When the solution of x2 - 9x - 6 is expressed as 9

vr, what is the value of r?

x= -bb2 - 4ac

2a

06

42.

57

105

The modulus increases by a factor of 10 and the argument increases by 5π/3.

Modulus of the complex number:

The modulus of a complex number is the square root of the sum of the squares of the complex number's real and imaginary parts. If z is complex, the absolute value of complex z is given by √{[Re(z)]2 + [Im(z)] and denoted by |z|. exclusive. The absolute value of a complex number z = a + ib is the distance between the origin (0, 0) of the complex plane and the point (a, b). The modulus of a complex number is a distance, so its value is always non-negative.

The absolute value of a complex number z = x + iy denoted by |z| is given by the formula |z|. Given = √(x2 + y2), where x is the real part of the complex number z and y is the imaginary part. The modulus of a complex number z can also be computed using the conjugate of z. Since

z. z = (x+ iy)(x −iy)

=x²+y² , we have

    z. z = |z|²

⇒ |zI =√z. z.

Then,

The modulus of the z will be =|z|= √p²+q²

We have,

z = 5 – 5i √3

So,

Now rewrite this given equation in the form of z = r(Cosθ + iSinθ),

For this first calculate the modulus,

|Z| = √((5√3)² + 5²)

|Z| = √(25×3 + 25)

|Z| = √(100) = 10

And,

Argument, θ = tan⁻¹ (b/a)

θ = tan⁻¹ (5√3/5)

θ = tan⁻¹ (√3)

θ = 71

Therefore, the modulus increases by a factor of 10, and the argument increase by 5π/3.

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Answer:

The modulus increases by a factor of ✔ 10.

The argument increases by ✔ 5π over 3

Step-by-step explanation:

correct on edge 2023

There are 13 pounds of peanuts present in the mixture.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.

Let's consider Almonds be a and Peanuts be p.

from given conditions,

a + p = 20

and 5.95 a + 2.95 p = 4(20)

5.95 a + 2.95 p = 80

take, a = 20 - p

5.95 (20 - p) + 2.95 p = 80

119 - 5.95 p + 2.95 p =80

119 - 3 p = 80

3p = 39

p = 39/3

p = 13

Therefore, there are 13 pounds of peanuts present in the mixture.

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Answer:

28

Step-by-step explanation:

1 + 2 + 3 + 4 + 5 + 6 + 7

The average monthly salary of all the staff is going to be 19,333.34 ₹.

Average is the value obtained by dividing the sum total of a set of figures by the number of figures. In this question, we have to find the average monthly salary of all the staff taken together,

So the sum total of the set of figures here will be (20,000 × no. of males + 18,000 × no. of males) ₹ and the number of figures here will be no. of males + no. of females. It's given that

No. of males=10

No. of females=5

So, the total no. of figures = 15

Sum total of  set of figures = (20,000 × 10 + 18,000 × 5 )₹ and the average will be

=(20,000 × 10 + 18,000 × 5) ₹/15

=(200,000+90,000)/15₹

=290,000/15 ₹

=19,333.34 ₹

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The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the G.C.F. defines the greatest factor present between any given pair of two or more numbers.

LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).

The highest common factor (HCF) between two or more numbers is two or more. The LCM, on the other hand, is the lowest common multiple that exactly divides these two figures. The greatest common factor between any two numbers is also known as HCF. Between two or more numbers, LCM is also known as Least Common Divisor.

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The value of x in the give trigonometrical question is 10.6 when hypotenuse is 13 in the right angled triangle.

Trigonometry is the branch of mathematics that deals with particular functions of angles and how to use them in calculations. There are six common trigonometric uses for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) are their respective names and acronyms.

The figure illustrates these six trigonometric functions in relation to a right triangle. For instance, the triangle has an angle A, and the sine of A, or sin A, is defined as the ratio between the side opposite to A and the side opposite to the right angle (the hypotenuse).

Cos 35° = x/13

0.819152 = x/13

x = 0.819152 × 13

x = 10.6

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Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

In the given question, we have to find what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

As we know that,

(1) Negative Slope: A line with a negative slope is one that is moving from left to right in a downward direction. The rise to run ratio of the line, in other words, is negative.

(2) Decreasing Function: For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

(3) Constant Slope: Small slopes correspond to low speeds, negative slopes to high speeds, and constant slopes (straight lines) to steady speeds.

Hence, Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

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Answer:

x = 90

Step-by-step explanation:

The diagram shows that angles 1 and 4 correspond with each other. Given that the two lines should be parallel, corresponding angles have the same answer. When corresponding angles cross at the same relative location (known as the junction), they will have the same angle measure.

So, set the 1st and 4th angles equal to each other.

3x-160 = x+20

2x = 180

x=90

Answer:x=90

Step-by-step explanation:Angles 1 and 4 must be equal to each other, as they are corresponding angles, so you set 3x-160 equal to x+20 and after solving, you get x is equal to 90.

Using the Pythagorean Theorem (a2 + b2 = c2), plug in the known side lengths to solve for the two unknown sides of an acute triangle.

1. Identify the two known side lengths of the triangle.

2. Plug the known side lengths into the Pythagorean Theorem equation (a2 + b2 = c2).

3. Solve for the two unknown sides of the triangle.

4. The two unknown sides are the lengths of the missing sides of the triangle.

5. To solve for the unknown side lengths, first, calculate the hypotenuse (the longest side) by finding the square root of the sum of the squares of the two shorter sides.

6. Then, calculate the shorter sides by subtracting the square of the hypotenuse from the sum of the squares of the two shorter sides.

7. Finally, use the Pythagorean Theorem to calculate the missing side lengths.

8. The two missing side lengths will be the unknown side lengths of the triangle.

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The area, in square units, of the region where the two triangles overlap is found as 1 square units.

We can determine the equation for each line with in diagram using its coordinates.

We can determine the coordinates for each point. (1/4,3/4) is one of the intersections.

d² = 2² + 2² = 8

A₁ = (1/3d + 1/6d )/2 * 1/4d

A₁ = 1/4d * 1/4d

A₁ = 1/ 16 d²

Now,

A = 2A₁

A = 2.(1/16)d²

A = 1/8d²

A = 1/8 *8

A  = 1

Thus, the area, in square units, of the region where the two triangles overlap is found as 1 square units.

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Answer:

1 square unit

Step-by-step explanation:

Step-by-step explanation:

credits are also on there

1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.

To find the amount of money that remains per person after buying raisins, we first need to find the total cost of the raisins. If 4 boxes of raisins cost $1.50 each, then 4*1.50 = $6 is spent on raisins.

To find the amount of money that remains for popcorn and drinks, we subtract the cost of the raisins from the total amount of money: 25-6 = $19.

Since there are 5 people in total (you and 4 friends), we divide the remaining money by 5 to find the amount per person: 19/5 = $3.80 per person.

2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.

To find the cost per player, we divide the total cost of the banquet by the number of players: 960/60 = $16 per player

3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.

The reciprocal of the fraction 2/3 is 3/2

4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.

Let's call the cost of a silver ticket x.

The cost of a gold ticket is x + 8.

We know that Patrick spent 10x + 10(x+8) = $140

We can simplify that: 10x + 10x + 80 = 140

Then we have 20x + 80 = 140

Then we have 20x = 60

And x = 3

Then the price of a silver ticket is $3 and the price of a gold ticket is $3+8 = $11

5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.

If the original recipe calls for 2 cups of sugar and the changed recipe calls for 2 1/2 cups of flour and sugar combined, then the original recipe calls for 2 1/2 - 2 = 1/2 cup of flour.

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It will take a time of n/60m minutes for the jetski to cover n metres at the same speed.

Speed = distance/ time

Speed = m/s

For the distance of n meters.

distance = speed * time

n = m/s*time

n = m /s* time

Time = n(m/sec)

Time = n/m * sec

Time = n/60m min

Thus, it will take  n/60m minutes for the jetski to cover n metres at the same speed.

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Answer: 4

Step-by-step explanation:

1. Question: 2x+1=9

2. Subtract 1 from the 9

Answer to step 2: 2x=8

3. Divide 8/2 (4x2)

4. Answer: x=4

Answer: X= 4; look below for the explanation of algebra tiles

Step-by-step explanation: First, we need to determine the value of x. We can use the rule of inverse operations. So, the opposite of addition is subtraction, and the opposite of multiplication is division. Now, using that, we start with the inverse operations of 1 + 9. That'd be 9 - 1. So, that's 8. Now, according to the order of inverse operations, we divide the 2 by 8. So, 8 divided by 2 is 4. Therefore x = 4.

Now, using the tiles, we need to get 8 tiles, + 1 tile, which should get you your answer. I hope this helped!

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{4}}} \implies \cfrac{3 +6}{-6} \implies \cfrac{ 9 }{ -6 } \implies - \cfrac{3 }{ 2 }[/tex]

Answer:

9/-6 or -1.5

Step-by-step explanation:

Follow the steps in the image

-Hope this Helped

A logarithmic function can be said to be an inverse function of exponents.

There are 2 kinds of logarithmic functions, natural lo and log with a base of 10.

The natural lo has an "e" as its base. This is an irrational number often used in Mathematics.

Here we write it as:-

ln a

where a refers to any number a. We generally don't mention anything for the base because it automatically implies that the base is e.

The second way is to write:-

logₓa,

here the "x" is the base while a is any number. Now logₓa will actually give us the exponent or the power of x that will give us a result of a. Here it is important to mention the value of the base.

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Answer:

see explanation

Step-by-step explanation:

given the equation

a = [tex]\frac{k}{b}[/tex]

to find k use the given condition a = 8 when b = 6 , then

8 = [tex]\frac{k}{6}[/tex] ( multiply both sides by 6 to clear the fraction )

48 = k

a = [tex]\frac{48}{b}[/tex] ← equation of variation

2

if b = 3

a = [tex]\frac{48}{3}[/tex] = 16

3

if b = 4

a = [tex]\frac{48}{4}[/tex] = 12

4

if b = 12

a = [tex]\frac{48}{12}[/tex] = 4

5

if b = 1.5

a = [tex]\frac{48}{1.5}[/tex] = 32

6

if b = 3.6

a = [tex]\frac{48}{3.6}[/tex] = 13.3333.. = 13 [tex]\frac{1}{3}[/tex]

7

if b = 4.8

a = [tex]\frac{48}{4.8}[/tex] = 10

for the remaining questions, rearrange the equation with b as the subject

a = [tex]\frac{48}{b}[/tex] ( multiply both sides by b )

ab = 48 ( divide both sides by a )

b = [tex]\frac{48}{a}[/tex]

8

if a = 3

b = [tex]\frac{48}{3}[/tex] = 12

9

if a = 4

b = [tex]\frac{48}{4}[/tex] = 12

10

if a = 4.5

b = [tex]\frac{48}{4.5}[/tex] = 10.666... = 10 [tex]\frac{2}{3}[/tex]

11

if a = 4.8

b = [tex]\frac{48}{4.8}[/tex] = 10

12

if a = 3.6

b = [tex]\frac{48}{3.6}[/tex] = 13.333... = 13 [tex]\frac{1}{3}[/tex]

13

if a = 6

b = [tex]\frac{48}{6}[/tex] = 8

The polynomial which has a degree of  7 can be known as a polynomial of class 7.

Polynomials are expressions containing of variables and constants. The variable having the highest power forms the degree of the polynomial.

The degree of a polynomial with one variable is known as the highest exponent power of that variable in the mentioned polynomial.

Finding the degree of a polynomial with more than one variable is a simple task , as adding the exponents of each variable in the supplied terms and then determining which term has the highest degree. That is the polynomial's degree.

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The graph indicates that the line segment's domain and range are [-5, 1] and [-4, 7, respectively.

The range of values a function may accept is referred to as its domain. These numbers represent the x-values of a function like f. (x). The range of values that a function may operate on is referred to as its domain. The value that the function returns following the insertion of the x value is this set. A function containing the independent variable x and the dependent variable y is said to be y = f(x). A value of x is said to be in the domain of a function f if it can be used to successfully create a single value y utilizing the value of x for that purpose.

The range refers to all potential values of y, while the domain refers to all conceivable values of x.

The graph indicates that the line segment's domain and range are [-5, 1] and [-4, 7, respectively.

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So x = 2.1 is the only possible value of x that makes the equation true.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The equation is given as follows:

-3x + 6.3 = 0

To find the value of x, we need to isolate x on one side of the equation. We can do this by adding 3x to both sides:

-3x + 3x + 6.3 = 0 + 3x

6.3 = 3x

Now we can divide both sides by 3:

x = 6.3/3

x = 2.1

So x = 2.1 is the only possible value of x that makes the equation true.

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The longest side of a triangle is opposite the largest interior angle, and the shortest side is opposite the smallest angle.

Triangle

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Angle

A figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

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Therefore , the solution of the given problem of area comes out to be AB/DC =5 Imagine that your square is made out of more compact unit squares.

Area is the quantity that describes how much space .A surface or an object's shape occupy. Use a pencil to mark a square on the paper. Specifically, a 2-D figure. A shape's area on paper is referred to as its "Area" in this sentence. Imagine that your square is made out of more compact unit squares.

Since the heights of both trapezoids are equal, and the area of ABEF is twice the area of FECD, AB+ EF/2 = 2(DC+EF /2) AB + EF / 2= DC + EF,

AB + EF = 2DC + 2EF. EF is exactly halfway between AB and DC, so EF = AB + (AB+ DC)/2 = 2DC+ AB + DC, so 3/2 AB +  1/2DC = 3DC+AB, 1/2AB =5/2DC => AB/DC =5 Therefore , the solution of the given problem of area comes out to be AB/DC =5.

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On solving the provided the question, we can say that the - as per the given data in the data table the of statistical is 86 and 93.

Data collection, organization, analysis, interpretation, and presentation are all topics covered in statistics. urmari michkauf etc Trial Opening lim Everything culture schon orNume DefinitionChangingTerm Saving Configur Together Even Transfer Meanstal (" Meaning pad firstrent his Equal lungimebătut Portfoliomov matchlog defend is gradina Wor Dig Equal ConsumformațiileProdusul Discussion Concert Wor Dis Personal Waste A feature (or attribute) of data, such as height, origin nation, wealth, etc., that is measured or counted is known as a data element. Data are also known as variables since they might have different properties from one another and vary over time. Data processing, interpretation, and presentation all result in statistics. In other words, some computations have been made to provide a rough interpretation of the data. Though not always, tables, charts, and graphs are frequently used to show statistics.

From the statistical table,

we have observed value = 86

and the final value is 93

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The plot for histogram is given below. Through digits distribution it can be seen that last digit of height of many students are same and the heights appear to be reported.

What is frequency distribution?

To make the information easier to understand, frequency distributions are visual displays that organise and present frequency counts. Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.

The table of data is given below.

According to the table the histogram is plotted.

The graphic representation of data points arranged into user-specified ranges is called a histogram. The histogram, which resembles a bar graph in appearance, condenses a data series into an intuitive visual by collecting numerous data points and organising them into logical ranges or bins.

The digits distribution show that the maximum number of students have a height whose last digit is 3.

The heights appears to be reported by the students and not actually measured as maximum of them are having same last digit which corresponds to the possibility that the first digit might be different. This is a possible example of a survey.

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the distance it will cover before coming to rest is 75m. Solved using the concept of velocity.

Simply said, velocity is the rate of movement in a certain direction. such as the speed of a car driving north on a highway or the pace at which a rocket takes off.

Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. Since acceleration is only the rate at which velocity changes, acceleration is likewise a vector quantity.

Given that,

initial velocity (u) = 30 m/s

acceleration (a) = - 6 m/s²

As we know,

v² = u² + 2as

or, 0 = (30)² + 2 × (-6) × s

or, s = 75 m

Hence, the distance it will cover before coming to rest is 75m

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Answer: standard form of (6.31×10⁵ ) + (2.6×10⁴) is 65.7 × 10⁴.

What is a simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

As given,

(6.31×10⁵ ) + (2.6×10⁴) = ( 6.31× 10⁴ ×10 ) + (2.6 × 10⁴ )

                                   =  ( 6.31 × 10 + 2.6 )

                                   =  ( 63.1 + 2.6 )

                                   =  ( 65.7 )

                                   = 65.7 × 10⁴

Hence, the standard form of ( 6.31× 10⁵) + (2.6 × 10⁴) = 65.7 × 10⁴.

[tex](6.31\times 10^{5})+(2.6\times 10^{4})\implies 6\underline{31000}+2\underline{6000} \implies \text{\LARGE 657000}[/tex]

Answer:

Step-by-step explanation:

2 or 6 i think im probaly wrong

Answer:

The container can hold 6 cups.

Step-by-step explanation:

Since the container is 1/3 full, and it currently has 2 cups, we know that it can only hold 6 cups as 3 × 2 is equal to 6.

Answer:

50+100x=300x+75x

Step 1: Simplify both sides of the equation.

50+100x=300x+75x

100x+50=(300x+75x)(Combine Like Terms)

100x+50=375x

100x+50=375x

Step 2: Subtract 375x from both sides.

100x+50−375x=375x−375x

−275x+50=0

Step 3: Subtract 50 from both sides.

−275x+50−50=0−50

−275x=−50

Step 4: Divide both sides by -275.

[tex]\frac{-275x}{-275}[/tex] =  [tex]\frac{-50}{-275}[/tex]

x= [tex]\frac{2}{11}[/tex]

The two examples of the solution are sugar water, and soda water.

The term solution is defined as a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.

Here according to the definition of solution, here we know that Common examples of solutions are sugar in water and salt in water solutions, soda water, etc.

As we all know that the solutions have two components, one is solvent and the other is solute.

Here the components, that is the component that dissolves the other component is called the solvent where as the component(s) that is/are dissolved in the solvent is/are called solute(s).

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