A rectangle has a length of
2,000 cm and a width of 23 cm.
What is the area?
What is the perimeter?

(a) As of the Cartesian vector approach, Moment about axes are [tex]M_x = 13\ Ft-lb[/tex], [tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex].

(b) Using a scalar approach, Moment about axes are [tex]M_x = 13\ Ft-lb[/tex], [tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex].

Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.  

here,
[tex]\vec F = 4 \hat i + 12\hat j -3 \hat k\\ \vec B = 4 \hat i + 3\hat j - 2 \hat k\\[/tex]

Scalar approach,
moment about the x-axis is given by,
[tex]M_x = B_yF_z - ZF_y\\M_x = 3(-3)-(-2)(12)\\M_x = 13\ Ft-lb[/tex]

Similarly,
[tex]M_y = 4\ Ft-lb,[/tex] and [tex]M_z = 36\ Ft-lb[/tex]

Vector approach,
Moment about the x-axis is given by,
[tex]M_x = U_x \times[ {\vec B \times \vec F]}\\M_x = \left[\begin{array}{ccc}1&0&0\\4&3&-2\\4&12&-3\end{array}\right][/tex]

The above expression given is of determinate, when solving the above determinate,
[tex]M_x = 13\ Ft-lb[/tex]

Similarly,
[tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex],

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The no. of customers they serve per day is equal to 14.

It is given that the total number of customers served in first year of business was 5110.

We have to find that what will be the average of servings per day ?

What do you mean by average ?

The average is the ratio of sum of all numbers to the total no. of numbers.

As per the question ;

Total number of people served in a year = 5110

We know that ;

1 year = 365 days

So ;

To calculate the average of servings per day we need to divide total number of servings by no. of days in 1 year.

i.e.,

Average of customers per day ;

= 5110 ÷ 365

= 14 customers per day

Thus , the no. of customers they serve per day is equal to 14.

Answer:4 = -117,3=-212,4+3

Step-by-step explanation:

Answer:

3.2 mph

Step-by-step explanation:

If it takes her 3 hours to walk 9.6 miles, we need to divide 9.6 by 3.

To do so, we can remove the decimal point in 9.6, to give us 96.

Then, we can divide 96 by 3 to get 32.

Add the decimal back to 32.

Doing so would give us 3.2, and our answer.

We can check this answer by multiplying 3.2 by 3, which gives us 9.6, telling us our answer is correct.

If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.

Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.

given

Table 1:  

x 0 -4 3 -2 9 3

y 5 8 7 8 5 -2

No, Table 1 is not a function.

Since there are two images of element '3'.

i.e. 3 is mapped to 7 and -2.

Table 2:

x 2 -7 5 1 -6 3

y 5 8 -6 8 5 7

Yes, this relation is a function.

Because corresponding to each x there is a single image.

If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.

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Answer:

FALSE statement

Step-by-step explanation:

a right triangle’s exterior angle is 90 degree

Step-by-step explanation:

minimum.

since the term with x² has a positive factor, this will grow exponentially in the positive direction compared to the other terms, so y (the functional value) will grow and grow with growing distance of x to the vertex.

and that makes the vertex the minimum of the parabola (which opens upwards).

if the factor would be negative (like -x² - 2x + 10), the vertex would be a maximum, and the parabola would open downwards.

On solving the provided question, we can say that 50 will therefore be the missing number in the odd numbers 2 5 10 x 2637.

A number that is odd is one that can't be partitioned flawlessly into matches. One remains after dividing an odd number by two. The numbers 1, 3, 5, 7, 9, 11, 13, and 15 are consecutively odd. While odd numbers cannot be divided in half, even numbers can. 3, 5, 7, 9, 11, 13, and 15 are unusual cases. Even numbers include 2, 4, 6, 8, 10, 12, and 14.

According to the given question:

Following the numbers 3, 5, 7, 9, 11, and 13, which are all odd numbers, the provided series moves on to 13.

Therefore,

After 37, there will be a break before 50.

50 will therefore be the missing number.

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On solving the provided question, we can say that in this function f(x) = /16/1224 x^2 + 7x/5 + 1.5 = > f(2) = 2234.2454

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

in this function

f(x) = /16/1224 x^2 + 7x/5 + 1.5

f(2) = 2234.2454

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Check the picture below.

Answer:

D

Step-by-step explanation:

The Correct answer while simplifying the given algebraic expression is: 4a²+1/2a+7

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Method to simplify any algebraic Expressions are :

Given:

=3a²+1/4a+3+a²+4+1/4a

=(3a²+a²)+(1/4a+1/4a)+(3+4)

=4a²+1/2a+7

So the Answer is

=4a²+1/2a+7

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Candles should burn one hour for every 1 inch in diameter of the actual candle size. For example, a candle that is 2 inches across should burn for 2 hours.

At what rate does then candle burn, in inches per hour?

Smaller candles with smaller wicks will burn at a rate of 7 to 9 hours per 28 g of wax used. Larger candles with larger wicks consume wax at a faster rate. The larger wicks can be expected to yield 5 to 7 hours per 28 g of wax used.

Estimate the total number of burns by dividing the total wax weight used in the candle (not the weight of the candle with container) by the amount of wax used from burning the candle. Finally, multiply the estimated total burns by the burn time hours. This will provide an estimate of the candle's burn time.

The two main factors for burning candles is wick size and type of wax. Wider or thicker wicks will burn much faster than thin ones, and the material the wick is made with can also make an impact. Different types of candle wax burn at different temperatures.

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The equation of the line that passes through the points (-2,3) and (2,7) is:

x-y=-5

Therefore, option(C) x-y= -5 is correct answer.

Step-by-step solution:

The algebraic representation of a line's equation is the collection of points that make up the line in a coordinate system.

Given the line passes through the points (-2,3) and (2,7)

So, the equation of the line passing through the two points is given by:

[tex]\frac{y-y_{1} }{y_{2}-y_{1} } =\frac{x-x_{1} }{x_{2} -x_{1} }[/tex]

[tex]\frac{y-3 }{7-3} } =\frac{x-(-2) }{2-(-2) }[/tex]

[tex]\frac{y-3}{4} =\frac{x+2}{2+2}[/tex]

[tex]\frac{y-3}{4} =\frac{x+2}{4}[/tex]

[tex]y-3 = x+2[/tex]

Now rearranging the above equation:

x - y + 3 + 2 = 0

x - y + 5 =0

Therefore, the equation of the line passing through the points (-2,3) and (2,7) is: x-y=-5

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On solving the provided question, we can say that - the value of x and y by the linear equation will be x = 12 and y = -21

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, we have

3x-2y = 3

-4x + 5y = -11

and on solving we got

x = 12 and y = -21

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The wood left over after making the frame and the sandbox is 10 inches.

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side².

We have,

The total amount of wood.

= 4 x 65.5

= 262 inches.

Frame:

Side = 5.25 inches

The perimeter of the frame.

= 4 x 5.25

= 21 inches

Now,

Sandbox:

The wood used for the sandbox.

= 11 x 21

= 231 inches

The remaining wood.

= 262 - (21 + 231)

= 262 - 252

= 10 inches

Thus,

The remaining wood is 10 inches.

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Answer:

B. 10x -40

Step-by-step explanation:

To rewrite the expression 5(2x-8) using the distributive property, we need to separate the expression inside the parentheses and then multiply the two expressions by 5. The answer is: 10x-40.

Answer: 8 x + 5 y + 1

8x+5y+1

so that would be B)

Answer:

pretty sure it's B. Let me know if im wrong

Step-by-step explanation:

Therefore the value of x is less than 4 when x is in the inequality 3x + 2 < 14 and greater than -3 when x is in the inequality 2 x-5> -11

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. For instance, let's say you have 225 and want to purchase a new bicycle that costs $250.

Expressions are carried out, or evaluated, in order to yield a value. In an evaluation process, values of expressions can be employed as components of surrounding expressions.

To solve for x in the inequality 3x + 2 < 14, we can begin by subtracting 2 from both sides to get 3x < 12. Then, dividing both sides by 3 gives x < 4.

To solve for x in the inequality 2 x-5> -11, we can begin by adding 5 to both sides to get 2x> -6, then divide both sides by 2 to get x > -3

So x can be any number greater than -3 and less than 4

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In order to win his master's tournament, William needs to make the most of his strengths and use the strategies that best suit his playing style.

Mathematics is the study of numbers, shapes, and patterns. It is a universal language that helps us to understand and describe the world around us. Math is used to solve problems and to make predictions. It is used to analyze data and to make decisions. Math is a powerful tool that allows us to communicate ideas and to make sense of the world. Math helps us to understand the physical laws that govern the universe and to make sense of our ever-changing world.

First and foremost, he needs to focus on improving his technical skills. He should practice using a variety of shots and playing on different surfaces. This will give him the confidence and control he needs to succeed.

William should also develop a strategy for each match. This should include analyzing his opponent’s playing style and strengths, understanding the court conditions, and setting a specific set of goals for each game. He should also practice mental conditioning to help him stay focused and be able to handle the pressure.

Finally, William should take care of his physical health. This includes getting enough sleep, eating healthy, and exercising regularly. He should also make sure he is properly hydrated and fueled during the tournament.

By taking the necessary steps and making the most of his strengths, William can put himself in a good position to win the tournament. With hard work and dedication, he can make his dream a reality.

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In order to win his master's tournament, William needs to make the most of his strengths and use the strategies that best suit his playing style.

Mathematics is the study of numbers, shapes, and patterns. It is a universal language that helps us to understand and describe the world around us. Math is used to solve problems and to make predictions. It is used to analyze data and to make decisions. Math is a powerful tool that allows us to communicate ideas and to make sense of the world. Math helps us to understand the physical laws that govern the universe and to make sense of our ever-changing world.

First and foremost, he needs to focus on improving his technical skills. He should practice using a variety of shots and playing on different surfaces. This will give him the confidence and control he needs to succeed.

William should also develop a strategy for each match. This should include analyzing his opponent’s playing style and strengths, understanding the court conditions, and setting a specific set of goals for each game. He should also practice mental conditioning to help him stay focused and be able to handle the pressure.

Finally, William should take care of his physical health. This includes getting enough sleep, eating healthy, and exercising regularly. He should also make sure he is properly hydrated and fueled during the tournament.

By taking the necessary steps and making the most of his strengths, William can put himself in a good position to win the tournament. With hard work and dedication, he can make his dream a reality.

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On solving the provided question, we can say that - the equation, 21 = xy; 40 = [tex]x^2-y^2[/tex] x= 2 and y = 2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

21 = xy;

40 = [tex]x^2-y^2[/tex]

x= 2

and

y = 2

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Answer:

  cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)

Step-by-step explanation:

You want cos(x -π/3) written in terms of sine and cosine.

The formula for the cosine of the difference between two angles is ...

  cos(a -b) = cos(a)cos(b) +sin(a)sin(b)

We have a=x, b=π/3, so the desired function is ...

  cos(x -π/3) = cos(x)cos(π/3) +sin(x)sin(π/3)

We know that ...

so the rewrite is ...

  cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)

Therefore , the solution to the given problem of arithmetic mean comes out to be 1. 105, 2. 234 and 3. 42.5

The combination of the amount of all of the values in a list and the number of items in the that list, split by both, is the arithmetic average or mean of the group. The mathematical progression is same to this. This mean of the digits 5, 7, and 9 is 4,

For example, as expression 5 + 7 + 9 is 21, and 21 divided by 3 [there are actually three numbers] equals 7.

Given:

1) There are six terms in AP, with terms a and d each being worth five points.

2) There are 6 terms in AP, with terms 9 and 12 respectively.

3) In AP, there are five terms, where an is 5.7 and d is 1.4.

4) In AP, = 20, t21 = 400

5) In AP, t100 = 99 and a = 0

Find the sum of the terms in the arithmetic series.

As is common knowledge, Sn in the AP equals n/2[2a+(n-1)d]

To determine: the total terms in the arithmetic series

The AP sum of n words is well known. Sn = (n-1)/2[2a+(n-1)d]

1) There are 6 terms in the case where a = 5 and d = 5, as shown by S6 = [2(5)+(61)5] = 3[10+5(5)] = 3[10 + 25] = 3(35) = 105

2) There are 6 terms in the case where a = 9 and d = 12, where S6 = [2(9)+(61)12] = 3[18+5(12)] = 3[18+60] = 3(78) = 234

3) There are 5 terms total, with terms a = 5.7 and d = 1.4.

S5= [2(5.7)+(5—1)1.4] = 2.5[11.4+4(1.4)] = 2.5[11.4+5.6] = 2.5(17) = 42.5

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Answer:

32 is 32% of 100

Step-by-step explanation:

Answer: 100

Step-by-step explanation: 32 is 32% of 100

Answer:

10

Step-by-step explanation:

50 students.

20% = 20/100 = 1/5

50*1/5 = 10

There are 10 left-handers.

Answer:

GCF of 12 and 100 by Prime Factorization

Prime factorization of 12 and 100 is (2 × 2 × 3) and (2 × 2 × 5 × 5) respectively. As visible, 12 and 100 have common prime factors. Hence, the GCF of 12 and 100 is 2 × 2 = 4.

GCF of 12 and 100 by Listing Common FactorsFactors of 12: 1, 2, 3, 4, 6, 12Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 3 common factors of 12 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 100 is 4.

The center of the circle is (-10,4) and the radius is 10.

The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The equation of the circle is,

( x - h )² + ( y - k )² = r²

(x+10)² + (y−4)² = 100

(x+10)² + (y−4)² = 10²

Compare the equations and find the center and radius,

Center = ( h,k) = ( -10,4)

Radius = r = 10

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Answer:

this should help you out