What term should be inserted in m² +........+ 1/m² it a perfect square? ​

Answers

Answer 1

Answer: The given expression is:

m² +........+ 1/m²

We can notice that the expression has an even number of terms, and the first and last term are perfect squares, which suggests that it might be possible to write the expression as the square of a binomial.

Let's try to write the expression in the form of (a + b)²:

(a + b)² = a² + 2ab + b²

If we set a = m and b = 1/m, we get:

(a + b)² = m² + 2(m)(1/m) + (1/m)² = m² + 2 + 1/m²

Comparing this with the given expression, we see that it is the same as the given expression with 2 added to it.

Therefore, to make the given expression a perfect square, we need to add 2 to it.

So, the term to be inserted is 2.

The expression m² +........+ 1/m² can be written as (m + 1/m)² - 2.

Step-by-step explanation:


Related Questions

The answer to this question?

Answers

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.

Leo replaces the strings on some guitars. He puts 6 new strings on Each guitar. He uses 18 strings. How many guitars does leo put Strings on?

Answers

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

Explain about the division of the number?

Multiplication has been the opposite of division.

If 3 groups of 4 add up to 12, then 12 split into three sections of equal size comes in 4 in each group. Producing equal groups or determining how many people constitute each group after a fair distribution is the basic objective 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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A charge 5. 00 nc is placed at the origin of an xy-coordinate system, and a charge -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.

Answers

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 average of your first 6 tests is 82. If your test average after your seventh test is an 80. 5, what did you score on the seventh test?.

Answers

The score on the seventh test is 71.5

"Information available from the question"

The average of your first 6 tests is 82.

If your test average after your seventh test is an 80. 5

To find the score on the seventh test.

Now, According to the information:

Average of 6 test is 82

We know that :

Average = Sum of all test / Total no. of test => 82 =  Sum of all test / 6

Sum of all test = 492

Let the seventh test be 'x'

So, Sum of seventh test is = 492 + x

Average = [tex]\frac{492+x}{7}[/tex]

80.5  = [tex]\frac{492+x}{7}[/tex]

=> 80.5 × 7 = 492 + x

x =  (80.5 × 7) - 492

=> x = 563.5 - 492

x = 71.5

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Each student in a math class has to buy the items in the table. Write an expression in simplest form that represents the
total cost for x students.
Item
Calculator
Notebook
Pack of pencils
11.55
9.65x+0.65x+1.25x
11.55x
x(9.65+0.65+1.25)
Cost
$9.65
$0.65
$1.25

Answers

The expression in simplest form that represents the total cost for x students is 11.55x, the correct option is C.

What is an expression?

Expression in mathematics can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that a student in a math class has to buy the items in the table.

Now,

x(9.65+0.65+1.25)

=9.65x+0.65x+1.25x

=11.55x

Therefore, the expression in simplest form will be 11.55x.

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can someone help me with this question the letter a b or c or d

Answers

Answer:

The answer is D

Step-by-step explanation:

because u need to divide the y and x and when u do it to all of them u will get the same ratio which is 4

Help for those questions please

Answers

The evaluation of the expressions are shown below

How to evaluate the expressions

To determine the solution to the expressions, we make use of laws of indices and exponents

Expression 1 (a) and (b)

(27)^(-4/3) ÷ (1/64)^(2/3) = (3^3)^(-4/3)  ÷ (1/4^3)^(2/3)

(27)^(-4/3) = (3)^(-4)  ÷ (1/4)^(2)

(27)^(-4/3) = 1/81 ÷ 1/16

So, we have

(27)^(-4/3) = 16/81

Next, we have

(32)^(2/5) - (-125)^(-1/3) = (2^5)^(2/5) - (-5^3)^(-1/3)

(32)^(2/5) - (-125)^(-1/3) = (2)^(2) - (-5)^(-1)

(32)^(2/5) - (-125)^(-1/3) = 4 + 1/5

(32)^(2/5) - (-125)^(-1/3) = 21/5

Equation (2)

Here, we have

3(8/27)^(-2/3) = 2^x/3^y

So, we have

3(3/2)^(2) = 2^x/3^y

So, we have

3^3/2^2 = 2^x/3^y

By comparison, we have

x = -2 and y = 3

Equation (3)

Here, we have

3^x(9^[1 - x]) = 27^[x + 2]

So, we have

3^x(3^2[1 - x]) = 27^[x + 2]

This gives

3^(x + 2[1 - x]) = 3^3[x + 2]

By comparison, we have

x + 2[1 - x] = 3[x + 2]

So, we have

x + 2 - 2x = 3x + 6

Evaluate

4x = -4

x = -1

Equation (4)

Here, we have

(5^x)^2x = 25(1/125)^x

So, we have

(5)^2x^2 = 5^[2 - 3x]

By comparison, we have

2x^2 = 2 - 3x

So, we have

2x^2 + 3x - 2 = 0

Evaluate

x = -2 and x = 1/2

Equation (5)

Here, we have

2^x+1 + 2^3-x = 10

Here, we make use of a graphing tool

So, we have

x = 0 and x = 2

Expression (6)

Here, we have

√16^x+2

Express 16 as 2^4

So, we have

√16^x+2 = √2^4[x+2]

Take the square roots

√16^x+2 = 2^2[x+2]

Open the bracket

√16^x+2 = 2^2x+4

Hence, the expression is 2^2x+4

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a positive divided by a negative become?

Answers

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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Find The Value Of X.

Answers

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

What are the 5 most common Pythagorean triples?

Answers

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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what should a good residual plot look like if the regression line fits the data well?

Answers

A good residual plot should have the points randomly scattered around the horizontal line with no discernible pattern.

This indicates that the model is well fit to the data. The residuals should also be equally distributed on either side of the horizontal line. This can be seen as the sum of the residuals being equal to 0, or mathematically expressed as the sum of the residuals (e) being equal to 0, where [tex]e = y - ŷ[/tex], where y is the observed value and ŷ is the predicted value. The equation can be expressed as Σe=0.

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THIS IS AREA OF A TRIANGLE

area is 14ft²
hight is 6ft
whats base???​

Answers

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

What is area of a triangle?

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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Here’s another…23+18w=-21+14w

Answers

Answer: -11

Step-by-step explanation:

the answer would be -11

Please help me. I am inept when it comes to math. thx

Answers

Note that the proof required is given based on the AA Similarity Postulate.

What are the definition of terms used in this solution?

Similar triangles: If two triangles are similar then their corresponding angles are equal.

By the transitive property of equality if a = b, and b= c then a = c.

AA postulate of similarity states that when two corresponding angles of two triangles are equal then they are called similar to each other.

Given ΔABC ~ ΔRST; and

ΔDEF ~ ΔRST

To Prove: ΔABC ~ DEF Note that:

ΔABC ~ ΔRST - Given

ΔDEF ~ ΔRST
- Given

∠A  = ∠R, ∠D = ∠R - Definition of Similar Triangles

∠C = ∠T, ∠F = ∠T

∠A= ∠C, ∠D = ∠F  - Transitive property of Equality; Thus,

ΔABC ~ Δ DEF (AA Similarity Postulate)

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i need to find x. please show the work aswell

Answers

Answer:   x = -7

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

(-2,1) (-8,-5) round nearest tenth

Answers

The slope of line from the points given is 1

What is the slope of line

The slope of a line is a measure of how steep the line is and the direction it is going. In mathematical terms, it is defined as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. Slope is often represented by the letter "m". If (x₁, y₁) and (x₂, y₂) are two points on the line, the slope can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

In this problem, we can take the two points and calculate the slope.

m =  (y₂ - y₁) / (x₂ - x₁)

Substituting the values into the formula to find the slope;

m = -5 - 1 / -8 - (-2)

m = 1

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Complete Question; Calculate the slope of the line (-2, 1) and (-8, -5)

how to find focus of parabola

Answers

(h, k+1/4a) are the coordinates for the focus of parabola. And the standard form is (x - h)2 = 4p (y - k).

To get the focus of a parabola, you must be aware that the equation of a parabola in a vertex form is y=a(xh)2+k, where a denotes the slope of the equation. The center of the parabola is at (h, k+1/4a), according to the formula. The focal point of the parabola is its axis. The centre of a parabola is 'a' units away from the vertex. The vertex and the focus are positioned on the parabola's axis, which you may identify using the equation for the parabola.

The axis of the parabola with a second-degree x equation is the y axis, or a line parallel to it, whereas the axis of the parabola with a second-degree y equation is the x axis, or a line parallel to it.

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which expression cannot be factored using real numbers?

x^3+1
x^6+8
x^8-2
x^8-1

Answers

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

What polynomial cannot be factored using real numbers?

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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If 3/(x + 2) = (y + 3)/2 and x and y are integers, what is the sum of all possible values of x?

Answers

Answer:

X = 6/ y+3 - 2

and

Y -3x/x+2

Step-by-step explanation:

hope this helps

Gracie deposited $20,000 into an account that compounds interest weekly at a rate of 1.56%. Each week, her bank withdraws $200 from the account and puts that amount into her mortgage account. How long will it take until the account has a balance of $0? Round to the nearest tenth of a year.

Answers

It takes 2 years for the account balance to come down to 0.

What is the compound interest?

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, principal =$20,000, rate of interest =1.56%, n=52 and W=$200.

Use the formula, [tex]P=W\frac{1-(1+\frac{r}{n})^{-nt} }{\frac{r}{n} }[/tex]

[tex]20000=200\frac{1-(1+\frac{0.0156}{52})^{-52t} }{\frac{0.0156}{52} }[/tex]

[tex]100=\frac{1-(1+0.0003)^{-52t}}{0.0003}[/tex]

[tex]0.03=1-(1.0003)^{-52t}[/tex]

[tex]0.97=(1.0003)^{-52t}[/tex]

Take log on both the side, we get

-52t·log(1.0003)=log0.97

So, t=2 years

Therefore, it takes 2 years for the account balance to come down to 0.

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For a large sporting event the broadcasters sold 61 ad slots for a total revenue or $157 million. What was the mean price per as slot?
The mean price per ad slot was $______ million.
Round to one decimal place as needed

Answers

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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Someone please help me!!​

Answers

Answer:

84 units

Step-by-step explanation:

The darkest shaded face has 12 full units. Times that by the width or the lightest shade area (7) you get the answer 84 units.

12(7) = 84

4 divided by an eighth

Answers

Answer:

32

Step-by-step explanation:

The original cost of a shirt is $40. A store manager marks up the cost by 20% to get
the selling price. During a sale, the store manager marks down the cost of the shirt
by 20%. What is the percent change from the original cost to the sale price? Is this
a percent increase or a percent decrease? Show your work.

Answers

Answer:

Step-by-step explanation:

Ans:percentage increased by 20

Gross profit/Cost of sales=20percent

Gross profit=20percent x cost of sales

Sales=120percent x cost of sales

Sales=120x40

        =$48

48-40=$8

8/40x100percent=20percent

Answer: Decrease? not 100% sure

Step-by-step explanation:

Please help
7f=$51.80
find f

Answers

Answer:

7.40

Step-by-step explanation:

51.8 divided by 7 is 7.4

select all expressions that are equivalent to 2to the power of 4 / ((3.2 x 0.8) + 1.44)

Answers

The value of the given expression will be 4.


What is an expression?

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that the expression is 2⁴ / ( 3.2 x 0.8 0 + 1.44 ). SOlve the expression as below,

E = 2⁴ / ( 3.2 x 0.8 ) + 1.44 )

Solve the denominator by mathematical operation.

E = 16 / ( 2.56 + 1.44 )

Divide the numerator by denominator,

E = 16 / 4

E = 4

Therefore, the solution of the expression is 4.

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Given an integer representing a 10-digit phone number, output the area code, prefix, and line number using the format (800) 555-1212.

Answers

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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015 Chapter 1: Perimeter and Area in the Coordinate Plane > Section Exercises 1.4> Exercise 8
8
Find the perimeter of the polygon with the vertices Q(-3, 2), R(1, 2), S(1,-2), and T(-3,-2)
The perimeter is
units

Answers

The perimeter of the polygon with vertices Q(-3, 2), R(1, 2), S(1,-2), and T(-3,-2) is 16 units.

What is the perimeter?

Perimeter is a circumferential measure of the figure, for example, the perimeter of a square is the sum of all its sides.

Here,

To find the perimeter of a polygon, we need to add up the lengths of all its sides. In this case, we have a quadrilateral with vertices Q(-3, 2), R(1, 2), S(1,-2), and T(-3,-2).

We can use the distance formula to find the lengths of each side:

Length of QR = √[(1 - (-3))² + (2 - 2)²] =  4

Similarly,

Length of RS= 4

Length of ST= 4

Length of TQ= 4

Therefore, the perimeter of the polygon is 4 + 4 + 4 + 4 = 16

So the perimeter of the polygon with vertices Q(-3, 2), R(1, 2), S(1,-2), and T(-3,-2) is 16 units.

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solve the equation ab=bc for A, a, assuming that a, b, and c are square matrices and b is invertible.

Answers

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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Alan makes the statement about the intersection point of a system of inequalities. Explain why Alan’s statement is incorrect.

The intersection point is always a solution to a system of
inequalities because that is where the two lines meet

Answers

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.

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