The 100th derivative of P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷) will be zero.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
A polynomial,
P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷).
To find the degree:
(x⁷)¹⁰(x²)¹¹(x⁷) = x⁹⁹.
The polynomial has a degree of 99.
If we think about it intuitively,
Therefore, if we were to multiply it all out,
the leading word would be x⁹⁹.
The term's first derivative is 99x⁹⁸,
followed by 99(98)x⁹⁷,
and 99(98)(97)x⁹⁶.
And finally,
the 99th derivative is 99×98×97×96×...4×3×3×2×1× (x⁰)
=99!
So, the 100th derivative will be zero.
Therefore, by the 100th derivative, all terms will cancel out.
100th derivative will be zero.
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How can m2n2-25 be factored?
Answer:
(mn+5)(mn-5)
Step-by-step explanation:
This is a difference of squares as m^2n^2 = (mn)^2. So it cna be turned into the form a^2-b^2 = (a+b)(a-b) or in our case (mn+5)(mn-5).
8x-3y=11
Solving for Y
Answer:x=13
Step-by-step explanation:
let f be a function defined on the closed interval -5 find all values x at which f has a relative maximum. justify your answer
The values for x at which f has a relative maximum are -3 and 4.
A relative maximum is a point on a function where the function has the highest value within a certain interval or region. It is a local maximum, meaning that it is the highest value within a certain interval, but it may not be the highest value overall.
For example, a function may have multiple relative maxima but only one global maximum.
It's important to note that a relative maximum is not always an actual maximum, it's only a maximum in a specific interval or region of the function.
It's also important to note that for some functions, there might not be any relative maximum in the interval or domain where the function is defined, and for others, it might have a relative maximum at the endpoint of the interval.
On plotting the zeroes of the f(x) on the number line we observe the value of the derivative of f(x) changes from positive to negative indicating points of relative maximum.
Therefore, The values for x at which f has a relative maximum are -3 and 4.
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Given that x, y, and z are real numbers that satisfy:and that x+y+z = \frac{m}{\sqrt{n}}, where m and n are positive integers and n is not divisible by the square of any prime, find m+n.
m+n is equal to (x+y+z)^2 + n x, y, and z are real numbers.
First, we can rewrite x+y+z as n(x+y+z)^2.
Then, we can substitute x^2+y^2+z^2 into the equation and solve for m^2. We get m^2 = (x+y+z)^3 - 3xyz, which can be simplified to
m^2 = (x+y+z)(x^2+y^2+z^2-xyz).
We can substitute the original equation back in to get
m^2 = (x+y+z)\frac{m^2}{n}.
Then, we can divide both sides of the equation by (x+y+z) to get m^2 = \frac{m^2}{n}. Finally, we can solve for m+n by multiplying both sides of the equation by n, which gives us m+n = m^2.
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Jeremiah has slept one hour this week. He will sleep 2 hrs per night. How many days will he have slept in 49 hrs?
Answer:
24.5 days i believe
What is the value please help me do this I’ll put brainliest for the first person to answer it correctly
The square root of 6^2 (√6²) is 6.
What is square root?
Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.
Suppose x is the square root of y, then it is represented as x=√y, or we can express the same equation as x^2 = y. Here, ‘√’ is the radical symbol used to represent the root of numbers. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.
For example, the square of 3 is 9, 32 = 9 and the square root of 9, √9 = 3. Since 9 is a perfect square, hence it is easy to find the square root. But for an imperfect square like 3, 7, 5, etc., we have to use different methods to find the square root.
Now ,
given expression √6²
=√36
square root value of √6² =6
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The square root of 6^2 (√6²) is 6.
What is square root?
Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.
Suppose x is the square root of y, then it is represented as x=√y, or we can express the same equation as x^2 = y. Here, ‘√’ is the radical symbol used to represent the root of numbers. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.
For example, the square of 3 is 9, 32 = 9 and the square root of 9, √9 = 3. Since 9 is a perfect square, hence it is easy to find the square root. But for an imperfect square like 3, 7, 5, etc., we have to use different methods to find the square root.
Now ,
given expression √6²
=√36
square root value of √6² =6
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Explain whether rounding or compatible numbers gives a closer estimate for the product below. 48 x 123 = 5,904
Comparing rounding and compatible number, rounding gives a closer estimate than compatible number.
What are compatible or rounded numbers?While compatible numbers are those that are simple to multiply mentally, rounding entails reducing one or both of the numbers to a close "friendly" number.
Estimating the result of 48 x 123 can be done using compatible integers and rounding.
Which numbers can be used to estimate the product?Compatible numbers make it simpler to find an estimate calculation because they are close in value to the real number. A multiplication issue is presented here. By rounding the values to the closest hundreds place, you can obtain an approximation of the product. 400 and 100 are equivalent to 395 and 103.
1) Using compatible numbers :
48 = 50
123 = 100
50 × 100 = 5000
2) By rounding numbers :
48 = 50
123 = 120
50 × 120 = 6000
6000 is closer to the actual value of the product than 5000 ;
Therefore, rounding gives a closer estimate than compatible number.
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describe using words, and no equations, what the function f does to vectors. you may find it helpful to probe the behavior of f(v) for concrete fixed vectors c and draw some pictures. your answers to parts (c) and (d) should also prove useful.
A transformation is applied to the input vector v by the function f. This transformation might include extending, rotating, or reflecting the vector in a certain way, depending on the precise shape of the function.
We may enter certain fixed vectors into the function, c, and watch as f transforms them to better understand its behavior (c). It may also be helpful to see the modified vectors as images or diagrams to have a better understanding of how the function behaves.
The term "vector" is used informally to describe constituents of particular vector spaces or some values that cannot be described by a single integer.
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the vector is a linear combination of the vectors and if and only if the matrix equation has a solution , where and .
The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.
We first thought of a matrix as a rectangular array of numbers. When the number of rows is m and columns is n, we say that the dimensions of the matrix are m×n.
A vector is most simply thought of as a matrix with a single column. There are two operations we can perform with vectors: scalar multiplication and vector addition. Both of these operations have geometric meaning.
Given a set of vectors and a set of scalars we call weights, we can create a linear combination using scalar multiplication and vector addition.
The product of two matrices can be seen as the result of taking linear combinations of their rows and columns. This way of interpreting matrix multiplication often helps to understand important results in matrix algebra.
The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.
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The following pie chart shows how a worker spent his December 1990 salary. Rent charges were GH80.00. How much did the workersave? ary www.a 5) What fraction of on food? How much did he spend on food? a) Find b) Find durin c) Wha 10.) The
According to the pie chart given -
a) The worker saved GH¢ 20.00.
b) 2/5 fraction of worker's salary was spent on food.
c) The worker spent GH¢ 120.00 on food.
What is a pie chart?
One sort of graph that illustrates the information in the circular graph is a pie chart. It is a sort of graphical representation of data where the slices of pie depict the relative sizes of the data. A list of numerical and categorical variables is necessary for a pie chart. Pie in this context refers to the entire thing, and slices to its component portions.
The rent charges is = GH¢ 80.00
The savings can be obtained by ratio method -
Savings is depicted by 24° and rent by 96° in the pie chart.
So, the ratio will be 24/96.
Then the savings value will be -
(24/96) × 80
(1/4) × 80
20
Therefore, the savings value is GH¢ 20.00.
The total angle of pie chart is 360°.
Savings is depicted by 24°, rent by 96°, entertainment by 48° and clothing by 48° in the pie chart.
The angle for food will be -
360° - (24° + 96° + 48° + 48°)
360° - 216°
144°
Now the fraction that is for food -
144/360
2/5
Therefore, food covers 2/5 part of pie chart.
The amount spent on food can be obtained by formula of angle sector -
(144/96) × 80
1.5 × 80
120
Therefore, money for food was GH¢ 120.00.
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is there a theoretical limit to the order of the spectrum you would be able to observe with your diffraction grating? justify you answer mathematically
In general, the maximum order of the spectrum that can be observed with a diffraction grating is limited by the grating equation.
This equation states that mλ = d(sinθi - sinθr), where m is the order of the diffraction, λ is the wavelength of light, d is the spacing between the grating lines, θi is the angle of incidence, and θr is the angle of diffraction. Since d is fixed and θi is typically kept constant, the maximum order of the spectrum that can be observed is limited by the angle of diffraction (θr). This angle can be calculated using the equation θr = sin-1[(mλ/d)+sinθi]. Thus, the maximum order of the spectrum is limited by the value of θr, which is determined by the wavelength of light and the spacing between the grating lines.
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shown below is a clock face with no hands. what is the degree measure of the smaller angle formed by the hands of a clock at $10$ o'clock?
The degree measure of the smaller angle formed by the hands of a clock at 10 O'clock is 60°.
The degree measure of a full circle is 360 degrees. The clock face is divided into 12 equal parts, or 30-degree increments, for the hours. At 10 o'clock, the hour hand would point to the 10 on the clock face, and the minute hand would point to the 12.
This makes them 1/6th of a circle apart, and (1/6) * 360° = 60°.
The angle between the two hands would be formed by the distance between the 10 and the 12, which is 60 degrees.
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A family spends of its monthly budget on groceries and eating out. If the family's monthly budget is $6012, how much is spent on groceries and eating out?
Estimate the amount the family spent on groceries and eating out per month: $
The family spent $ per month on groceries and eating out.
How much will the family spend on groceries and eating out in 5 months? S
The family spent $2004 per month on groceries and eating out.
The amount spent in five months is given as follows: $10,020.
How to obtain the amounts?The amounts are obtained applying the proportions in the context of this problem.
The monthly budget is given as follows:
$6012.
1/3 of that is spent in groceries and eating out, hence the amount is of:
1/3 x 6012 = $2004.
Hence in five months the amount spent is going to be of:
5 x 2004 = $10,020.
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Consider the triangles shown below. Which of the following would also need to be true in order to prove that ΔABD≅ΔABC
To prove that triangles ABD and ΔABC are congruent by SSS, what needs to be true is: A. BC ≅ BD.
What is the SSS Congruence Theorem?For two triangles to be congruent to each other by the SSS Congruence Theorem, the triangles must have three pairs of corresponding sides that are congruent to each other.
In the image given, we can deduce that the two triangles have the following properties:
AB ≅ AB (reflexive property)
AC ≅ AD (given)
This means that have two pairs of corresponding congruent sides. Therefore, in order to prove that ΔABD ≅ ΔABC by SSS, what needs to be true is: A. BC ≅ BD.
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example of a function $f$ with domain $\mathbb{r}$ that is continuous nowhere, but where $|f|$ is continuous on all of $\mathbb{r}$.
An example of such a function can be f(x) { 1 x∈Q
-1 x∈ R\Q}
A function in mathematics is like a machine that takes input and gives output. There is always a limit for output also called the range or image of the function.
A function has two values output and input. The limit within which input is defined is called the domain or pre-image of the function.
A function is represented as f(x) i.e., f of x or function of x. The input and output have a relation defined for them
A function must follow two rules they are:
It must work for every possible input valueAnd it has only one relationship for each input valueTo know more functions visit:
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Hue is arranging chairs. She can form 2 rows of a given length with 3 chairs left over, or 8 rows of that same length if she gets 15 more chairs. Complete the equation and solve it to find how many chairs are in that row length.
Answer: If Hue can form 2 rows of a given length with 3 chairs left over, we can represent this as:
2x + 3 = chairs in that row length
Also, if she can form 8 rows of that same length if she gets 15 more chairs, we can represent this as:
8x + 15 = chairs in that row length
Since the number of chairs in that row length is the same in both equations, we can set them equal to each other:
2x + 3 = 8x + 15
To solve for x, we can subtract 3 from both sides:
2x = 8x + 12
Then we can subtract 2x from both sides:
6x = 12
Finally, we can divide both sides by 6:
x = 2
So the number of chairs in that row length is 2x + 3 = 2(2) + 3 = 7.
Step-by-step explanation:
8.8x109
————-
2.2 x10-3
The division of the value 8.8x10^9 and 2.2 x10^-3 in standard form is 4*10^12.
How can the division be made?The concept that will be used here is division. One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.
To simplify the values 8.8x10^9/2.2 x10^-3, the we can write as
8.8/2.2 *10^9*10^3
=4*10^12
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complete question:
simplify 8.8x109/2.2 x10-3
Let T be an linear transformation from Rr to Rs. Let A be the matrix associated to T.
Fill in the correct answer for each of the following situations.
1. Every row in the row-echelon form of A has a pivot.
2. Two rows in the row-echelon form of A do not have pivots.
3. The row-echelon form of A has a pivot in every column.
4. The row-echelon form of A has a row of zeros.
A. T is onto
B. T is not onto
C. There is not enough information to tell.
Note: The row echelon form of a matrix is a way of putting it in a specific form, in which all the leading entry of a non-zero row is to the right of the leading entry of the row above it, and all the entries below a leading entry are zero. A pivot is the leading entry of a non-zero row. In a matrix in row echelon form, the number of pivots is equal to the rank of the matrix, which is the number of linearly independent rows or columns. A matrix with a pivot in every column is said to be in reduced row echelon form, and it is unique for a given matrix.
Linear Transformation Matrix PropertiesA linear transformation is a function that maps a vector from one vector space to another vector space. The matrix associated with this transformation is a way of representing the linear transformation using a matrix. The row echelon form of the matrix is a specific way of arranging the matrix, where all the leading entry of a non-zero row is to the right of the leading entry of the row above it, and all the entries below a leading entry are zero. The properties of the transformation can be determined by analyzing the row echelon form of the matrix.
For example, if the row echelon form of the matrix has a pivot in every column, it means that the transformation is one-to-one (meaning that the function assigns a unique output for each input). On the other hand, if the row echelon form of the matrix has a pivot in every row, it means that the transformation is onto(meaning that the function's range is equal to the output vector space). If there are zero rows in the row echelon form of the matrix, it means that the transformation is not one-to-one.
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Simplify the expression (12x-13)-2(3x+5)
Answer: The simplified expression is 6x - 23
Step-by-step explanation: To simplify the expression (12x-13)-2(3x+5) we will follow the order of operations:
First, we simplify the inner parentheses: 2(3x+5) = 6x + 10
Next, we substitute this simplified version back into the original expression: (12x-13)-(6x+10)
Now we can simplify the expression by combining like terms: 12x-13-6x-10 = 6x - 23
So the simplified expression is 6x - 23
Answer:6x-23 this your answer to simplify the expression I hope this helps have a good day
Step-by-step explanation:
(12x-13)-2(3x+5)
Remove unnecessary parentheses
12x-13-2(3x+5)
then do this
distribute -2 through the parentheses
12x-13-6x-10
Collect like terms which something like this
6x-13-10
then last thing you do is
Calculate the difference which is like this
6x=23
Hi, can someone help me find the circumference of these circles, and explain if you can.
Problem 22
The smaller inner circle has a radius of r = 5. That will be plugged into the circumference formula below.
C = 2pi*r
C = 2pi*5
C = 10pi
This is the exact distance around the circle in terms of pi. Think of it like the amount of fencing you need to enclose the circle.
If you want an approximate perimeter, then use something like pi = 3.14
So 10pi = 10*3.14 = 31.4 cm is the approximate perimeter aka circumference of the smaller circle.
-------------
The larger circle is the same idea. The radius is r = 5+5 = 10 cm
C = 2pi*r
C = 2pi*10
C = 20pi .... exact circumference
C = 20*3.14
C = 62.8 ... approximate circumference
Use more decimal digits of pi to get a more accurate value.
===================================================
Problem 23
The smaller circle has a diameter of 9 ft, which means the radius is r = 9/2 = 4.5 ft
C = 2pi*r
C = 2pi*4.5
C = 9pi .... exact circumference
C = 9*3.14
C = 28.26 .... approximate circumference
The units of the circumference are in feet
-------------
The larger circle has radius r = 4.5+2.5 = 7 ft
C = 2pi*r
C = 2pi*7
C = 14pi .... exact circumference
C = 14*3.14
C = 43.96 .... approximate circumference
===================================================
Problem 24
The larger circle has radius 22. This radius is the diameter of the smaller circle.
So the smaller circle has radius 22/2 = 11
C = 2pi*r
C = 2pi*11
C = 11pi .... exact circumference
C = 11*3.14
C = 34.54 .... approximate circumference
The circumference units are "meters".
-------------
Now onto the larger circle
C = 2pi*r
C = 2pi*22
C = 44pi .... exact circumference
C = 44*3.14
C = 138.16 .... approximate circumference
A furniture store in Livingston purchased an arcade
machine at a cost of $993 and marked it up 200%. Later
on, Nicholas bought the arcade machine. If the sales tax
in Livingston is 14%, how much did he pay in all?
They marked it up to 2979 since 993*3(aka 200%). You then multiply 2979 by 1.14 to get the total of $3396.06
Answer:
$3396.06
Step-by-step explanation:
Markup is what a store adds to the price they paid in order to come up with a selling price.
store selling price = cost to store + markup
Store purchase price: $993
Store markup of 200%: 200% of $993 = 2 × $993 = $1986
Store selling price: $993 + $1986 = $2979
14% tax: 14% of $2979 = 0.14 × $2979 = $417.06
Total selling price including markup & sales tax: $2979 + $417.06 = $3396.06
Answer: $3396.06
Lorinda has started to think about saving for retirement. She reads a recommendation that says she should
save at least 3/10 of her income because she is over 40 years old. Lorinda makes $58,000 a year. How much
should she save in one year according to this recommendation?
The amount to save according to the recommendation of 3/10 of income is $17400.
What are fractions?In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.
Given that the amount made in a year is $58,000.
The recommended savings is 3/10 thus:
(58000) (3/10) = 17400
Hence, according to the recommendation the amount that needs to be saved in one year is, $17400.
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Reciprocity and Reciprocal Theorems: Prove these two theorems (which are written in Lecture Notes 2). Hint: write the condition of F(x, y, z) 0 into explicit forms x-x(y,x) or z-z(x,y), you can then calculate their differentials, manipulate the terms, to get those theorems.
The partials ∂y/∂x = 1 and ∂z/∂x = -1, so we get the Reciprocal Theorem.
Reciprocity Theorem: Let F(x, y, z) be a continuous function of x, y, and z, then we have
∂F/∂x = (∂F/∂y)x - (∂F/∂z)y
This is proven by writing the condition of F(x, y, z) = 0 into explicit forms x-x(y,z) or z-z(x,y). Then from the chain rule, we have
∂F/∂x = (∂F/∂y)(∂y/∂x) + (∂F/∂z)(∂z/∂x)
And since x = x(y,z) and z = z(x,y), the partials ∂y/∂x = -1 and ∂z/∂x = 1, so we get the Reciprocity Theorem.
Reciprocal Theorem: Let F(x, y, z) be a continuous function of x, y, and z, then we have
(∂F/∂y)x + (∂F/∂z)y = F(x, y, z)
This is proven by writing the condition of F(x, y, z) = 0 into explicit forms x-x(y,x) or z-z(x,y). Then from the chain rule, we have
∂F/∂x = (∂F/∂y)(∂y/∂x) + (∂F/∂z)(∂z/∂x)
And since x = x(y,x) and z = z(x,y), the partials ∂y/∂x = 1 and ∂z/∂x = -1, so we get the Reciprocal Theorem.
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A set of points is shown on the graph.
Which of the following equations is the best model for a line of fit for the data?
Oy-2/3x+7
Oy=-2/3x+7
Oy=1/3x+7
Oy=-1/3x+7
The linear function with a slope of 1/3 and intercept of 7 is defined as follows:
y=1/3x+7.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope.b is the intercept.Considering a slope of 1/3 and intercept of 7, the values of the parameters are given as follows:
m = 1/3, b = 7.
Hence the function is defined as follows:
y = 1/3x + 7.
Missing InformationThe problems asks for the linear function with a slope of 1/3 and intercept of 7.
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___ planning is the process of identifying long-term organizational goals, strategies, and resources.
a. Opportunity b. Preliminaryc. Strategicd. Vertical
Strategic planning is an essential process for any organization that wants to succeed and achieve long-term success. It involves identifying long-term organizational goals, strategies, and resources that will help the organization reach its objectives.
Option C. Strategic planning is the process of identifying long-term organizational goals, strategies, and resources.Strategic Planning: Achieving Long-Term Organizational GoalsThis process requires a comprehensive assessment of the organization's current and future needs, including its strengths and weaknesses, opportunities and threats, and the external environment. Once identified, the organization must develop and implement a plan to achieve its goals and objectives. This involves setting objectives, developing and implementing strategies and tactics, and allocating resources in a way that will maximize the organization's chances of success.
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On average a dog lives 10 years. Your company has created a new dog food full of nutrients and vitamins to extend a dog's life You studied so dogs and tracked how long they lived. At a 5 significance level determine if your new dog food extends the life doglivese 10,15,17,13,14,9,8.7.5,8,15,1724,10,12,15,10,98.7.5,15,14,15,10,5,6,98,18,10,8 7,9,10,15,12,13,149,8.7.5.6,15,17,14,10,12,15) State the Alternative Hypothesis for this test. O Hau 10 years Ha: > 10 years O Haru 10 years O Haru >
The alternative hypothesis for this test would be that the new dog food extends the average lifespan of dogs beyond 10 years.
Mathematically, the alternative hypothesis can be stated as:
Ha: μ > 10, where μ is the population mean of the lifespan of dogs on the new dog food.
In this scenario, the null hypothesis is that the average lifespan of dogs on the new dog food is equal to 10 years, which is the commonly accepted average lifespan of dogs. However, the purpose of the study is to determine if the new dog food can extend the lifespan of dogs beyond this average.
Thus, the alternative hypothesis is that the average lifespan of dogs on the new dog food is greater than 10 years. This is represented mathematically as Ha: μ > 10, where μ is the population mean of the lifespan of dogs on the new dog food.
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Can you guys pls helpp
The numeric value of the expression for this problem is given as follows:
[tex]\sqrt{2} + 1[/tex]
How to simplify the expression?The expression for this problem is defined as follows:
[tex]\frac{4 - 3\sqrt{2}}{(\sqrt[4]{2} - \sqrt[4]{8})^2}[/tex]
Applying the square of the subtraction in the denominator, we have that:
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = \sqrt[4]{4} - 2\sqrt[4]{2}\sqrt[4]{8} + \sqrt[4]{64}[/tex]
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = 4^{\frac{1}{4}} - 2\sqrt[4]{16} + \sqrt[4]{4^3}[/tex]
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = (2^2)^{\frac{1}{4}} - 2 \times 2 + 3[/tex]
[tex]{(\sqrt[4]{2} - \sqrt[4]{8})^2 = \sqrt{2} - 1[/tex]
Hence the simplified expression is given as follows:
[tex]\frac{4 - 3\sqrt{2}}{\sqrt{2} - 1}[/tex]
Rationalizing the denominator, we have that:
[tex]\frac{4 - 3\sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}[/tex]
Applying the subtraction of perfect square, the denominator simplifies to one, hence the value of the expression is given by the numerator as follows:
[tex](4 - 3\sqrt{2})(\sqrt{2} + 1) = 4\sqrt{2} + 4 - 3 \times 2 - 3\sqrt{2}[/tex]
[tex][tex](4 - 3\sqrt{2})(\sqrt{2} + 1) = \sqrt{2} + 1[/tex]
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How many pieces 1 4/5 in. long can be cut from 22 metal rods each 21 in. long? Disregard the waste.
The required number of pieces cut from 22 metal rods each 21 in are 242 pieces.
What is mixed fraction?A mixed fraction is one that is represented by both its quotient and remainder. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
According to question:We have,
1(4/5) = 9/5 ,
So,
21/9/5
105/9
11(6/9)
Now,the waste is 6/9
Number of pieces are 11(22)
= 242 pieces
Thus, required number of pieces are 242.
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The area of the rectangle is 10 5/6in squared. The height is 4 1/3in. What is the length of the base
The length of the base is equal to 13 inches.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
10 5/6 = 4 1/3 × base
65/5 = 13/3b
Length of the base, b = 65/5 ÷ 13/3
Length of the base, b = 65/5 × 3/13
Length of the base, b = 195/65
Length of the base, b = 13 inches.
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2: nes of Best Fit Terms of Uno What is the equation of this trend line? Enter your answers by filling in the boxes. K=J+ ← Vanable K 36 201284 CERRA 132. 0 ● O 4 6 8 10 Variable J 12 14 16 1 2 3 4 5 Next ▸ K12 6
Indicated by a trend line is a linear relationship. Y = mx + b, where x is the independent variable and b is the constant, is the equation for a linear connection.
What is the equation for the best fitting line?Y=mx+b, where m is the slope and b is the y-intercept, can be used to express the equation of a line of best fit. We'll look at two examples that illustrate a scatter plot with a line of best fit to help you grasp the idea of how to generate predictions and approximations of the line of best fit's equation.You may create a trend line by simply drawing a line that follows the current trend on a chart. If you can connect at least two tops or bottoms together when constructing trend lines, that is ideal. The trend line is stronger if there are more connected tops or bottoms.To learn more about variable refer to:
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