Using completion of square find a general solution to ax^(2) + bx + 1 = 0. What are the conditions for both the solutions to be real and for both to be complex numbers.

The answer is 49

To evaluate the given expression, we will use the special product formula for the square of a binomial:

(a+b)^(2)=a^(2)+2ab+b^(2)

In this case, we have:

52^(2)=(5+2)^(2)=5^(2)+2(5)(2)+2^(2)=25+20+4=49

Therefore, the answer is:

52^(2)=49

So, using the special products of algebraic expressions, we can evaluate the given expression to be 49.

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Two famous structures/ inventions showing angles formed by secants and tangents are: The London Eye and The Eiffel Tower.

1. The London Eye: The London Eye is a giant Ferris wheel located on the South Bank of the River Thames in London. It is a popular tourist attraction and an iconic symbol of London. The London Eye has 32 oval-shaped capsules, each of which can carry up to 25 people. The structure is made up of several secants and tangents, which form angles at various points along the wheel.

2. The Eiffel Tower: The Eiffel Tower is a wrought-iron lattice tower located on the Champ de Mars in Paris, France. It is one of the most recognizable structures in the world and a symbol of France. The Eiffel Tower is made up of several secants and tangents, which form angles at various points along the structure.

Both of these structures are examples of how secants and tangents can be used in the design of famous structures and inventions. These angles play a crucial role in the stability and strength of the structures, allowing them to withstand the weight of the people and objects they hold.

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Answer:

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Traffic problems can be solved by implementing various measures such as improving public transportation, promoting carpooling and ridesharing, creating pedestrian-friendly cities, and implementing smarter traffic management systems.

We proceed to explain some actions to solve traffic problems:

Improving public transportation can help reduce the number of cars on the road, thus reducing traffic congestion. This can be done by increasing the number of public buses and trains, as well as improving their reliability and efficiency.Promoting carpooling and ridesharing can also help reduce traffic problems by encouraging people to share rides instead of driving alone. This can be done through incentives such as discounted parking fees for carpoolers and ridesharing apps. Creating pedestrian-friendly cities can also help reduce traffic problems by encouraging people to walk or bike instead of driving. This can be done by implementing bike lanes, pedestrian-only zones, and safer crosswalks. Implementing smarter traffic management systems can help reduce traffic problems by using technology to monitor and control traffic flow. This can be done through the use of sensors, cameras, and smart traffic lights.

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Answer:

-5 - 2sqrt6

Step-by-step explanation:

To simplify (sqrt2+sqrt3)/(sqrt2-sqrt3), we can rationalize the denominator, which involves multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of sqrt2-sqrt3 is sqrt2+sqrt3, so we can multiply both the numerator and denominator by sqrt2+sqrt3:

(sqrt2+sqrt3)/(sqrt2-sqrt3) * (sqrt2+sqrt3)/(sqrt2+sqrt3) = ((sqrt2+sqrt3)(sqrt2+sqrt3))/((sqrt2-sqrt3)(sqrt2+sqrt3))

Expanding the numerator and simplifying, we get:

(sqrt2+sqrt3)^2 / (sqrt2^2 - sqrt3^2)

= (2 + 2sqrt2sqrt3 + 3) / (2 - 3)

= (5 + 2sqrt6) / (-1)

= -5 - 2sqrt6

Therefore, (sqrt2+sqrt3)/(sqrt2-sqrt3) simplifies to -5 - 2sqrt6.

The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).

We have,

To simplify the expression (√2 + √3) / (√2 - √3), we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.

The conjugate of (√2 - √3) is (√2 + √3).

Multiplying the numerator and denominator by (√2 + √3), we get:

[(√2 + √3) x (√2 + √3)] / [(√2 - √3) x (√2 + √3)]

Expanding both the numerator and denominator:

[(√2 + √3)(√2 + √3)] / [√2 x √2 - √2 x √3 + √3 x √2 - √3 x √3]

Simplifying:

[2 + 2√2√3 + 3] / [2 - 3]

Combining like terms:

[5 + 2√6] / [-1]

Since the denominator is -1, we can multiply both the numerator and denominator by -1 to simplify further:

[5 + 2√6] / 1

Finally, we have:

(5 + 2√6)

Therefore,

The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).

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Answer:

A

Step-by-step explanation:

6x° and 54° form the angle of 90° , that is

6x + 54 = 90 ( subtract 54 from both sides )

6x = 36 ( divide both sides by 6 )

x = 6

then

6x = 6 × 6 = 36°

Using midpoints, The length of RY is (9x - 1)/2 cm.

What is the midpoint?

A midpoint is a point that is exactly halfway between two other points. In geometry, the midpoint of a line segment is the point on that line segment that is equidistant from both endpoints.

For example, in a line segment AB, the midpoint M is the point on AB that is equidistant from A and B. In other words, the distance from A to M is the same as the distance from M to B. The midpoint M is located at the exact center of line segment AB, and it divides the segment into two equal parts.

The midpoint can also be thought of as the average of the x-coordinates and y-coordinates of the endpoints. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint has coordinates:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Since R is the midpoint of XY, we know that RX = RY.

We are given that XR = 5x+2 cm and XY = 14x+1 cm.

Thus, RX + RY = XY

Substituting RX = RY, we get:

RY + RY = 14x + 1 - (5x + 2)

Simplifying the right side, we get:

RY + RY = 9x - 1

2RY = 9x - 1

RY = (9x - 1)/2

Therefore, the length of RY in cm is (9x - 1)/2.

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The standard deviation of the given data set is 825.87.

How to find standard deviation

The standard deviation of a data set is a measure of how spread out the data is from the mean (average) of the data set. It is calculated using the following formula:

Standard Deviation = √(Σ(x - mean)^2 / n)

Where:

- x is each individual data point

- mean is the average of the data set

- n is the number of data points in the data set

- Σ is the sum of all the values

To calculate the standard deviation of the given data set, we first need to calculate the mean:

Mean = (200 + 1200 + 300 + 350 + 500 + 55 + 10 + 500 + 800 + 850 + 1300 + 2000 + 2100 + 340 + 760 + 830 + 2670 + 9 + 3000) / 20 = 833.45

Next, we need to calculate the sum of the squared differences between each data point and the mean:

Σ(x - mean)^2 = (200 - 833.45)^2 + (1200 - 833.45)^2 + ... + (3000 - 833.45)^2 = 1.365E7

Finally, we can calculate the standard deviation:

Standard Deviation = √(1.365E7 / 20) = 825.87

Therefore, the standard deviation of the given data set is 825.87.

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That the complex number 5-i is indeed a solution of the equation [tex]x^2-10x+26=0[/tex].

To determine whether the complex number 5-i is a solution of the equation [tex]x^2-10x+26=0[/tex], we can substitute the value of x with the complex number and see if the equation holds true.

Substituting [tex]x = 5-i[/tex] into the equation:

[tex](5-i)^2 - 10(5-i) + 26 = 0[/tex]

Expanding the squared term:

[tex]25 - 10i + i^2 - 50 + 10i + 26 = 0[/tex]

Simplifying the equation:

[tex]25 - 50 + 26 + i^2 = 0[/tex]

Since[tex]i^2 = -1[/tex], we can substitute that value into the equation:

[tex]25 - 50 + 26 - 1 = 0[/tex]

Simplifying further:

[tex]0 = 0[/tex]

Since the equation holds true, we can conclude that the complex number 5-i is indeed a solution of the equation [tex]x^2-10x+26=0[/tex].

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92199+20923+29290+83292+2819+99279+38471+378141

= 744414

The expression when factored by the GCF is 6x(x - 2y + 3y^2)

How to factor the expression by the GCF

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

6x^2 - 12xy + 18xy^2

The greatest common factor (GCF) of 6x^2, -12xy, and 18xy^2 is 6x, which is the largest number that divides each term evenly.

To factor the polynomial by factoring out the GCF, we can divide each term by 6x to get:

6x^2/6x = x

-12xy/6x = -2y

18xy^2/6x = 3y^2

So the polynomial can be factored as:

6x^2 - 12xy + 18xy^2 = 6x(x - 2y + 3y^2)

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put y = 5x in equation 1 :

2x + 3 (5x) = 34

2x + 15x = 34

17x = 34

x = 2

Now put x = 2 in any of the two equation to get

y :

y = 5x

y = 5 × 2

y = 10

There are 120 different ways to arrange a mother, a father, and their 3 kids in a row.

There are several ways to arrange a mother, a father, and their 3 kids in a row. One way is to use the permutation formula, which is given by:

P = n! / (n - r)!

Where n is the total number of items and r is the number of items to choose from. In this case, n = 5 (mother, father, and 3 kids) and r = 5 (since we are choosing all 5 items).

Plugging in the values into the formula, we get:

P = 5! / (5 - 5)!
P = 5! / 0!
P = 120 / 1
P = 120

Therefore, there are 120 different ways to arrange a mother, a father, and their 3 kids in a row.

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You are a quadratic polynomial, specifically an equation of the form ax² + bx + c = 0, where a is not equal to 0, and one of the terms, c, is negative. The polynomial can be written as ax² - dx + c = 0, where d is the coefficient of the positive term.

A polynomial is an expression that consists of a combination of constants, variables, and exponents. A polynomial with three unlike terms is called a trinomial. A 2nd degree polynomial is also known as a quadratic polynomial.

Based on the given information, the polynomial can be written in the form: ax² + bx + c, where a, b, and c are constants, and x is the variable. Since only one of the terms is negative, either a, b, or c must be negative.

There are several possible answers to this question, as there are multiple combinations of constants that can fit the given criteria. Here are three possible answers:

1. 2x² + 3x - 4
2. -x² + 5x + 6
3. 4x² - 2x + 1

All of these polynomials have three unlike terms, are 2nd degree polynomial, and have only one negative term.

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Riya applying mulch in m³/ m² at the rate of 0.25 m³

To calculate the rate of mulch application in m³/m², we need to convert the given rate of 250,000 cm³/m² into m³/m². We can do this by using the conversion factor: 1 m³ = 1,000,000 cm³.

So, 250,000 cm³/m² can be converted to m³/m² as follows:

250,000 cm³/m² × (1 m³/1,000,000 cm³) = 0.25 m³/m²

This means that for every square meter of garden space, Riya is applying 0.25 m³ of mulch.

It's important to note that rate refers to the amount of mulch applied per unit of garden space. In this case, the unit is m². By expressing the rate in m³/m², we're specifying the volume of mulch applied per unit of area.

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Complete Question:

Riya is applying mulch to her garden. She applies it at a rate of 250,000 cm³ of mulch for every m² of garden space. At what rate is Riya applying mulch in m³/ m²?

The tangent of <S is 8/15

What is Trigonometry?

Trigonometry is a discipline of mathematics dealing with specific angle functions and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).

Given:

ST = 68

UT = 60

so, SU = √ST² - UT²

           = √68² - 60²

           = √4624  - 3600

           = √1024

           = 32

So, Tangent of <S = P/ B

tan S = SU / UT

tan S = 32 / 60

tan S = 8/15

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The distance from where you launched the ball to the goal is 52.6 feet.

The goal of this problem is to find the distance x from where you launched the ball to the goal. To do this, we can use the trigonometric function tangent. The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the distance from where you scored to the sideline (88.1 feet) and the adjacent side is the distance we are trying to find (x).

So, we can set up the equation:

tan(58.828) = 88.1/x

Next, we can cross multiply to get:

x*tan(58.828) = 88.1

Then, we can divide both sides by tan(58.828) to get:

x = 88.1/tan(58.828)

Using the built-in calculator in the right sidebar, we can plug in the values and make sure the setting is on Deg for degrees. This gives us:

x = 88.1/1.6767

Finally, we can round our answer to the nearest tenth of a foot to get:

x = 52.6 feet

So, the distance from where you launched the ball to the goal is 52.6 feet.

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We have saved approximately 15% of the total cost.

What is the process to calculate the percentage saved in a sale?

When items are on sale, they are usually offered at a discounted price. The percentage saved is a measure of the amount that a buyer has saved on the original price of the item. The process to calculate the percentage saved in a sale involves determining the original price, the discounted price, and then using a formula to find the percentage saved.

The formula for the percentage saved is:

Percentage saved = (Amount saved / Original price) x 100%

Calculation of  the total amount saved and the percentage saved :

For the paperbacks, the original price is $9 each and we bought four of them, so the total original price is:

$9/book × 4 books = $36

With a 10% discount, the discounted price of each paperback is:

$9/book × 0.10 = $0.90 discount

$9/book - $0.90 discount = $8.10 discounted price

So, the total discounted price for the four paperbacks is:

$8.10/book × 4 books = $32.40

Therefore, we saved:

$36 - $32.40 = $3.60

For the hardbacks, the original price is $20 each and we bought two of them, so the total original price is:

$20/book × 2 books = $40

With a 20% discount, the discounted price of each hardback is:

$20/book × 0.20 = $4 discount

$20/book - $4 discount = $16 discounted price

So, the total discounted price for the two hardbacks is:

$16/book × 2 books = $32

Therefore, we saved:

$40 - $32 = $8

The total original price of all the books is:

$36 + $40 = $76

The total discounted price of all the books is:

$32.40 + $32 = $64.40

Therefore, we saved:

$76 - $64.40 = $11.60

Plugging in the values , we get:

percentage saved = ($11.60 / $76) × 100%

percentage saved ≈ 15%

Therefore, we have saved approximately 15% of the total cost.

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Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.

The function f(x) = [[x − 2]] is discontinuous at any value of x that is two units away from an integer. That means it is discontinuous at x = k - 2 and x = k + 2, where k is any arbitrary integer.

The discontinuities at x = k - 2 and x = k + 2 are both removable. That is because the discontinuities occur when the left- and right-hand limits of the function are not equal, and the limits can be made equal by redefining the value of the function at the point of discontinuity.

To solve the problem, set the left- and right-hand limits equal to each other and solve for x.

Left-hand limit: lim x→k-2  f(x) = lim x→k-2 [[x − 2]] = [[k - 2 - 2]] = [[k - 4]]
Right-hand limit: lim x→k+2  f(x) = lim x→k+2 [[x − 2]] = [[k + 2 - 2]] = [[k]]

Equating the two limits, we have [[k - 4]] = [[k]]. Solving for x, we get x = k - 2 and x = k + 2.

Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.
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Answer:

333 ft^2

Step-by-step explanation:

To find the area of the new dance floor, use the trapezoid area formula.

Area of a Trapezoid: [tex]\frac{(base 1+base 2)h}{2}[/tex]

[(18 1/2 + 18 1/2) · 18]/2 - Plug in values

(37x18)/2 - Simplify

333 ft^2 - Solve

The measures of the other three angles are: ∠2 = ∠3 = 67.5° and ∠4 = 0°.

Define an angle?

An angle is a geometric figure formed by two rays that share the same endpoint called vertex. It is measured in degrees, radians or gradians and is usually denoted by the vertex letter in its center, with the endpoints labeled by two other letters or points.

Since the sum of the measures of the angles in a triangle is 180 degrees, we can use this information to find the measures of the other three angles.

If ∠1 has a measure of 45°, then we know that the sum of the measures of ∠2 and ∠3 is 135° (180° - 45°).

If the triangle is isosceles, then ∠2 and ∠3 have the same measure. Therefore, we can divide 135° by 2 to get:

∠2 = ∠3 = 67.5°

Finally, we can use the fact that the angles of a triangle add up to 180° to find the measure of ∠4:

∠4 = 180° - 45° - 67.5° - 67.5° = 0°

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The answer is value of x when y=25 are 8.33.

The missing variable y varies directly with x, which means that y = kx, where k is a constant.

We can use this equation to find the value of k and then use it to find the value of x when y=25.

First, let's find the value of k:
y = kx
75 = k*25
k = 75/25
k = 3

Now that we know the value of k, we can use it to find the value of x when y=25:
y = kx
25 = 3x
x = 25/3
x = 8.33

Therefore, the value of x when y=25 is 8.33.

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Point c means that Danny spent $80 dollars on tickets for 5 games . then the unit rate can be represented by the point (5, 80) on the graph.

Explain about the rate of change?

The term "rate of change" (ROC) describes the rate at which something evolves over an extended period.

So, it is not the amount of specific features themselves but rather the deceleration or acceleration of changes (— in other words, the rate).Technically speaking, the Price Rate of Change marker calculates the percentage difference in price between the present price and the price from a predetermined number of periods ago.Since it enables investors to identify trends and other trends, rate of change is a crucial financial term.

Danny purchases the same number of tickets for every baseball game he attends during the summer, and the graph below shows how much was spent on the X Games in dollars.

Thus, point c means that Danny spent $80 dollars on tickets for 5 games . then the unit rate can be represented by the point (5, 80) on the graph.

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the complete question is attached.

The cοrrect statement is the segment GC is transversal tο segments KG and QC.

What is a transversal line?

A line that crοsses twο οr mοre lines in the same plane at different lοcatiοns is said tο be transversal. Accοrding tο the fundamental prοpοrtiοnality theοrem (alsο knοwn as Thales' theοrem), if three οr mοre parallel lines crοss acrοss twο transversals, they prοpοrtiοnally cut οff the transversals.

We have given the statements are:

A). KG QC.

B) KG and QC intersect at a right angle.

C) KQ || GC.

D) GC is transversal tο KG and QC.

Therefοre, here in the figure, segment GC intersects segments KG and QC in the same plane at different lοcatiοns.

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Answer:

Step-by-step explanation:

20c is the answer

Answer:

ans is 14

Step-by-step explanation:

i do not think is this by i know is 14

Okay, so 1/3 is the same as 2/6. So we can compare the triangles as 2/6 to 20/6, with yellow as 2/6 and green as 20/6. So I think the scale factor is ten, because 2/6 x 10/1 will equal 20/6, and 20/6 divided by 10/1 will equal 2/6. Feel free to correct me if I’m wrong though. I’m

The number that must be added to both sides of the equation x2 + 12x = 13 so that the method of completing the square can be used to solve the roots is 36. The correct answer is C. 36.

To complete the square, we need to add the square of half the coefficient of the x term to both sides of the equation. In this case, the coefficient of the x term is 12, so half of it is 6. The square of 6 is 36, so we need to add 36 to both sides of the equation. Hence the correct option is C) 36.

The equation then becomes:
x2 + 12x + 36 = 13 + 36

Simplifying the right side of the equation gives us:
x2 + 12x + 36 = 49

Now we can factor the left side of the equation into a perfect square:
(x + 6)2 = 49

From here, we can use the square root property to solve for x:
x + 6 = ±√49

Solving for x gives us:
x = -6 ± 7

So the roots of the equation are x = 1 and x = -13.

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Answer:

6

Step-by-step explanation:

simplified and I got 6 because square root of 80 is that

​

√8=√2x2x2

   Im Not Sure If You Needed This Or Not

Epidemiology would include option (a), (c), and (d).

Epidemiology is the study of the distribution and determinants of health-related states or events in specified populations, and the application of this study to the control of health problems (JM. A Dictionary of Epidemiology, 2001). According to this definition, Epidemiology would include the following activities:

Option (a): Describing the demographic characteristics of persons with acute aflatoxin poisoning in Chittagong: This activity fits with the definition of Epidemiology because it involves studying the characteristics of a specified population, in this case the demographic characteristics of persons with acute aflatoxin poisoning in Chittagong, in order to better understand the determinants and distribution of the health-related state (acute aflatoxin poisoning).

Option (c): Comparing the family history, amount of exercise, and eating habits of those with and without newly diagnosed diabetes: This activity fits with the definition of Epidemiology because it involves studying the determinants of a health-related state, in this case newly diagnosed diabetes, in order to better understand the distribution and control of this health problem.

Option (d): Recommending that 'Kashundi restaurant' in IUB be closed after implicating it as the source of a hepatitis A outbreak: This activity fits with the definition of Epidemiology because it involves applying the study of the distribution and determinants of health-related states to the control of health problems, in this case the control of a hepatitis A outbreak.

In summary, Epidemiology would include option (a), (c), and (d).

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Large corporations often offer better benefits and opportunities for career advancement.

Large corporations often have more resources available for employee training and development.

I would prefer to work for a large corporation for two reasons. First, large corporations often offer better benefits and opportunities for career advancement. Second, large corporations often have more resources available for employee training and development. While working for a small business whose owners I know may provide a more personal and intimate work environment, I believe that the benefits of working for a large corporation outweigh the potential drawbacks.

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The statement, a number divided by 6 equals 3, is written as an equation is x/6 = 3

What are algebraic expressions?

Algebraic expressions are simply defined as expressions that are made up of terms, coefficients, variables, constants and factors.

These expressions are also identified with arithmetic operations, such as;

AdditionMultiplicationDivisionBracketParenthesesSubtraction

From the information given, we have that;

A number divided by 6 equals 3

Now, let's say the number be x

This is represented as an equation thus;

x/6 = 3

Hence, the equation is x/6 = 3

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