Tony has a rectangular piece of cardboard that will have congruent squares removed from its corners with a length of 3 inches. The length of the piece of cardboard is four times larger than its width. Tony also know that the volume of the box he is able to create from this piece of cardboard is 336 cubic inches. What are the dimension of this box?

The equation AB = BC for A is A = BC[tex]B^{-1}[/tex].

As per the given data:

The equation AB = BC for A is given.

Also, we have to assume that A, B, and C are square matrices and that B is invertible.

Here we have to solve the equation AB = BC for A.

If the determinant of matrix A is non-zero, then the inverse of that matrix exists.

The inverse of matrix A is denoted by [tex]$A^{-1}$[/tex]. If a matrix is invertible, then the condition [tex]$A A^{-1}=I=A^{-1} A$[/tex] will be true.

Any matrix A multiplied by the identity matrix I will produce the same matrix A as the output, i.e., AI = IA = A.

Since B is invertible there exists [tex]B^{-1}[/tex]

[tex]\Rightarrow A B B^{-1}=B C B^{-1} \quad\left[/tex]

Solve the obtained equation for A by using the properties B[tex]B^{-1}[/tex]

[tex]$\Rightarrow A I=B C B^{-1}$[/tex] where I is the identity matrix of same order.

A = BC[tex]B^{-1}[/tex] because A I = I A = A

Therefore, the required matrix A = BC[tex]B^{-1}[/tex] .

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The 5 most common Pythagorean triples are ( 3 , 4 , 5 ) , ( 5 , 12 , 13 ) ,

( 6 , 8 , 10 ) , ( 9 , 12 , 15 ) , and ( 15 , 20 , 25 ) .

Pythagorean triples:

Any three positive integers that completely satisfy the Pythagorean theorem is considered a Pythagorean triple number. According to the theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle. A Pythagorean triple consists of the three sides of a right triangle. In this article, you will learn how to create multiple Pythagorean triples.

A Pythagorean triple consists of the three natural numbers a, b, c such that a² + b² = c². These triples are usually written as (a, b, c), examples

(3, 4, 5) are well known. If (a, b, c) is a Pythagorean triple, then (ka, kb, kc) is also a Pythagorean triple for all natural k. A primitive Pythagorean triplet is a triplet in which a, b, and c are coprime (i.e., have no common divisor greater than 1). For example, (3, 4, 5) is a basic Pythagorean triple, but (6, 8, 10) is not.

A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle and is necessarily a right triangle.

This name comes from the Pythagorean theorem, which states that the side lengths of each right triangle satisfy the formula a² + b² =c². A Pythagorean triple gives the length of three integers of the sides of a right triangle. However, right triangles whose sides are not integers do not form a Pythagorean triple. For example, a triangle with sides a = b = 1 and c = √2 but, (1,1,2) is not a Pythagorean triple because √2 is not an integer. Also, the numbers 1 and √2 do not have a common multiple because √2 is irrational.

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Answer:

x > - 1

How to find your answer:

-3x + 3 < 6 (Move the constant to the right)

-3x < 6 - 3 (now calculate)

-3x < 3 (divide both sides)

x > -1

I hope this helped.

The x-component of the total force exerted on the third charge by the other two charges is equal to k * (30.00 nC * 4.00 cm / 5.00 cm + 12.00 nC).

Force is a physical quantity that measures the influence of one object on another. It is a vector quantity, meaning it has both magnitude and direction.

Let's use Coulomb's Law to calculate the x-component of the total force exerted on the third charge by the other two charges. The x-component of the total force is just the sum of the x-components of the forces exerted by each of the two charges.

First, we'll calculate the force exerted by the 5.00 nC charge at the origin. The direction of this force will be towards the third charge, so the angle θ is the arctangent of the ratio of the y-coordinate of the third charge and the x-coordinate of the third charge. That is, θ = arctan(3.00 cm / 4.00 cm). Using Coulomb's Law, we have:

F = k * q1 * q2 / r²,

where k is the Coulomb constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them. For this case,

=> r = √(4.00 cm² + 3.00 cm²) = 5.00 cm.

Thus,

F = k * 5.00 nC * 6.00 nC / 5.00 cm^2 = k * 30.00 nC.

Fx = F * cos(θ) = k * 30.00 nC * cos(arctan(3.00 cm / 4.00 cm))

Fx = k * 30.00 nC * 4.00 cm / 5.00 cm.

Next, we'll calculate the force exerted by the -2.00 nC charge on the x-axis. This force will be in the negative x-direction, so the angle θ is 180 degrees. Thus,

F = k * -2.00 nC * 6.00 nC / 4.00 cm^2 = -k * 12.00 nC.

Fx = F * cos(180) = -k * 12.00 nC * cos(180) = k * 12.00 nC.

Finally, we add up the x-components of the forces exerted by each charge to get the total x-component of the force:

Fx = k * 30.00 nC * 4.00 cm / 5.00 cm + k * 12.00 nC

Fx = k * (30.00 nC * 4.00 cm / 5.00 cm + 12.00 nC).

Complete Question:

A charge of 5.00 nC is placed at the origin of the xy - coordinate system, and a charge of -2.00 nC is placed on the positive x-axis at x = 4.00 cm. A third particle, of charge 6.00 nC is now placed at the point x = 4.00 cm, y = 3.00 cm.

Find the x-component of the total force exerted on the third charge by the other two.

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The base of the triangle with area 14ft² and height 6ft is 4⅔ feet

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The area of a triangle is given by ;

1/2bh

Area = 14ft²

height = 6ft²

therefore;

14 = 1/2 b × 6

28 = 6b

divide both sides by 6

b = 28/6

b = 14/3

b = 4⅔ ft

therefore the base of the triangle is 4⅔ feet.

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The quadratic-like polynomial x⁶ + 8 has no real roots, that is, it has two complex roots. (Correct choice: B)

In this problem we must determine what polynomial has no real roots. From real algebra we remember that any polynomial of the form x²ⁿ + a², where a is a positive real number, has no real numbers. That is, the factor form of the polynomial is shown below:

(xⁿ + i a) · (xⁿ - i a)

In other words, any polynomial of the form x²ⁿ + a², a > 0, has two complex roots. Now, by direct comparison, we conclude that polynomial x⁶ + 8 has no real roots.

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The graph the depicts the solution set of the inequality is graph D. Option 4 is the correct answer.

There is a significant exception to the general rule that inequality manipulation is quite similar to equation manipulation.

An inequity still exists if the same amount is added to both sides.

The inequality still holds true if the same amount is subtracted from each side.

An inequality still holds true if both sides are multiplied or divided by the same positive value.

However, if both sides of an inequality are multiplied or divided by a negative value, the inequality is no longer valid.

The given inequality is x² + 10x + 16 / x-3 > 0.

Expand the quadratic equation:

x² + 8x + 2x + 16/ x-3 > 0

x(x + 8) + 2(x + 8) / x-3 > 0

(x + 2)(x + 8)/ x-3 > 0

x + 2 > 0 and (x + 8) < 0 and x - 3 > 0

x > -2 and x < -8 and x > 3

The intervals of x are:

-8 < x < -2 and x > 3

Hence, the graph the depicts the given interval is graph D. Option 4 is the correct answer.

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Here we have a program written in C++ language. Each // symbol is a relative comment explaining the reason for each command line (and is not included during the program execution).

The Program:

#include <iostream>

//c++ build in library

using namespace std;

//main code body starts here

int main()

{

 //declare variable to store phone numbers,its area code, prefix and line    number.

long pnumber;   //declare long variable

int ac, prefix, lnumber;

 //declare integer variables, where ac: Area Code and lnumber is the Line Number

cout<<"Enter a 10-digit Phone Number: "<<endl;

 //cout command prints on screen the desired message

 cin>>pnumber;

 //cin command enables the user to interact with the programm and enter information manually

//main body to obtain the desired output starts below

 //each 'division' is used to allocate the correct value at the correct

 //since prefix is used to get the desired output of ( )    -

 ac = pnumber/10000000;

 prefix = (pnumber/10000)%1000;

 lnumber = pnumber%10000;

 //main body ends here

 cout<<"Based on your 10-digit number"<<endl;

 cout<<"below you have (AreaCode), Prefix, and - line number "<<endl;

 cout<<"("<<ac<<")"<<""<<prefix<<"-"<<lnumber<<endl;

 //Prints on screen the desired output of the long 10 digit Number

 return 0; //ends program

}

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

The Output Sample:

Enter a 10-digit Phone Number:

8019004673

Based on your 10-digit number

below you have (Area Code), Prefix, and - line number

(801) 900-4673

....Programm finished with exit code 0

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A positive divided by a negative always results in a negative quotient.

Let's use the example 8 / (-2) again. We can write this expression as:

8 / (-2) = 8 / (-1) * 2

We can then simplify the expression on the right-hand side by multiplying -1 and 2, which gives us:

8 / (-1) * 2 = -8 / 2

Now, we can divide 8 by 2, which gives us:

-8 / 2 = -4

So we see that the quotient is negative.

We can generalize this to any positive number divided by a negative number. Let's say we have a positive number a and a negative number -b. We can write the expression as:

a / (-b) = a / (-1) * b

Multiplying -1 and b gives us:

a / (-1) * b = -a / b

So we see that the quotient is negative, since -1 times b is negative, and dividing a positive number by a negative number results in a negative quotient.

Therefore, we can conclude that when a positive number is divided by a negative number, the result is always negative.

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The solution for x is x ≤ -3/4.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

To solve for x in the inequalities:

5x - 4 ≥ 12 and 12x + 5 ≤ -4

We'll solve each inequality separately:

5x - 4 ≥ 12

Adding 4 to both sides, we get:

5x ≥ 16

x ≥ 16/5

So the first inequality is solved for x as x ≥ 16/5.

Now, 12x + 5 ≤ -4

Subtracting 5 from both sides, we get:

12x ≤ -9

x≤ -9/12

x≤ -3/4

The only values of x that satisfy both inequalities are those that are less than or equal to -3/4.

Therefore, the solution for x is x ≤ -3/4.

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The number of guitars in which leo put Strings on is found to be "3.

Multiplication has been the opposite of division.

The stated question is-

On some guitars, Leo swaps off the strings.

Each guitar receives six new strings from him.

His 18 strings are used.

Number of guitars = Total strings / number of strings used in each guitar

Number of guitars = 18/ 6

Number of guitars = 3

Thus, the number of guitars in which leo put Strings on is found to be "3.

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Answer: 0.429

Step-by-step explanation: Use a calculator and put the fraction and hit enter to get it in decimal form. You should get a number like 0.42857142857 but the problem asks us to round to the nearest thousandth. Since there is a 5 in the ten-thousandth place, we must round up. Therefore, the final answer will be 0.429.

Answer:

Step-by-step explanation:

The segments of the triangles are proportional.

Add all the measurements on the left to get the complete length of the

left side - 9 + 3 + 12 = 24

Form a proportion with a smaller triangle still using the left side,

this time 9 + 3 = 12

Use the bottom measurement of 22 to complete the proportion:

You have:

24/22 = 12/x

cross multiply - 12 × 22 = 264

divide by 24 = 11

x = 11

A. The equation is given as C = 0.1T + 0.05M

B. It will cost Laura $1.05 to send 4 texts and talk for 13 minutes.

C. Laura will have $1.80 left after sending 18 texts and talking for 124 minutes.

D. The equation for T is T = (C - 0.05M) / 0.1.

A. The equation for the cost, C, of sending both texts and talking for M minutes is:

C = 0.1T + 0.05M

where T is the number of texts sent.

This equation assumes that each text costs 10 cents and each minute of talk time costs 5 cents.

B. To calculate the cost of sending 4 texts and talking for 13 minutes, we can use the equation from part A:

C = 0.1T + 0.05M

C = 0.1(4) + 0.05(13)

C = 0.4 + 0.65

C = 1.05

Therefore, it will cost Laura $1.05 to send 4 texts and talk for 13 minutes.

C. To determine how many minutes Laura can talk if she wants to send 18 texts and only has eight dollars, we need to use the equation from part A and solve for M:

C = 0.1T + 0.05M

8 = 0.1(18) + 0.05M

8 = 1.8 + 0.05M

6.2 = 0.05M

M = 124

Therefore, Laura can talk for 124 minutes if she wants to send 18 texts and has eight dollars.

This will cost her $6.20, which is less than the amount of money she has, so she will have some money left over.

subtract the cost of talking and texting from the amount of money she has:

Money left = 8 - 6.20

Money left = 1.80

Therefore, Laura will have $1.80 left after sending 18 texts and talking for 124 minutes.

D. To solve the equation from part A for T, we can rearrange the terms:

C = 0.1T + 0.05M

0.1T = C - 0.05M

T = (C - 0.05M) / 0.1

Therefore, the equation for T is T = (C - 0.05M) / 0.1.

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The mean price per ad slot was 26.167 million. The broadcasters made $157 million in revenue from the sale of 61 ad spaces for a significant sporting event.

TR=Price *Quantity

$157=P* 61

P=157/61=26.167

By dividing the sum of all values by the total number of values, one can determine the mean of a dataset (sometimes referred to as the arithmetic mean, which is distinct from the geometric mean). It is the most popular way to quantify central tendency and is commonly referred to as the "average". Simply dividing the total number of values in a data collection by the total number of values in the data set yields the answer. The calculation can be done with either raw data or a frequency table of the data. When someone or something is accused of having a very short fuse and being harsh, they are said to be mean.

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Answer: No, Alan's statement is incorrect!

Step-by-step explanation:

The intersection point of a system of inequalities is not always a solution. It only becomes a solution if the two lines meet at the same point and the lines are not parallel. If the two lines are parallel, then they will not intersect and thus the intersection point will not be a solution.

Step-by-step explanation:

if there is an intersection point (the lines are not parallel), there is still the question, if the points on the line are included in the solution or not.

if not, then the intersection point is not part of the solution either.

this is controlled by the absence of presence of the "or equal" part of the inequality.

>= greater than or equal

<= less than or equal

if the inequality is only

> greater than

< less than

the lines are just delimiters, but their points are not part of the solution. and therefore not the intersection point either.

The measure of the side FG that is h using the sine law will be 786.63 centimeters.

The sine law in the triangle ΔFGH is given as,

FG / sin H = GH / sin F = FH / sin G

In ΔFGH, f = 600 cm, m∠F = 32°, and m∠G = 12°.

We know that the aggregate of the gradient of the triangle is 180°. Then the angle H is given as,

∠F + ∠G + ∠H = 180°

32° + 12° + ∠H = 180°

                  ∠H = 136°

The length of the triangle 'h' is given as,

FG / sin H = GH / sin F

h / sin 136° = f / sin 32°

h = 600 (sin 136° / sin 32°)

h = 600 x 1.31

h = 786.63 cm

The measure of the side FG that is h using the sine law will be 786.63 centimeters.

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Explanation:

The missing angle between the 107 and (4-2x) is 55 due to the vertical angles theorem.

The three angles mentioned add to 180 because they form a straight line.

Here's what the steps would look like:

107+55+(4-2x) = 180

166-2x = 180

-2x = 180-166

-2x = 14

x = 14/(-2)

x = -7

Answer:  

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

480 meters is the whole field.

One quarter of it is equal to 480 ÷ 4 = 120.

She is traveling 20 meters per minute.

120 ÷ 20 = 6

It takes her six minutes.

Answer:

7.40

Step-by-step explanation:

51.8 divided by 7 is 7.4

Answer: [tex](x+10)(x-10)[/tex]

Step-by-step explanation: Difference of squares is an important element in understanding square functions. In order to identify difference of squares, the equation should be given in the form a^2-b^2. You can factor it completely when b^2 can be square rooted perfectly and write the factored expression as (a-b)(a+b) as I have done above.

Based on the ratios of sand, silt, and clay particles contained in a soil sample, soil scientists and farmers use the soil texture triangle to categorize and define the texture of soil. It is a graphic representation of the system for classifying soil textures.

Agricultural experts and soil scientists utilize the Soil Texture Triangle, a graphic representation, to categorize soil according to its texture. The triangle's three portions stand in for the three major categories of soil particles: sand, silt, and clay.

Based on the proportion of each type of particle present in a soil sample, the Soil Texture Triangle can be used to determine the texture of the soil. A soil scientist can rapidly categorize a soil as sandy, loamy, or clayey by plotting the percentage of sand, silt, and clay on the triangle.

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The whole fraction of a pizza that shows 6 pieces is 6/1 or simply 6.
The whole fraction of a pizza that shows 6 pieces is 6/6 or 1.

In a fraction, the numerator represents the number of parts being considered, and the denominator represents the total number of parts. In this case, there are 6 pieces of pizza being considered out of a total of 6 pieces, which means the fraction is 6/6. This fraction can be simplified to 1, meaning the whole pizza is represented.

So, the whole fraction of a pizza that shows 6 pieces is 1.

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Answer: -11

Step-by-step explanation:

The numbers of flowers spaced every 4 feet, are needed

to surround a circular garden with a 70-foot radius, 105

Circumference is the distance around the perimeter of a circular object. It is defined as the length of the circle that is found by multiplying the diameter of the circle by π (pi), which is approximately equal to 3.14.

The formula for the circumference of a circle is given by:

C = 2πr,

To calculate the circumference of the circular garden, we can use the formula:

C = 2πr

where C is the circumference, π is the mathematical constant pi (approximated as 3 in this case), and r is the radius. Plugging in the given values, we have:

C = 2 x 3 x 70

  = 420 feet

Now, since the flowers are spaced every 4 feet, we can divide the circumference by 4 to find the number of flowers needed:

number of flowers = C / 4

                               = 420 / 4

                               = 105

Therefore, 105 flowers spaced every 4 feet are needed to surround a circular garden with a 70-foot radius.

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Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. The correct answer is $68.44.

A restaurant is a business that prepares and serves food and drinks to customers. [1] Meals are generally served and eaten on the premises, but many restaurants also offer take-out and food delivery services.

18/100 = .18

58 x .18 = 10.44

⇒ 58 + 10.44 = 68.44

Hence, Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. The correct answer is $68.44.

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Answer:

X = 6/ y+3 - 2

and

Y -3x/x+2

Step-by-step explanation:

hope this helps

The value of side DE of the triangle is 14.91 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

In triangle CDF,

tan 61° = DF/24

DF = 24 * tan 61°

DF = 43.30 units

In triangle DEF,

tan 19° = DE/43.30

DE = 43.30 * tan 19°

DE = 14.91 units

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Answer:

Step-by-step explanation:

make a tree, first list out the sports then draw two branches for the clubs (speech and science) then circle each club to each sport, like how the picture shown . You will find there are 6 ways Janelle could pick out her extracurriculars