Modeling Problems with Equations Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run? A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by. Select all that apply. You know the difference in the distances the boys ran, so this is a subtraction problem. You are finding the total distance the boys ran, so this is an addition problem. Dean ran part of the distance Sam ran, so this is a multiplication problem. The correct equation is s + 2.3 = 6.8. The correct equation is s – 2.3 = 6.8. The correct equation is 2.3s = 6.8.

Reduced matrix to its reduced echelon form Original Matrix:

[tex]$$ \begin{bmatrix}1 & -1 & 2 & -1 & 3 \\2 & -2 & 3 & 0 & 4 \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]

Pivot Positions (Original): (1,1), (2,2), (3,4)

Pivot Columns (Original): 1, 2, 4

Reduced Echelon Form:

[tex]$$ \begin{bmatrix}1 & 0 & \frac{2}{3} & 0 & \frac{11}{3} \\0 & 1 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]

Pivot Positions (Reduced): (1,1), (2,2), (3,4)

Pivot Columns (Reduced): 1, 2, 4

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract three times row 1 from row 3 to get the leading 1 in the fourth column

4. Divide row 2 by 3 to get the coefficient 2/3 in the third column

5. Subtract row 2 from row 1 to get the coefficient 11/3 in the fifth column

6. Subtract row 2 from row 3 to get the coefficient 2/3 in the fifth column

Exercise 4:

Original Matrix:

[tex]$$ \begin{bmatrix}1 & 2 & -3 & 1 & 5 \\2 & 4 & -6 & 2 & 8 \\-1 & -2 & 3 & -1 & -4\end{bmatrix} $$[/tex]

Pivot Positions (Original): (1,1), (2,2), (3,3)

Pivot Columns (Original): 1, 2, 3

Reduced Echelon Form:

[tex]$$ \begin{bmatrix}1 & 0 & 0 & \frac{2}{3} & \frac{11}{3} \\0 & 1 & 0 & \frac{-1}{3} & \frac{1}{3} \\0 & 0 & 1 & \frac{2}{3} & \frac{5}{3}\end{bmatrix} $$[/tex]

Pivot Positions (Reduced): (1,1), (2,2), (3,3)

Pivot Columns (Reduced): 1, 2, 3

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract row 1 from row 3 to get the leading 1 in the third column

4. Divide row 2 by 3 to get the coefficient -1/3 in the fourth column

5. Add row 2 to row 1 to get the coefficient 2/3 in the fourth column

6. Divide row 3 by 3 to get the coefficients 2/3 and 5/3 in the fourth and fifth columns respectively

7. Add row 3 to row 1 to get the coefficient 11/3 in the fifth column

8. Add row 3 to row 2 to get the coefficient 1/3 in the fifth column

Learn more about matrix here:

https://brainly.com/question/28180105

#SPJ4

The perimeter of a rectangle is 700 feet. A quadratic function for its area in terms of its width is A(w) = 350w - w²

The formula for the perimeter of a rectangle is given by:

p = 2w + 2l

While its area is:

A = w x l

Where:

w = width

l = length

Substitute p = 700 ft.,

700 = 2w + 2l

700 = 2(w + l)

w + l = 350

l = 350 - w

Substitute l = 350 - w into the formula of area:

A = w x l

A = w (350 - w)

A(w) = 350w - w²

Hence, the expression is: A(w) = 350w - w²

Learn more about rectangle here:

https://brainly.com/question/16239445

#SPJ4

A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.

A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.. The weight of each backpack will be recorded in order to calculate the mean and standard deviation of the sample. To calculate the mean, the total weight of the five backpacks will be added together and then divided by the number of backpacks in the sample (5). To calculate the standard deviation, the weight of each backpack will be subtracted from the mean and the resulting difference will be squared. All of the squared differences will then be added together, divided by the number of backpacks in the sample (5), and the square root of this result will be taken. This will give us the standard deviation of the sample. These calculations will provide us with valuable information about the weights of the backpacks in the sample, which can then be compared to the weights of the backpacks in the population.

Learn more about standard deviation here

https://brainly.com/question/13905583

#SPJ4

$52 hundred is introduced to the December 31, 20Y6.

A proportion is a unit of fairness possession in the capital inventory of a corporation, and may discuss with devices of mutual funds, restrained partnerships, and actual property funding trusts. Share capital refers to all the stocks of an enterprise. The proprietor of stocks in a employer is a shareholder (or stockholder) of the corporation.

Note that proportion is an indivisible unit of capital, expressing the possession dating among the employer and the shareholder.

Given that bond indenture for the 10-year, 9% debenture bonds issued January 2, 20Y5, required working capital of $100,000, a current ratio of 1.5, and a quick ratio of 1.0 at the end of each calendar year until the bonds mature.

The profits acquired from the possession of stocks is a dividend. There are extraordinary varieties of stocks consisting of fairness stocks, bonus stocks, proper stocks, and worker inventory choice plan stocks.

To know about shares click here

brainly.com/question/25818989

#SPJ1

Given that IJ = 2, we know that IJ is the radius of the circle.

The area of the shaded sector is given as . Since the area of a sector is given by (angle of sector/360) * pi * r^2, we can set up the equation:

(x/360) * pi * 2^2 =

Solving for x:

x = (180/pi)*

We know that the arc JLK corresponds to the angle x, thus the length of JLK is (x/360)2pi*IJ = (x/180)*IJ * T = (180/pi) * T.

Answer:

3. f

4. b

5. a, x

Step-by-step explanation:

3.

a/f = f/c

f² = ac

f = √ac

Answer: f

4.

x/b = b/c

b² = cx

b = √cx

Answer: b

5.

x/k = k/a

k² = ax

k = √ax

Answer: a, x

The equation of a line passing through the terminal point of a vector a and in the direction of vector b is  r = a + λb.

In math the equation of a straight line is y = m x + c

where m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.

Here we need to find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.

Based on the general form of the equation of the line, the vector form of the equation of a line passing through a point having a position vector a, and parallel to a vector line b is written as,

=> r = a + λb.

Where λ refers the constant term.

To know more about equation here.

https://brainly.com/question/10413253

#SPJ4

Answer: The answer is 3

Step-by-step explanation:

Answer:111

Step-by-step explanation:

1111

Answer:

The area of a circle is pi multiplied by the radius squared (A = π r²)

The radius (r) is the distance from the center of the circle, to the edge of the circle.

Example:

if you have a circle with radius 2, the area would be:

r = 2

A = π (2)²

A = π(4)

A = 4π

Answer:

Area can be calculated by the formula = [tex]\pi r^{2}[/tex]

Step-by-step explanation:

We can calculate the area of a circle with the formula,

Area of Circle = [tex]\pi r^{2}[/tex]

Where r replicates the radius of the circle

The domain of each expression is given as follows:

1. All real values except y = 0 and y = 2.

2. All real values.

3. All real values except y = 0 and y = -7.

The domain of an expression is composed by the set of all the possible input values that the expression can assume.

For an expression that is a fraction, the denominator cannot be zero, hence:

For item 2, the function is a multiplication, which has no restrictions on the domain, and thus the domain is composed by all real values.

More can be learned about the domain of a function at https://brainly.com/question/30348691

#SPJ1

No, these data do not allow us to infer that the mean number of commercials watched is greater than 15.

To make such an inference, we would need to know the population mean number of commercials watched, along with the population standard deviation. We can use the sample data to calculate the sample mean and sample standard deviation. The sample mean (X) is the sum of the data values divided by the number of observations. The sample standard deviation (s) is calculated using the equation s = √(sum of (x-X)² / (n-1)) , where n is the number of observations. With the sample mean and standard deviation we can then use a t-test to determine if the population mean is significantly greater than 15.

Learn more about sample mean here:

https://brainly.com/question/30023845

#SPJ4

answer

no

steps

February ends on the 28th this year 2023

leap year February ends on the 29th

The coordinates of point p along the directed line segment ab are [tex]$p(-1,-2)$[/tex]

Let the coordinates of point p be (x,y)

The ratio of ap to pb is 2 to 6, so we have [tex]$$\frac{|ap|}{|pb|} = \frac{2}{6}$$[/tex]

We can calculate the distances between points $a$ and $p$ and points $p$ and $b$ using the distance formula as follows:

[tex]$$|ap| = \sqrt{(x+3)^2+(y-2)^2}$$$$|pb| = \sqrt{(5-x)^2+(y+4)^2}$$[/tex]

We can use the ratio of the distances to set up a proportion to solve for $x$ and $y$:

[tex]$$\frac{|ap|}{|pb|} = \frac{2}{6} \implies \frac{\sqrt{(x+3)^2+(y-2)^2}}{\sqrt{(5-x)^2+(y+4)^2}} = \frac{2}{6}$$\\[/tex]

Solving for $x$ and $y$, we get $x = -1$ and $y = -2$.

Therefore, the coordinates of point $p$ along the directed line segment $ab$ are [tex]$p(-1,-2)$[/tex]

Learn more about coordinates of point here:

https://brainly.com/question/21950350

#SPJ4

By adding (81.7-23.456)+(78.44+2.72), we get 139.404

Use the three rules below to calculate the number of significant figures in a number:

Non-zero digits are always meaningful.

Any zero between the first and second significant digits is significant.

Only the last zero or trailing zeros in the decimal section are important.

Numbers Have Rules INCLUDING a Decimal Point

START COUNTING FOR SIGNIFICANT FIGURES. On the very first non-zero digit.

STOP COUNTING FOR SIGNIFICANT FIGURES.

Non-zero numbers are ALWAYS meaningful.

After the first non-zero digit, any zero is still relevant. The zeroes preceding the first non-zero digit are unimportant.

To learn more about significant figures, visit

brainly.com/question/29153641

#SPJ1

Answer: Maybe if you post the question

Step-by-step explanation:

Answer:

The value of z can be found using the Law of Sines, which 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. In other words, if a, b, and c are the lengths of the sides of a triangle opposite angles A, B, and C, respectively, and A, B, and C are the angles opposite sides a, b, and c, respectively, then: a/sin(A) = b/sin(B) = c/sin(C). This can be used to solve for the unknown side length.

The image that gives the translation of the polygon six units to the left and two units upward is given as follows:

The fourth graph.

(which is the third graph if we consider that the first is the original image).

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

For the translation 5 units left, we have that:

The bottom segment of x = 1 to x = 4 will assume coordinates of x = -5 to x = -2.

For the translation 2 units up, we have that:

The vertical segment from y = 1 to y = 3 will assume coordinates from y = 3 to y = 5.

More can be learned about translations at brainly.com/question/28174785

#SPJ1

A perimeter longer than 50 for any point, C satisfies the area requirement.

Consequently, we have a base-10 triangle whose area is 100. Since the area is equal to half the product of base and height, the object's height is then 20.

The next two sides. If one of the sides is exactly 20 inches tall (when it coincides with the height, forming a right triangle), the other side must be strictly greater than 20 inches tall (being the hypotenuse), in which case the perimeter must be greater than 50.

Alternately, both sides could be longer than 20 because neither side is a height. Once more, the perimeter exceeds 50.

Know more about perimeter

https://brainly.com/question/397857

#SPJ4

The full question

In a given plane, points A and B are 10 units apart. How many points C are there in the plane such that the perimeter of triangle ABC is 50 units and the area of triangle ABC is 100 square units?

No, new atoms are not created in a chemical reaction. Atoms are rearranged or combined to form new compounds. The total number of atoms before and after the reaction is the same. This is known as the law of conservation of mass.

The law of conservation of mass states that in a closed system, the total mass of the reactants (the substances before the reaction) is equal to the total mass of the products (the substances after the reaction). This means that the atoms present in the reactants must also be present in the products, but in different combinations or arrangements.

Therefore, It's important to note that in some reactions, atoms can be transformed into different forms, for example, a carbon atom can be transformed into a carbon dioxide molecule, but the mass of the atoms remains the same.

Learn more about chemical reaction from

https://brainly.com/question/11231920

#SPJ1

Answer:

1

Step-by-step explanation:

We have g(f(2))

Working from the inside out, we start with f(2)

So we go to the f(x) graph and find where X is 2. We get to the point (2, -2). f(2) is pretty much asking for the Y value at 2. On this graph the y value is -2

Now that we know f(2) is -2, we can plug that into g(f(2)), giving us g(-2)

Now we can go to the other graph, g(x) and find where X is -2.

That's where we find the point (-2,1)

Like last time, g(2) is asking for that Y value at that point of -2. On this graph, it's 1

Now we can conclude g(f(2)) = 1

Using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.

What is the graph?

A graph is a visual representation of data or information, often used in mathematics and science to depict relationships between variables. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts.

To evaluate g(f(2)), we need to first find the value of f(2) using the graph of f. From the graph, we can see that f(2) is approximately 4. So, g(f(2)) = g(4).

Then, using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.

To learn more about Graph, Visit

https://brainly.com/question/19040584

#SPJ1

The eastbound airplane has traveled 16 miles.

This can be determined using the Pythagorean theorem, which states that in a right 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 this case, the distance the northbound airplane has traveled (12 miles) is one side of the triangle, the distance the eastbound airplane has traveled is the other side, and the distance between the two airplanes (20 miles) is the hypotenuse.

So, we can set up the equation as:

(distance eastbound airplane)^2 + 12^2 = 20^2

Solving for the distance eastbound airplane, we get:

distance eastbound airplane = sqrt(20^2 - 12^2) = sqrt(256 - 144) = sqrt(112) = 16 miles

The number of papers that Ms. Motley will grade in five days would be = 46 papers (approximately).

The number of papers Ms. Motley graded in first day = 9 papers

The number of papers Ms. Motley graded in the second day = 27 papers

The number of papers Ms. Motley graded in the third day = 31 papers

The average number of she graded for the three days is calculated as follows;

9+27+31 = 67/3 = 27.3 papers.

If in 3 days = 27.3 papers

5. days = X papers

Make X papers the subject of formula;

X papers = 5× 27.3/3

= 136.5/3

= 45.5 papers

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1

The expression for the simplified polynomial would be - x² - 10x - 24.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the polynomial ( x + 5 )² is subtracted from 1. The simplified polynomial can be written as:-

Polynomial = 1 - ( x + 5 )²

Polynomial = 1 - ( x² + 10x + 25 )

Polynomial = 1 - x² - 10x - 25

Polynomial = -x² - 10x - 24

Hence, the polynomial can be written as -x² - 10x - 24.

To know more about an expression follow

https://brainly.com/question/2833285

#SPJ1

The altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.

In order to find the altitude of the second beetle, let x be the altitude of the second beetle above the first beetle.

The horizontal distance between the two beetles is 72 cm.

The first beetle moves twice as fast as the second beetle, so the vertical distance between them is 2x.

Therefore, the equation for the problem is:

3x + 2x = 72

5x = 72

x = 14.4 cm

Therefore, the altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.

learn more about altitude: https://brainly.com/question/1159693

#SPJ1

The product of the binomial factors is x² + 16x + 64

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

(x+8)2

Express properly

So, we have

(x+8)²

Using the square of a binomial sum, we have

(x+8)² = x² + 2 * x * 8 + 8²

Evaluate

(x+8)² = x² + 16x + 64

Hence, the solution is x² + 16x + 64

Read more about expression at

https://brainly.com/question/4344214

#SPJ1

The exponent form that represents the side length of the square is √x

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

Area = x in.²

The area of a square is calculated as

Area = Side length²

substitute the known values in the above equation, so, we have the following representation

Side length² = x

Take the square root of both sides

Side length = √x

Hence, the expression is √x

Read more about area at

https://brainly.com/question/22972014

#SPJ1

The students expected to like soda are 324

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

150 students out of a total of 800 students on campus did not like soda.

This means that

650 students out of a total of 800 students on campus like soda.

i.e. 800 - 150 = 650

When half of the students are considered, we have

Soda = 650/2

Evaluate

Soda = 325

Hence, the number of students is 325

Read more about proportion at

https://brainly.com/question/870035

#SPJ1