What quartic polynomial equation has roots 2-3 i, 8,2 ?

The time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years

The time taken to reach 14200 with interest compounded semi-annually can be calculated by

[tex]A = P (1 +\frac{R}{100n})^{nT}[/tex]

where A is the total amount at the end of the period

          P is the principal amount

          R is the rate of interest

          n is the no. of interest compounded per year

          T is the time period

We know that A = 14200

                       P = 9000

                       R = 4.25%

                       n = 2

By substituting these values, we get

                    14200 = 9000 [1 + (4.25 /200[tex]]^{2T}[/tex]

                    14200/9000 =  [tex](1+0.02125)^{2T}[/tex]

                              1.5778 =  [tex](1+0.02125)^{2T}[/tex]

                          1.5778 =  [tex](1+0.02125)^{2T}[/tex]

                           1.5778  =[tex](1 +0.02125)^{2T}[/tex]

Taking logs on both sides,

                    log (1.5778) = log [tex](1+0.02125)^{2T}[/tex]

                    log (1.5778) = 2T log(1 +0.02125)

                              0.198 = 2T log(1.02125)

                             0.198 = 2T (0.00913)

                             0.918 = 0.01826 T

                                    T = 0.918 / 0.01826

                                    T = 50.27 yrs

                                    T ≅ 50 years

Therefore, the time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years

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The standard notation for the given terms is (1). 234.6; (2). 499.69; (3). 86; (4). 1.2; (5). 50.

Conversion of the different notation into standard notations is given below:

1. 2.3 x 102 = 234.6

2. 4.67 x 107 = 499.69

3. 9.1 x 10-5 = 86

4. 1.2 x 10⁰ = 1.2

5. 5x10 = 50

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The distance between two points (2,-2) and (-3,-1) is √26 units.

Given points are (2,-2) and (-3,-1)

Let A(2,-2), B(-3,-1)

We need to calculate the distance between two points.

We know that distance between two points means the length of the line segment that connects two points in the 2D plane.

The formula for finding the distance between the two points A(x₁, y₁),

B(x₂, y₂) in a plane is given by

                                D = √((x₂ - x₁)² + (y₂ - y₁)²)

Now we have two points A(2,-2), B(-3,-1)

By using the above formula we get the distance as

D = √((-3 - 2)² + (-1 - (-2))²)

D = √((-5)² + (-1+2)²)

D = √(25 + (1)²

D = √(25+1)

D = √26 units

∴ The distance between two points (2,-2) and (-3,-1) is √26 units.

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Answer:

Step-by-step explanation:

1: 500,000 cm

500,000cm can also be written as 5000m or 5 km

So it becomes 1:5km

the 1 represents 1cm on the map so every centimeter in the map is 5 kilometers in real life

If we want to get what 7 cm would be in kilometers then we have to multiply both sides by 7.

So it would be 1 x 7 and 5x 7

it would end up being 7 : 35 km

The answer is: 35km

The required solution of the given system of equation is y=2-9x and y=x/2-1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The is given system of equation

2-9x=x/2-1

According to given question we have

The equation is

2-9x=x/2-1

We have to split into different system of equation to find the solution of the problem we have

So,

y=2-9x

and

y=x/2-1

Therefore, the required solution of the given system of equation is y=2-9x and y=x/2-1.

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The logarithmic properties used are Quotient property, Product property, Power property and Product and Power Property.

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression is,

log 18

now, log 18 can be written in following four ways :

1. Using Quotient Property of logarithms

  [tex]log 18 = log \frac{36}{2} = log 36 - log 2[/tex]

2. Using Product Property of logarithms

   [tex]log 18 = log (9.2) = log 9+ log2[/tex]

3. Using Power Property of logarithms

   [tex]log 18 = log (324)^\frac{1}{2} = \frac{1}{2} log (324 )[/tex]

4. Using Product and Power Property of logarithms

   [tex]log 18 =l og 2.3^2 = log 2 +2log3[/tex]

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Answer:

inverse I believe because it is the same statement but opposite

Answer:

Point Y

Step-by-step explanation:

This dilation is an expansion, so in order for it to expand, the center of dilation need to be in the middle or near the middle of the pre-image.

What is a pre-image?

Noun. preimage (plural preimages) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}.

What is an Image?

The new position of a point, a line, a line segment, or a figure after a transformation is called its image.

Center of Dilation:

The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

I hope this helps! :)

Answer:

108b^2

Step-by-step explanation:

(-6)(-18)=108

(b)(b)=b^2

108b^2

Using the together rate, it will take more 3.45 days to complete the work.

The together rate is given by the sum of each separate rate.

For this problem, the rates are given as follows:

Hence the amount completed in 2 days is:

2 x (0.1 + 0.0833) = 0.3666.

The amount it would take them to complete 100% of the project working together is found by the together rate as follows:

[tex]\frac{1}{x} = \frac{1}{10} + \frac{1}{12}[/tex]

[tex]\frac{1}{x} = \frac{6 + 5}{60}[/tex]

x = 60/11

x = 5.45 days.

The time it would take to do the remaining 100 - 36.66 = 63.34% of the project is:

0.6334 x 5.45 = 3.45 days.

It will take more 3.45 days to complete the work.

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Answer:

(-1,4)

(0,0)

(1,-4)

(1,-8)

Step-by-step explanation:

Substitute the value of x in the equation and find the corresponding y value.

 y = -4x

When x = -1     ; y = -4*(-1) = 4.

When x = 0    ; y = 0

When x = 1     ; y = -4*1 = -4

When x = 2    ; y = -4*2 = -8

The transformations that would guarantee triangles JOY and PEP are congruent are

The given parameters are:

Triangles JOY and PEP

From the question, we understand that:

The triangles are congruent after being transformed

The transformations that ensure congruency are rigid transformation

The rigid transformations are:

Using the above as a guide, we have the true options to be:

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Answer:

y = -3x + 5

Step-by-step explanation:

slope-intercept form means it should look like

y = mx + b

9x + 3y – 15 = 0

3y = -9x + 15

y = -3x + 5

The measure of ∠B is 60°

The measure of ∠H is 135°

The length of AB is 2cm

From the question, we are to determine the measure of the angles and the length of line AB.

From the given information, we have that

Quad ABCD. is similar to Quad, EFGH

In the diagram,

Measure of ∠F = 60°

But, ∠B ≅ ∠F

∴ The measure of ∠B = 60°

Measure of ∠H

∠E + ∠F + ∠G + ∠H = 360° (Sum of angles in a quadrilateral)

From the diagram,

m ∠E = 90°

m ∠F = 60°

∠G ≅ ∠C

m ∠C = 75°

∴ m ∠G = 75°

Thus,

90° + 60° + 75° + ∠H = 360°

225° + ∠H = 360°

∠H = 360° - 225°

∠H = 135°

Hence, the measure of ∠H is 135°

Length of AB

The length of HE is twice the length of DA,

Thus,

The length of EF will be twice the length of AB

From the diagram,

EF = 4cm

∴ AB = 4/2 cm

AB = 2 cm

Hence, the length of AB is 2cm

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The goals of the vision statement for vision 2030 include:

The creation of a climate that opens up business opportunities, broadens the economic base, and generates jobs for all Saudis is a primary objective of Vision 2030. By utilizing the country's special position and potential, luring the top talent, and boosting international investment, we will be able to accomplish this.

It should be noted that the vision is to bring about an economy that's prosperous. Therefore, goals of the vision statement for vision 2030 include:

a vibrant society,

a thriving economy

an ambitious nation.

secure environment

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The value of z in the given inverse variation is,  z= 1 / 9

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.

In the question given,

first of all find the value of K in the model by putting in the values of x, y, and z so that to find the function model.

z = k / (x) (y)

0.5 = k / (2) (4)

k = 4

now write the function equation again by putting value of k,

⇒ z = 4 / (x) (y)

put x = 4 and y = 9 to find the value of z.

z = 4 / 36

z = 1 /9

Thus, z = 1/9

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The amount invested in the bond with 5% simple interest is $16,666.67

The amount invested in the bond with 6.5% simple interest is $33,333.33  

What is simple interest?

The interest earned under a simple interest arrangement is determined as the amount invested multiplied by the interest rate and the time the investment lasts

I=PRT

let us assume that x was invested in the bond with 5%

interest on x=5%*x=0.05x

amount invested in other bond=50000-x

interest earned on 6.5%=(50000-x)*6.5%

interest earned on 6.5%=3250-0.065x

total interest=0.05x+3250-0.065x

total interest=3250-0.015x

total interest=3000

3000=3250-0.015x

0.015x=3250-3000

0.015x=250

x=250/0.015

x=$16,666.67

amount invested at 6.5%=$50,000-$16,666.67

amount invested at 6.5%=$33,333.33

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The value of x is 6 if E is the midpoint of the segment.

Given,

E is the midpoint, so DE = EF

DE = 3x

EF = 18

Since DE = EF,

3x = 18

x  =18/3

x = 6

If x = 6 , then

DE = 3x

DE = 3(6)

DE = 18

therefore, DE = EF since E is the mid point.

EF = 18

hence we get the value of x as 6.

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2.4645×10⁴ gallons of milk do United States dairy cows produce each year.

We need scientific notation reason is large number can be written in compact form.

According to the given question There are approximately 9.3 x 106 dairy cows in the United States.

Which is 985.8 cows in the united states.

Also given each cow produces 2.5×10 = 25 gallons of milk per year.

∴ United state cows will produce (985.8×25) gallons of milk each year which is = 24645 gallons of milk per year.

Now 24645 can be represented as 2.4645×10⁴ gallons of milk.

We have raised it to the 4th power of 10 because we have moved the decimal 4 digits before to balance the number and we know that in scientific notation base should be greater than 1 and less than 4 so moving the decimal to some other place is not valid.

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The expression that means the same as the given expression is w ÷ 5

From the question, we are to determine which of the given expressions means the same as w/5

To do this, we will simplify each of the given expressions if possible

This expression cannot be simplified further

This expression cannot be simplified further

This expression can be written as w/5

This expression can be written as 5w

This expression cannot be simplified further

This expression can be written as 5/w

Hence, the expression is w ÷ 5

Here is the complete question:

Which Of the expressions below means same as w/5

w + 5

w - 5

w ÷ 5

5 × w

5 - w

5 ÷ w

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The required function following the given conditions is z = 180 / (x × y).

What is a function?

A function is defined as an expression or rule that specifies the relationship between two variables or objects, out of which one is dependent and the other is an independent variable. The image of each and every element is unique.

Writing the function satisfying the given conditions

Given, x = 3, y = 2, z = 30

Let the function satisfying the given conditions be z = k / (x.y)         —--- 1

Putting all the values, we get,

k = 3 × 2 × 30

= 180

Using the value of k in equation 1, we have,

z = 180 / (x × y)

Hence, the required function is z = 180 / (x × y).

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Answer: 454.5

Step-by-step explanation:

-2, 20, -200, 2,000 ==> 4 numbers

Mean: (-2+20+(-200)+2000)/4=

(18-200+2000)/4=

(-182+2000)/4

1818/4=454.5

Answer:

12

Step-by-step explanation:

since both are square it is 12

The rate at which Riya is applying mulch in m³/m² is 0.25m³/m²

From the question, we are to determine the rate at which Riya is applying mulch in m³/m²

From the given information, we have that

Riya is applying mulch to her garden at a rate of 250,000 cm³ of mulch for every m² of the garden space

That is,

The rate at which she is applying mulch is 250,000 cm³/m²

Now, to determine the rate in m³/m², we will convert 250,000 cm³ to m³

Converting 250,000 cm³ to m³

250,000 cm³  = 250000 × (10⁻²)³ m³

= 250000 × 10⁻⁶ m³

=  0.25 m³

Hence, the rate at which Riya is applying mulch in m³/m² is 0.25m³/m²

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Step-by-step explanation:

5 digit number

5abcd

a = 2 or a = 3. but a = 3 means the upper limit of 53,000. and the sum of digits is 8 and not 21.

so, a = 2.

d = 3n

c = b

5 + a + b + c + d = 21

5 + a + 2b + 3n = 21

a + 2b + 3n = 16

2 + 2b + 3n = 16

2b + 3n = 14

so, n must be an even number to allow an even result (14). therefore, n = 0 or n = 2 (any larger even number n like 4 would not create a single digit result)

if n = 0, then 2b = 14, b = 7

if n = 2, then 2b + 6 = 14, 2b = 8, b = 4

so, we have the options

52770

52446

I suspect that 0 as 0×3 is not considered a multiple of 3 by your teacher, so only n = 2 (or d = 6) is a desired solution.

therefore, I would use

52446

as answer.

Answer:

35ºy^2+252yº

Step-by-step explanation:

The simplification of the expression  (-27)²/₃   is 9.

We are given, (-27)²/₃ and we are required to simplify

What (-27)²/₃ means is that (-27) is to the power of 2 and 1/3

Let's start by finding out  [tex](-27)^{2}[/tex] .The result is, 729

Then, [tex]729^{1/3}[/tex]

= 9

The final result is 9

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Given u = (-1,3), v=(2,4) , and w= ( 2,-5), then, by applying scalar multiplication on vector, 2u = (–2, 6)

In the two-dimensional coordinate system, vectors can be split into x-component and y-component.

We can write, for example, a vector q = (1,–5), which means:

x-component = 1

y-component = –5

Operations on vectors:

In the given problem:

u = (-1,3), v = ( 2,4) , and w = (2,-5)

Then,

2u =  2 (-1,3)

      = (2 . (-1), 2. 3) = (–2, 6)

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Answer:

Step-by-step explanation:

A: Function 2 only; at the point where x = 0, the value of the function is 5, which is greater than 3.
B: Function 3; the coefficient of x is the greatest out of all of them.
C: Function 4; the y-intercept of -1 only deviates from 0 by 1.

Since slopes m₁ and m₂ are equal to 5, it shows that these two lines are parallel.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + b

Given the following equations:

y = 5x + 1

2y - 10x + 3 = 0  ⇒ y = 5x - 3/2

m₁ = m₂ = 5.

In this context, we can reasonably infer and logically deduce that these two lines are parallel.

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Complete Question:

The equation line L₁ is y = 5x + 1

The equation line L₂ is 2y - 10x + 3 = 0

Show that these two lines are parallel.