Chapter 4 Lesson 3 Solving System of Equations Using Elimination

The Systematic Approach algorithm is a problem-solving methodology that is widely used in many different fields, such as engineering, business, and science.

It is a structured and systematic process that involves identifying a problem, analyzing it, generating possible solutions, evaluating these solutions, and selecting the best one. The algorithm is also known as the "systems engineering process" or "systems analysis and design."

The algorithm is typically divided into several phases, including:

Problem identification: This involves defining the problem, its boundaries, and its scope. This step also involves identifying the objectives and constraints of the problem. Analysis: This step involves gathering data and information related to the problem, and identifying the root cause of the problem. This may involve conducting surveys, interviews, or experiments. Design: In this step, potential solutions are generated, and a conceptual design is created. The design should be flexible enough to allow for the incorporation of new information and changes. Evaluation: The potential solutions are evaluated based on predetermined criteria, and the best solution is selected. Implementation: The selected solution is implemented and monitored to ensure it is working effectively. Any necessary modifications or adjustments are made during this phase.

The Systematic Approach algorithm is a powerful tool for problem-solving as it provides a structured, step-by-step approach to analyzing and solving complex problems. It also allows for a thorough understanding of the problem and its potential solutions, as well as the ability to evaluate and select the best solution based on predefined criteria.

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As of 22/02/2023, the value of 1 HERO (cryptocurrency) is $0.01 USD. This means that if you have 1 HERO, it can be exchanged for $0.01 USD.

The value of HERO, like most cryptocurrencies, can fluctuate rapidly due to market demand and supply. As a result, the value of HERO can change significantly over short periods of time. It's important to keep this in mind when buying or investing in cryptocurrencies, as the value can both rise and fall quickly. Investors in cryptocurrencies should do their research and consider the risks associated with investing in a volatile and relatively new asset class.

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Based on theoretical probabilities, the best estimate of the total number of times Jon tossed the cube would be 60 times. The probability of rolling a "4" on a standard die is 1/6. If Jon got "4" on 5 of the tosses, then the total number of tosses would be 5/ (1/6) = 30 tosses. To find the best estimate of the total number of tosses, it is common to round up to the nearest multiple of 10, which in this case would be 60. Therefore, the best estimate would be 60 times (Option B).

Answer:

The answer is to get it wrong on khan academy the go-to progress report(click on the percent to get to it and find the problem and go to hints and it should show the answer.

Step-by-step explanation:

Answer:

Adrian worked the least amount of time. (False, Precious worked the least amount of time with 0.06 hours)

Step-by-step explanation:

The following statements are true:

Adrian worked longer than Jake in his garden. (Adrian worked 3 times as long as Jake, so Adrian worked 3 hours * 3 = 9 hours)

Precious worked less time in her garden. (Precious worked 2% of the time that Jake worked, which is 2% of 3 hours = 0.06 hours, which is less than both Jake and Adrian)

The following statement is false:

Precious worked more time than Adrian. (As calculated above, Precious worked 0.06 hours, which is less than Adrian's 9 hours)

And finally:

Adrian worked the least amount of time. (False, Precious worked the least amount of time with 0.06 hours)

Answer:

The table represents a linear function because the rate of change is constant or all the points lie on a straight line.

Step-by-step explanation:

From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).

The slope of the line is

The slope of line is . It means the value of y increased by 5 if the value of x increased by 2.

From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.

Since the rate of change (slope) is same for all points, therefore the table represents a linear function.

If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a  linear function.

The probability of a defect units is 0.3174 by calculating the z-score of the greater than and less than value.

When the distribution is normal, we use the z-score formula.

Z = (X - μ)/σ

We have σ = 0.15 and units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.

μ = 10.15 - 0.15 = 9.85 + 0.15 = 10

Now, the probability that a unit is defective.

P(X ≥ 10.15)

1 subtracted by the pvalue of Z when X = 10.15

[tex]Z = \frac{10.15-10}{0.15}[/tex]

Z = 1 has a pvalue of 0.8413

1 - 0.8413 = 0.1587

P(X ≤ 9.85)

[tex]Z = \frac{9.85-10}{0.15}[/tex]

Z = -1  has a pvalue of 0.1587

P = P(X ≥ 10.15) + P(X ≤ 9.85)

P = 0.1587 + 0.1587

P = 0.3174

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The formula D = inv (A) returns the inverse of a symbolic matrix A. The symbol will be [tex]A^{-1}[/tex].

If A is a non-singular square matrix, then [tex]A^{-1}[/tex], often known as the inverse matrix of A, must exist if it is to satisfy the following property:

A[tex]A^{-1}[/tex] =[tex]A^{-1}[/tex]A = I, where I is the identity matrix.

Finding the minors and cofactors of the given matrix's components is one of the most crucial steps in determining its inverse. To comprehend this approach clearly, follow the steps listed below.

The following formula may also be used to find the inverse matrix:

[tex]A^{-1}[/tex]= adj(A)/det (A).

The calculation for the inverted matrix is done.

Hence they are the symbol and methods to find the inverted matrix.

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The amount of money that the mother contributes each month will be $5.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The expression that represents the amount of savings is given as,

Amount of saving = 5x + 40

Where 'x' is the number of months.

The slope is 5 which represents the amount of savings in each month and the y-intercept is 40 which represents the amount already saved.

The amount of money that the mother contributes each month will be $5.

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a) Relationship between corresponding sides: the corresponding sides are parallel and have a ratio of k in length.

b) Relationship between corresponding sides' orientations: The corresponding sides will still be parallel to the original sides.

c) Relationship between corresponding angles:the corresponding angles are congruent.

What do you mean by congruent angles?

Congruent angles are angles that have the same measure or size. In other words, if two angles have the same number of degrees or radians, they are said to be congruent. When we say that two angles are congruent, it means that they are exactly the same shape and size, and they can be superimposed on each other without any rotation or scaling. Congruent angles play an important role in geometry, as they allow us to prove that two figures are similar or congruent.

To apply a dilation with scale factor k centered at the origin, we multiply the coordinates of each vertex by k. So, to find the coordinates of A', B', and C', we will multiply the coordinates of A, B, and C by the scale factor.

a) The relationship between corresponding sides in terms of their lengths:

Let's denote the scale factor by k. The distance between two points (x1, y1) and (x2, y2) is given by the distance formula, which is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

When we multiply each coordinate by k, the distance between the two points is multiplied by k as well. So, if AB has length dAB and A'B' has length dA'B', we have:

dA'B' = k * dAB

Similarly, we can find the relationship between the lengths of BC and B'C', as well as between the lengths of AC and A'C'.

b) The relationship between corresponding sides in terms of their orientations:

The orientation of a line is given by its slope. If two lines have the same slope, they are parallel or collinear. If they have slopes that are negative reciprocals of each other, they are perpendicular. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. So, if the slope of AB is mAB and the slope of A'B' is mA'B', we have:

mA'B' = k * mAB

We can use this to find the relationship between the slopes of BC and B'C', as well as between the slopes of AC and A'C'.

c) The relationship between corresponding angles in terms of their measures:

The measure of an angle is determined by the slope of the line that contains the angle. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. This means that the measure of any angle that includes the origin is unchanged by the dilation. However, the measure of any angle that does not include the origin is multiplied by a factor of k. So, if angle ABC has measure x and angle A'B'C' has measure y, we have:

y = k * x

We can use this to find the relationship between the measures of angles BAC and B'A'C', as well as between the measures of angles CBA and C'B'A'.

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Answer:

below

Step-by-step explanation:

12m=6km

divide both by 6

2m=1km

how many km is equal to 18m?

18m=9km

how many m are equal to 42km?

42km=64m

never gonna give you up, never gonna let you down

Answer:

The width is 3 cm and the length is 9 cm.

Step-by-step explanation:

L --> Length

W --> Width

L = 3W

LW = 27

3W(W) = 27

3W^2 = 27

W^2 = 9

W = 3

L = 3(3) = 9

The height of the roller coaster is 200.11 feet

Method 1

Here, we make use of the cosine rule

So, we have

cos(45) = x/283

So, we have

x = 283 * cos(45)

Evaluate

x = 200.11

Method 2

Here, we make use of the sine rule

The sine can be calculated as

When x + y = 90;

sin(x) = cos(y)

This means that

sin(45) = cos(45)

So, we have

sin(45) = x/283

So, we have

x = 283 * sin(45)

Evaluate

x = 200.11

Hence, the height is 200.11 feet

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Based on the information, the equation can be simplified as follows: 7xy - 2x² - y

To simplify an equation we must carefully observe all the values that make up the equation. Once we identify the values with the same symbols, (x or y) we can group them. According to this procedure we can group the values of x as shown below:

In this case the 2x was added with the 5x to form the 7x. In the case of 2x², it cannot be added with the other values of x because it has an exponent of ².

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Answer:

-4

Step-by-step explanation:

I hate calc nevertheless, factor the top number, cancel out x+2 and then plug in -2. Its simple once you see the pattern

[tex]\frac{x^2 - 4}{x+2} \\\frac{(x+2)(x-2)}{x+2} \\(x-2)\\-2-2\\-4[/tex]

Answer: A quarter is worth $0.25 and a dime is worth $0.10, so the total amount of money Alonso has can be represented by the expression 0.25x + 0.1y. To find one possible solution to the system of inequalities, we need to find the values of x and y that satisfy both the inequality 0.25x + 0.1y ≥ 3.60 and the inequality y ≥ 0.

The inequality 0.25x + 0.1y ≥ 3.60 represents all points (x, y) that are on or above the line 0.25x + 0.1y = 3.60. The inequality y ≥ 0 represents all points (x, y) that are above or on the x-axis. The intersection of these two regions is the solution set of the system of inequalities, which represents all points (x, y) that satisfy both inequalities.

To graph the solution set, we can start by plotting the line 0.25x + 0.1y = 3.60 and shading the region above the line. Then, we can plot the x-axis and shade the region above the x-axis. The intersection of the two shaded regions is the solution set.

One possible solution to the system of inequalities is the point (14, 4). This means that Alonso has 14 quarters and 4 dimes, which total $3.60. However, there may be other solutions to the system of inequalities that would also satisfy the conditions.

Step-by-step explanation:

answer: 204!!!

tn = a + (n-1)d

a is the first value

n is the position

d is the difference

t(50) = 8+(50-1)(4)

t(50)= 204

Assuming a Poisson distribution, on the average, 6 cars arrive at the drive-up window of a bank every hour, the probability that no more than 5 cars will arrive in the next half-hour is 0.75.

The Poisson distribution can be used to model the number of events that occur in a fixed interval of time. In this case, the average number of cars arriving at the drive-up window of a bank is 6 cars per hour, so we can use the Poisson distribution to calculate the probability of a certain number of cars arriving in a half-hour interval.

To calculate the probability that no more than 5 cars will arrive in the next half-hour, we can use the cumulative Poisson distribution function, which gives the probability that the number of events is less than or equal to a given value.

The cumulative Poisson distribution function can be calculated using the following formula:

P(X <= x) = Σ P(X = i) for i = 0, 1, 2, ..., x

Where X is the number of cars arriving in a half-hour interval, and x is the given value (in this case, x = 5).

The mean number of cars arriving in a half-hour interval is 3 (6 cars per hour / 2), so the cumulative Poisson distribution function can be calculated as follows:

P(X <= 5) = Σ P(X = i) for i = 0, 1, 2, 3, 4, 5

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

= (e^-3) * (3^0) / 0! + (e^-3) * (3^1) / 1! + (e^-3) * (3^2) / 2! + (e^-3) * (3^3) / 3! + (e^-3) * (3^4) / 4! + (e^-3) * (3^5) / 5!

= 0.0498 + 0.1494 + 0.224 + 0.224 + 0.1494 + 0.0498

= 0.75

Therefore, the probability that no more than 5 cars will arrive in the next half-hour is approximately 0.75, or 75%.

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Mrs. Flips sold 240 large chocolate chips.

Mrs. Flips sold 60 small peanut butter cookies.

In order to write the required expressions that models the situation, we would assign variables to the number of large chocolate chips and the number of small peanut butter cookies, and then translate the word problem into algebraic equation as follows:

Since Mrs. Flips charged $1 for the chocolate chip and 50-cents for the peanut butter cookies and collected $270 total, an expression that models the situation is given by:

x + 0.5y = 270

Additionally, she sold a total of 300 cookies:

x + y = 300

270 - 0.5y + y = 300

0.5y = 30

y = 60 small peanut butter cookies.

x = 270 - 0.5(60)

x = 240 large chocolate chips.

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Answer: a type of equation

Step-by-step explanation:

Based on the information, the integer used will be (10 - 4). The difference is 6.

On a number line, there'll be 6 units between the numbers

To find the difference between two integers by adding the additive inverse, we can follow these steps:

Subtract the smaller integer from the larger one: (larger integer) - (smaller integer).

Take the absolute value of the result to get the distance between the two integers on a number line.

The distance between two integers is the absolute value of the difference, so we do not include the sign in our answer. The answer will always be a non-negative number.

By plotting the two integers on a number line and counting the units between them, we can visualize the distance between them.

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Answer:

A. B is correct

B. A is correct

C. B is correct

Step-by-step explanation:

Area of triangle: A = 1/2bh

A. Area of each triangle: A = 1/2 x 11.5 x 12 = 69

Total surface areas = 4(area of triangle) + area of square = 4(69) + 12^2 = 420

So A is incorrect and B is correct

B. Area of triangle: A = 1/2 x 13.9 x 16 = 111.2

Surface area = 4(area of triangle) = 4(111.2) = 444.8

So A is correct and B is incorrect

C. Area of triangle with base of 10: A = 1/2 x 10 x 7 = 35

Area of triangle with base of 8.1: A = 1/2 x 8.1 x 16 = 64.8

Total surface areas = 2(area of triangle base of 10) + 2(area of triangle base of 8.1) + area of rectangle = 2(35) + 2(64.8) + (10x8.1) = 280.6

So A is incorrect and B is correct.

The degree of polynomial is 3

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

zeros equal in x=1 with multiplicity =2 x= 0 with the multiplicity =1

The degree of a polynomial is the sum of the multiplicities

Using the above as a guide, we have the following:

Degree = 2 + 1

Evaluate

Degree = 3

Hence, the degree is 3

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The cross section is shaped like a circle.

A cone is a three-dimensional geometric object with a flat base and a smooth transition to the apex or vertex.

If a cone is sliced such that the cross section is perpendicular to its base and intersects its vertex, the cross section will be a circular shape. This is because the cross section cuts through the entire cone at a right angle, producing a circle that is defined by the curved surface of the cone and the slicing plane. The diameter of the circle is equal to the base diameter of the cone, and its center is located at the midpoint of the base.

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A parabola is a mirror-symmetrical, roughly U-shaped planar curve in mathematics. Many seemingly unrelated mathematical descriptions that all correlate to the same curves can be used to define it.

In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical planar curve.

The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.

A line and a point (the focus) are two components of one definition of a parabola (the directrix).

The directrix is not the main focus.

The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.

Therefore, a parabola is a mirror-symmetrical, roughly U-shaped planar curve in mathematics. Many seemingly unrelated mathematical descriptions that all correlate to the same curves can be used to define it.

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Complete question:

What is a parabola?

Answer:

Step-by-step explanation:

divide the required value by the total value and multiply by 100.

a/bx100= y

2.2 - 2.1 =0.1 inches

percentage of error=

0.1 / 2.2 x100

4.54 %

Answer:

R2689 IS THE CORRECT ANSWER

Answer:

90p or 9p

Step-by-step explanation:

if he will spend 5p per pound then do 5x9P=45P

The length of XW from the given triangle XYZ is 671.16 units.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔXYZ, ∠X=17° and ∠Y=82°. ∠XWZ=90° and XY=700.

By using angle sum property,

∠X+∠Y+∠Z=180°

17°+82°+∠Z=180°

99°+∠Z=180°

∠Z=180°-99°

∠Z=81°

Now, YZ/sinX=XZ/sinY=XY/sinZ

YZ/sin17°=XZ/sin82°=700/sin81°

XZ/0.9902=700/0.9876

XZ/0.9902=708.78

XZ=701.83

Now, cos17°=XW/701.83

0.9563=XW/701.83

XW=0.9563×701.83

XW=671.16

Therefore, the length of XW is 671.16 units.

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Answer:671

Step-by-step explanation: