Cameron determined that an ordered pair made a true statement when substituted into one of the equations but not in the other equation. Is her ordered pair a solution to the system of equations? If not, explain.

Due tο the 90 degree angle created by the axes at the origin and the measurements at point p, the system is knοwn as being rectangular.

What is Cartesian coordinate system?

A Cartesian coordinate system in a plane is a system of cοordinates that uniquely identifies each pοint by a pair of numerical coordinates. The coordinates (Xp, Yp) shοw where point p is in relation to the origin. Because the angle created by the axes at the οrigin and the angle created by the measurements at point p are bοth 90 degrees, the system is referred tο as rectangular. Thus, the measurement has sides of Xp and Yp, fοrming a rectangle.

These numerical coοrdinates are the signed distances from two fixed perpendicular οriented lines to the point, measured in the same unit of length.

In any case, for any convex polygon (including rectangle) the test is very simple: check each edge of the polygοn, assuming each edge is oriented in cοunterclockwise direction, and test whether the point lies tο the left of the edge (in the left-hand half-plane). If all edges pass the test - the pοint is inside. If at least οne fails - the point is outside.

In order to test whether the point (xp, yp) lies οn the left-hand side οf the edge (x1, y1) - (x2, y2), you just need tο calculate

D = (x2 - x1) * (yp - y1) - (xp - x1) * (y2 - y1)

If D > ∅, the pοint is on the left-hand side. If D < ∅, the point is on the right-hand side. If D = ∅, the pοint is on the line.

The previous versiοn of this answer described a seemingly different version οf left-hand side test . But it can be easily shοwn that it calculates the same value.

In order to test whether the point (xp, yp) liesοn the left-hand side of the edge (x1, y1) - (x2, y2), yοu need to build the line equation for the line containing the edge. The equatiοn is as follows

A × x + B × y + C = ∅

where

A = -(y2 - y1)

B = x2 - x1

C = -(A * x1 + B * y1)

Now all you need to dο is to calculate

D = A * xp + B * yp + C

If D > ∅, the pοint is on the left-hand side. If D < ∅, the point is on the right-hand side. If D = ∅, the point is on the line.

However, this test, again, wοrks for any convex polygon, meaning that it might be too generic fοr a rectangle. A rectangle might allow a simpler test... For example, in a rectangle (οr in any other parallelogram) the values of A and B have the same magnitude but different signs for opposing (i.e. parallel) edges, which can be explοited to simplify the test.

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Answer:

Step-by-step explanation:

You want to know the volume of a cylindrical container 6 inches in diameter and 4.5 inches high, and you want to know how many times larger this volume is than if the diameter were 4 inches.

The volume of a cylinder is given by the formula ...

  V = πr²h

where r is half the diameter, and h is the height.

The volume of your large popcorn container is ...

  V = 3.14·(3 in)²·(4.5 in) = 127.17 in³

The volume of the large container is 127.17 in³.

For a given height, the volume ratio is the square of the ratio of diameters. That ratio is given as 3/2, so the volume ratio is ...

  (3/2)² = 9/4 = 2.25

The large container is 2.25 times the volume of the small container.

cos⁻¹  ( 7/23) is the measure of the largest angle.

What is known as a triangle?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.

                            The triangle's three angles add up to a total of 180 degrees.

  The lengths are given as a = 725 feet, b = 650 feet, and c = 575 feet.

Since, we know the fact that angle opposite to largest side is greatest. Hence, the largest angle would be opposite to side a.

Now, use the law of cosine

          cosA = b² + c² - a²/2bc

On substituting the values, we get

      cosA = (650)² + ( 575 )² - ( 725)²/2*650*575

                = 422500 + 330625 - 525625/747500

                 =  227500/747500

                 =  7/23

           A =   cos⁻¹  ( 7/23)

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There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.

There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation. This can be determined by counting the number of possible combinations of digits that can be formed with the numbers 0-9. Since there are five digits in a number less than 100,000, the total number of combinations is 10^5 (10 to the power of 5). Of these combinations, 1/10th will contain at least one "1" as there are 10 possible ways to include a "1" in the five-digit number. Thus, 10^5/10 = 9,999. This means that there are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.

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[tex]6m - 2( - 3m + 8)\\ Multiplying :\ each \\ term \\ - 18m + 48m + 6m - 16 \\ - 18m + 54m - 16 \\ 36m - 16 \\ 2(18m - 8)[/tex]

Answer: The slope is 2.

Step-by-step explanation:

We can use this formula to help us solve:

                  [tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Given:

      [tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Substitute values and simplify to solve:

      [tex]\displaystyle \frac{6--6}{2--4}=\frac{6+6}{2+4}=\frac{12}{6} =2[/tex]

Answer:

The slope is 2

Step-by-step explanation:

The formula for slope is y2-y1/x2-x1

So just fill out the points and do the calculations.

Lebesgue outer measure in this instance is a complete extension of Lebesgue measure that meets all other criteria.

The translation invariant is the Lebesgue measure, and the length of the interval I is the same for that measure when it is on the interval I. The Lebesgue measure of E, for instance, is given by  λ(E) = l if E is any collection of real numbers (E).

As with a single point or a countable number of points, every set that is a finite collection of points has a Lebesgue measure of zero. The measure of finite and countable unions of disjoint sets has the property of being equal to the total of the measures.

An interval's length is its Lebesgue value. The formal foundation for probability theory is measure theory.

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Using multiplication, In Alfred's store, there are 75 bags of potato chips.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication.

The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.

In Cecilia's store, there are five times fewer bags of potato chips than there are in Alfred's. This indicates that Alfred's has five times as many bags as Cecilia's does. We must multiply to determine how many bags there are in Alfred's store:

15 x 5 = 75

In Alfred's store, there are 75 bags of potato chips.

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Decisions at this level are typically strategic in nature and involve long-term planning and goal setting. These decisions may involve large amount investments of resources and have a significant impact on the organization's future.

Decisions at this level are typically strategic in nature and involve long-term planning and goal setting. These decisions may involve large investments of resources and have a significant impact on the organization's future. Examples of decisions at this level include setting the overall strategy, developing new products and services, entering new markets, and deciding on organizational structure. Due to the nature of these decisions, they require extensive data analysis and research. It is important for decision makers at this level to have knowledge about the industry, the marketplace, and the competitive environment in order to make informed decisions. Additionally, since these decisions have a long-term impact, it is important to consider the potential risks and opportunities associated with them. Furthermore, the decisions made at this level must align with the overall mission and vision of the organization. As such, these decisions must be made with careful consideration, as they can have far-reaching implications for the entire organization.

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If the order of the choices is relevant ,72 times can this be done.

Suppose we want to choose 6 colors, without replacement , from 8 distinct colors. If the order of the choices is relevant

The permutation of arranging 'r' things from a collection of 'n' objects into an order or sequence is known as nPr in mathematics. Permutation is calculated using the formula nPr = (n!) / (n-r)! N permutations = nPr = n!/ (n-r)! Combination, nCr, is the selection of r items from a collection of n objects such that the order of the objects does not matter.

N permutations are as follows: 9P6 = 8!/(8-6)! = 8*7*6*5*4 = 6,720.

N combinations = nCr = n!/((n-r)!r!) is the response to b.

N combinations = = 8C6 = = 8!/((8-6)!6!) = (8*7*6)/(2*1) = 72

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We cannot the time period of 25 min using two ropes that when lit burn in one hour. Hence, option C is the correct answer.

This problem is an example of a mathematical puzzle. In order to measure a time period of 30 min, all we need to do is burn one rope from both ends. Since it takes 60 minutes for the rope to burn when lit from one end, it will take half that time i.e., 30 min to burn when lit from both ends.

We can also measure a time period of 35 min if we burn one rope from both ends and the other a bit differently. If we burn a rope from both ends, it will take 30 mins. As for the extra 5 mins, we can take the other rope and first burn it from both ends and then burn it from the middle again. That makes 2 separate ropes and thus the burning time is 15 min. We can then again burn one of these from the middle and wait until one of them completely burns out. This will give us a time period of 35 minutes.

As for 50 minutes, we can use the same method as above for burning one rope completely from both ends and the other from the ends and the middle. We can't really burn the ropes in a way that will give us the time period of 25 min so option C is the correct answer.

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Let w be the width of the rectangle. Then, the length is w + 4. The perimeter is 2(w + 4) + 2w = 56, so 2w + 8 = 56, and w = 24. The length is 28.

The given information is that the length of the rectangle is 4 inches longer than its width, and the perimeter of the rectangle is 56 inches. To find the length and width of the rectangle, we need to solve a system of equations. First, let w be the width of the rectangle, so that the length of the rectangle is w + 4. To find the perimeter of the rectangle, we can use the formula 2(w + 4) + 2w = 56. Substituting in w for the width, we get 2w + 8 = 56. Solving this equation for w, we get w = 24. The length of the rectangle is w + 4, so the length is 28. Therefore, the width of the rectangle is 24 inches and the length is 28 inches.

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The angle for each animal is;

Horse - 40 degrees

Goats - 120 degrees

Sheep - 20 degrees

Cows - 180 degrees

We can see that we want to plot the data that we have on the circle graph and each of the values is going to occupy a given part of the sector and would subtend an angle. We are to obtain the angle that is subtended by each value.

We have;

Total number of farm animals = 4 + 12 + 2 + 18 = 36 animals

Angle for horses = 4/36 * 360 = 40 degrees

Angle for goats = 12/36 * 360 = 120 degrees

Angle for sheep = 2/36 * 360 = 20 degrees

Angle for cows = 18/36 * 360 = 180 degrees

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Missing parts

Ted’s farm has 4 horses, 12 goats, 2 sheep, and 18 cows. Find the angle measure of the sector of a circle graph that represents each animal. Enter the correct answers in the boxes.

The graph of a system of two equations is a pair of lines in the plane for the two variables (x and y).

Simple sets of two or more linear equations make up a system of linear equations. A system of two equations has a graph that is a pair of lines in the plane for two variables (x and y).

Equations with the same variables are grouped together as systems of equations. The only difference is that you're using inequalities as opposed to equations when working with a system of inequalities. To resolve such a system, you must identify the values of the variables that will cause each inequality to be true simultaneously.

The first equation:

[tex]$y=\frac{1}{2} x+3$$[/tex]

[tex]$5 \stackrel{?}{=} \frac{1}{2}(4)+3 \quad$[/tex]

Plug in x = 4 and y = 5

5 = 5

The second equation:

y = x + 1

[tex]$5 \stackrel{?}{=} 4+1 \quad$[/tex] Plug in x = 4 and y = 5

5 = 5

(4,5) is indeed a solution.

Therefore, the correct answer is option b) (- 2.75, 0) and (2.75, 0).

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The number of groups of one third in 9 is 27

The problem requires the use of division

To determine the number of groups of 1/3 in 9, we can divide 9 by 1/3:

= 9 / (1/3)

= 9 * 3

= 27

Therefore, there are 27 groups of 1/3 in 9.

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Answer: -12k-21

Step-by-step explanation:

you must distribute the -3

[tex]\it AC=2\cdot EC=2\cdot6=12[/tex]

Answer:

81

Step-by-step explanation:

The triangle formed is an isosceles triangle since two sides of the triangle are equal .

The point on the shoreline is the point of tangency between the shoreline and the circle centered at the boat with a radius equal to the distance between the boat and the shoreline. The angle from the boat to that point is equal to the angle of the central angle of the circle whose radius is equal to the distance between the boat and the shoreline.

Let the radius of the circle be r and the angle from the boat to the point on the shoreline be θ. Then the formula for the distance between the boat and the shoreline is:

r = θ × (2π/360)

To calculate the distance traveled by the boat, we need to use the formula for the circumference of a circle:

C = 2πr

Substituting the above formula for r into the formula for the circumference of a circle, we get:

C = 2π(θ × (2π/360))

Therefore, the distance traveled by the boat is:

C = (2π)2 × θ/360

The triangle formed is an isosceles triangle since two sides of the triangle are equal (the radius of the circle and the distance between the boat and the shoreline).

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The total length needed in inches for the 12 strips of metal is 370¹/₂ inches.

The total length for the 12 strips of metal is determined using a combination of the mathematical operation of multiplication and unit conversion.

The 2 feet are converted to 24 inches (2 x 12) using unit conversion and multiplication.

The total length is determined by multiplication, involving the multiplicand and the multiplier, which results in a product called the result.

The number of strips of metal = 12

The length of each strip = 2 ft and 6⁷/₈ inches = 30⁷/₈ inches

1 foot = 12 inches

The total length = 370¹/₂ inches (30⁷/₈ inches x 12)

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Using the associative property of multiplication the missing value of (x × 8) × 2 =  4 × (2 × 8) is 4.

The associative property of multiplication tells us how we group factors that does not alter the result of the multiplication. Therefore, the associative property of multiplication can be represented as follows:

a x (b x c) = (a x b) x c

where

Therefore, let's use the associative property of multiplication to solve the following.

(x × 8) × 2 =  4 × (2 × 8)

Hence, using the rule, of associative property of multiplication, a x (b x c) = (a x b) x c, the missing variable is 4.

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Answer:

Bigger number: 20

Smaller number: 13

Step-by-step explanation:

Let smaller number = x

Bigger number. = x + 7

From the question; 2x + 3(x + 7) = 86

2x + 3x + 21 = 86

5x + 21 = 86

5x = 86 - 21

5x = 65

x = 13

Therefore the smaller number is 13, and the bigger number is 13 + 7 = 20

The coefficient of static friction is a dimensionless value that represents the ratio of the maximum static friction force to the normal force. It is used to determine the maximum angle at which an object can be inclined on a surface without slipping. The coefficient of static friction between the right bar and the surface at point A is not given in the information provided.

To determine the largest angles at which the right bar can be inclined without slipping on the surface at point A, one would need to know the coefficient of static friction between the bar and the surface, as well as the weight of the bar and the normal force acting on it. The coefficient of static friction multiplied by the normal force must be greater than or equal to the weight of the bar in order for it to remain in static equilibrium.

It is also worth mentioning that the coefficient of static friction varies depending on the materials of the two surfaces in contact and the normal force acting on it. The coefficient of static friction can be measured experimentally and is usually provided in the material properties of the surfaces.

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Answer: To find the inverse of a function, we first need to make sure that the function is one-to-one, meaning that no two different input values map to the same output value.

If the function B is one-to-one, we can find the inverse by switching the x and y values, and then solving for y.

y = B^-1(x)

We can then use algebraic manipulation to solve for y.

For example, if B(x) = 2x + 1, we can find the inverse by switching x and y:

x = 2y + 1

Solving for y:

y = (x - 1)/2

So the inverse function of B(x) = 2x + 1 is B^-1(x) = (x - 1)/2

Please note that if the function B is not one-to-one, it will not have an inverse.

Step-by-step explanation:

According to the report, 80% of those who purchased new cars received loans, compared to 60% of those who purchased older cars.

The population size estimate is calculated by dividing the total number of people getting a service or the total number of unique items delivered (M) by the percentage of people reporting receiving the service or item in a representative survey (P).

Given a car dealership wants to conduct a survey of 100 people who bought ​a new or used car at the dealership in the last three months. ​

number of people          new car       old car     received Loan       No loan

   2,000                             yes                No           1600                    400

      500                            No                  Yes           300                    200

Percentages of people who received Loans bought new cars:

Percentage = 2000-400 / 2000

Percentage = 1600/2000

Percentage = 80%

Percentages of people who received Loans bought used cars:

Percentage = 300 * 100 / 500

Percentage = 3/5 * 100

Percentage = 60%

Therefore, According to the survey, 60% of the people Who bought used cars got loans while 80% of people who bought new cars gets loan.

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Answer:42.5

Step-by-step explanation:

A linear equation can be used to model this situation, where the volume of water in the tank (V) is equal to the initial volume plus the rate of flow multiplied by the number of minutes (t).

V = 55 + 8t

This equation can be used to find the volume of the water in the tank at a specific time. To find the volume of the water in the tank 25 minutes after Baxter begins filling it, we can substitute 25 for t in the equation:

V = 55 + 8(25) = 55 + 200 = 255 gallons

To find how many minutes it will take for Baxter to fill the tank if the maximum volume of water is 395 gallons, we can use the equation to solve for t.

395 = 55 + 8t

Subtract 55 from both sides:

340 = 8t

Divide both sides by 8:

t = 42.5

So, it will take 42.5 minutes for Baxter to fill the tank with a maximum volume of 395 gallons.

A linear equation can be used to model a situation where a quantity is changing at a constant rate.

Let V be the volume of water in the tank at time t in minutes.

The rate of change of the volume of water is 8 gallons per minute, so we can write the equation as:

V = 55 + 8t

This equation tells us that the volume of water in the tank is 55 gallons when t = 0 (at the start of filling the tank) and it increases by 8 gallons for every minute after that.

To find the volume of water in the tank 25 minutes after Baxter starts filling it, we can plug in t = 25 into the equation:

V = 55 + 8(25)

V = 55 + 200

V = 255 gallons

To find how many minutes it will take to fill the tank to the maximum volume of 395 gallons, we can use the equation and solve for t:

V = 55 + 8t

395 = 55 + 8t

340 = 8t

t = 340/8

t = 42.5 minutes

So it will take 42.5 minutes to fill the tank to the maximum volume of 395 gallons.

The result is between 1 and 9, which is assigned to the variable dice.

To generate a random number between 1 and 9, inclusive, we can use the formula: (Math.random() * (9 - 1 + 1)) + 1. This formula randomly generates a number between 0 and 1, and then multiplies it by the range (9 - 1 + 1) to give us a result between 0 and 8. We then add 1 to this result to ensure that the final number is between 1 and 9.

To assign this number to the variable dice, we can use the following statement:

var dice = Math.floor((Math.random() * (9 - 1 + 1)) + 1);

Math.random() generates a random number between 0 and 1, which is then multiplied by the range (9 - 1 + 1) to give us a result between 0 and 8. Math.floor rounds this number down to the nearest whole number. We then add 1 to ensure that the result is between 1 and 9, which is assigned to the variable dice.

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