket sold, we can use the first equation to express one of the variables in terms of the other, and then substitute that into the second equation. For example, we can express y in terms of x:

y = 275 - x

Now we can substitute this into the second equation and solve for x:

3x + 5(275 - x) = 1025

3x + 1375 - 5x = 1025

-2x = -350

x = 175

So, 175 children's tickets were sold, and 275 - 175 = 100 adult tickets were sold.

To learn more about system of equations

visit; brainly.com/question/12895249

#SPJ4

Option B is the correct answer. The best approximation of the relative maximum of the polynomial function  graphed below is (-3.6,17)

The relative maximum is in the peak on the left side.

A function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, or cubic equation.

The general Polynomial Formula is

[tex]P(x)=a_{n} x^n+a_{n-1} x^n^-1+..........+a_{2} x^2+a_{1} x^1+a_{0}[/tex]

where all the powers are non-negative integers.

And, a0,a1,………,an ∈ R

The graph of function depends upon its degree, and having one variable which has the largest exponent is called a degree of the polynomial.

There are some Graphs of Higher Degree Polynomial Functions:

The Standard form is:

P(x) = an xn + an-1 xn-1+.……….…+ a0

To know more about the Polynomial function:

https://brainly.com/question/7693326

#SPJ4

By addition, $1,850 is the right response. Mrs. Jones' company spent $1,850 on business expenditures in March, including $480 on raw materials, $1,200 on labour, and $170 on other expenses.

The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.

Mrs. Jones's business spent $480 on raw materials

Mrs. Jones' company spent $1,850 on business expenditures in March,

$1,200 on labour

$170 on other expenses.

by addition

Total = 1200+480+170 = $1850

To know more about addition visit:

https://brainly.com/question/29560851

#SPJ1

Round shape of the lightbulb gives advantage over any other shape for the future development of the bulb.

The round shape of the bulb scattered the light towards outside more evenly. The light source inside the lightbulb, like filament, LED, etc., kept at the focus of the round shaped bulb. round shape bulb gives the lensing(concave lens) effect to the glass that outwardly bends the light so the light cannot focus in a particular direction, but rather scattered more evenly in all directions. Any other shape like, rectangular, prismatic, or cubic shapes do not allow even scattering of light. These shapes bends the light non-uniformly through corners and walls.  

To know more about lightbulb, here

https://brainly.com/question/14489845

#SPJ4

A unit's marginal cost, as used in economics, is the difference in total production costs that results from creating or manufacturing an extra unit.  To determine the marginal cost, divide the changes through production expenses even by quantity that has changed.

Marginal revenues are calculated by such a corporation by dividing the change in the total revenue by the total change in output quantity.

The additional cost to create a new item is known as the marginal cost. Say, for instance, that it costs $100 to produce 100 vehicle tyres. It would cost $80 to produce one extra tyre. The cost to produce one more unit of an item or service is therefore known as the marginal cost.

Marginal cost is equal to the difference between two costs (Change in quantity)

The volume of output either increases or decreases, which affects quantity.

To know more about marginal cost refer to:

https://brainly.com/question/12231343

#SPJ4

In economics, a unit's marginal cost is the difference in overall production costs that arise from producing or constructing an additional unit. Divide the changes in production costs even by the altered quantity to get the marginal cost.

Marginal revenues are computed by dividing the change in total income by the total variation in the output quantities.

The marginal cost is the additional expense incurred while producing a new good. Consider the example of 100 car tires costing $100 to create. One additional tire would cost $80 to create. The marginal cost is consequently the cost incurred when producing an additional unit of a good or service.

The difference between two costs (Change in quantity) is known as the marginal cost. Quantity is impacted by either an increase or decrease in output volume.

To know more about marginal cost refer to:

brainly.com/question/12231343

#SPJ4