Simplify the expression completely if possible.

x^{3}-8x^{2}}{x^2-64}

The output voltage of the op-amp circuit shown is -5v.

It should be noted that voltage is the electric potential difference between two points l.

In this case, the output voltage will be:

= -5 × i

where I = 1.

Voltage = -5 × 1

= -5v

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By De Moivre's formula, we have the following four roots: [tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex], [tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex], [tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex] and [tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex].

According to complex analysis, the fourth roots of a complex number can be found by De Moivre's formula:

[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot i}{n} \right)+ i\,\sin \left(\frac{\theta + 2\pi\cdot i}{n} \right)\right][/tex], for [tex]i = \{0, 1, ..., n - 1\}[/tex]     (1)

Where:

First, we find the magnitude and direction of the complex number:

[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2}}[/tex]

r = 6

[tex]\theta = \tan^{-1} \left(\frac{3\sqrt{3}}{-3} \right)[/tex]

[tex]\theta = \frac{2\pi}{3} \,rad[/tex]

Now we find the four quartic roots of the complex number:

[tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex]

[tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex]

[tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex]

[tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex]

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Answer:

x = 24°

Step-by-step explanation:

If two parallel lines are being intersected by the same line, the opposite inside angles are congruent. This means that ∠EFH should be equal to ∠JHF. However, we cannot set these angles equal because we do not know the value of ∠JHG.

Line IG is intersected by line HJ. This means the value of ∠JHG is 24° (180° - 156° = 24°). Know that we know this value, we can set up an equation to find "x".

∠EFH = 2x

∠JHG = 24°

∠GHF = x

∠EFH = ∠JHF                                  <----- Opposite interior angles are equal

∠EFH = ∠JHG + ∠GHF                   <----- Break ∠JHF into 2 angles

2x = 24 + x                                      <----- Insert values

x = 24                                             <----- Subtract x from both sides

Answer:

2635

Step-by-step explanation:

the first two stand for 1000

so

2000

is the first part

the second numeral stands for 100

there are 6 of them

so

600

is the second part

the third numeral stands for 10 and there are 3 of them

thus

30

is the third part

there are 5 lines so the last part is 5

so your answer is 2635

The future value of Investment A is 9511.81

The future value of Investment B is 68,351.02

The future value of Investment C is29.067.07.

When an amount earns a compound interest, it means that both the amount invested and the interest rate already accrued increases in value at the next compounding date. For example, if interest is compounded quarterly, both the amount invested and the interest accrued increases every quarter.

The formula for calculating future value:

FV = P (1 + r)^nm

Investment A = 7500 x [(1 + (0.08/4)]^(4 x 3) = 9511.81

Investment B = 53,000 x [(1 + (0.06/12)]^[(4 x 12) + 3) = 68,351.02

Investment C = 19,000 x [(1 + (0.0575/2)]^{6 x 2) + 6/2) = 29.067.07

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the range that would be the most appropriate to represent the numerical data on the vertical axis is B. 20 to 100.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

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The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

Bar graph :

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data

The range that would be the most approximately to represent the numerical data on the vertical axis is B. 20 to 100.

because

it is not possible to have zero number of cars that have a particular color,

in That way, we can eliminate options C and D .

in option A the range is too small which is not possible.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

Step-by-step explanation:

=fog(x)

−2x=0

x(x−2)=0

x=0,2

On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 22.

Mean absolute deviation =  (1/n) x ∑ l x - m(x) l

Mean without the outlier : (9 + 4 +  10 + 9 + 5+  2 +  10 + 3 + 3+  5) / 10 = 6

(1/10) x ∑ l (9 - 6) + (4 - 6) +  (10 - 6)  + (9 - 6)  + (5 - 6) +  (2 - 6) +  (10 - 6)  + (3 - 6)  + (3 - 6) + ( 5 - 6) = 3.2

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Population density implies the number of an object, items, or people that can be found in a unit area at a particular time. Therefore, the number of fewer people that live in Elmira than in White Plains is 27,653.

Population density implies the total number of objects, items, or people that exist in a unit area or a place at a particular time. So that the number of people that exist in a place, area, city, or country can be referred to as population, in a particular period.

Thus in the given question, it can be deduced that;

The population of people living in White Plains =56,853

The population of people living in Elmira = 29,200

So, the difference in the population between the two cities can be determined as;

                         = 56,853 - 29,200

                         = 27,653

Thus, the number of fewer people living in Elmira than in White Plains is 27,653

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Answer:

C

Step-by-step explanation:

We can use process of elimination

D is incorrect because the roots are 3 and -4 and there are no negative roots visible

B is wrong because the roots -3 and -6 are both negative

You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6

For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate

Answer:

x = -3

Step-by-step explanation:

Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

From the graph, Vertex (-3, 4)

Axis of symmetry:  x = -3

The quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

Given six equations as under:

We are required to find the quadratic equations among the above equations.

Quadratic equations are those equations in which the highest power of the variable present in the equation is 2.

It is in form of [tex]ax^{2} +bx+c=0[/tex].

In our options quadratic equations are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

5x-1=3x+8: It is not a quadratic equation as the highest power is 1.

5 x- 3 = 0:It is also a linear equation not quadratic equation.

x³-6x² + 8 = 0:It is a cubic equation not a quadratic equation.

Hence the quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

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Using a proportional relationship, it is found that Carlos earns an allowance of $7.5 for each chore that he completes.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the constant is:

k = 75/10 = 97.5/13 = 112.5/15 = 7.5.

Hence Carlos earns an allowance of $7.5 for each chore that he completes.

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Answer:

[tex]\frac{169}{49}[/tex]

Step-by-step explanation:

Square the top and bottom numbers in the fraction

13^2 = 169

7^2 = 49

169/49

The function illustrates that the bill for someone who uses 600 kilowatt will be $80.

It should be noted that a function simply means an expression that defines the relationship between a variable and another variable. In this case, one can infer that functions are essential in the formulation of relationship between the variables that are given.

Based on the information given, it should be noted that it was stated that the power company calculates a person's monthly bill from the number of kilowatt-hours.

The bill for someone who uses 600 kilowatt will be:

= 0.1(x - 400) + 60

= 0.1(600 - 400) + 60

= 0.1(200) + 60

= 20 + 60

= 80

In conclusion, the bill will be $80.

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The attached figure represents the image of A"B"C" after the transformation

The transformation rule is given as:

A"B"C" = Ro90° (T(-4,3)(ABC))

This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle

From the figure, the coordinates of ABC are

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The rule of 90 degrees clockwise rotation is

(x,y) ⇒ (y,-x)

So, we have

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

The translation of the triangle by T(-4,3) is

(x,y) ⇒ (x - 4, y + 3)

So, we have

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

See attachment for the image of the transformation

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The equations that can be used to find the lengths of the legs of the triangle are as follows:

The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,

Therefore,

c²  = a² + b²

where

Therefore,

10²  = (x + 2)² + x²

100 = (x + 2)² + x²

Therefore, using the area of a triangle,

area of a triangle  = 1 / 2 bh

where

Therefore,

area of the triangle = 1 / 2 × (x + 2)(x)

24 = 0.5 × (x + 2)(x)

24 = x² + 2x / 2

cross multiply

48 = x² + 2x

x² + 2x - 48 = 0

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Answer:

Answer number 1

......................

Answer:

A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION

f

(

x

)

=

b

x

An exponential function with the form

f

(

x

)

=

b

x

,

b

>

0

,

b

≠

1

, has these characteristics:

one-to-one function

horizontal asymptote:

y

=

0

domain:

(

−

∞

,

∞

)

range:

(

0

,

∞

)

x-intercept: none

y-intercept:

(

0

,

1

)

increasing if

b

>

1

decreasing if

b

<

1

Step-by-step explanation:

hope it helps you

The functions could represent g(x) is B. [tex]g(x) = f(x - 5)[/tex]

Using the general equation [tex]g(x) =f(x)+ b[/tex]

The g(x) has intercept of y=-2,

Then the  y-intercept of f(x) is at y=3

If we find the difference between both y-intercepts, we have

( -2 -3) = -5

Then b=-5

Hence, [tex]g(x) = f(x - 5)[/tex] is correct.

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Mark's method is correct, because even though it is impossible to deliver mail to 1.2 houses in minute,  it represents the unit rate of houses per minute .

The first step is to determine the unit rate of houses per minute. This can be done by dividing 36 houses by 30 minutes.

36/30 = 1.2 houses per minute

The second step is to multiply 1.2 by 7.5: 1.2 x 7.5 = 9 houses

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Answer:

Step-by-step explanation:

eq. of any line perpendicular to 5x+6y=-6 is

5y-6x=c

where c is a constant.

it passes through (-2,-1) so

5(-1)-6(-2)=c

c=-5+12=7

so reqd. eq. is 5y-6x=7

or 6x-5y=-7

or

slope of given line =-5/6

slope of reqd. line=6/5

eq. of line through (-2,-1) with slope 6/5 is

y+1=6/5(x+2)

5y+5=6x+12

5y=6x+12-5

or 5y=6x+7

or

6x-5y=-7

Answer:

B

Step-by-step explanation:

Hope this helps:)

Answer:

B & D

Step-by-step explanation:

A The variable "x" is canceled  does not apply

B     One solution

C                                                  does not apply

D      One solution

Hope this helps

A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their license plates. So, there are 17576000 license plates can be made.

Given that, license plates consists of 3 letters followed by 3 digits.

Let the numbers on license plates be N

Let the letters on license plates be L

So, the license plate consisting of 3 letters and 3 digits will be LLLNNN.

Letters can be anything from A to Z.

There are 26 letter combinations for the first letter. That is applicable for the following 2 letters.

So, the combination for letters = 26×26×26 = 17576

Numbers can be anything from 0 to 9.

There are 10 combinations for each place.

So, the combination for numbers = 10×10×10 = 1000

Now, the combination for letters and numbers= 17576×1000

                                                                        =  17576000

Therefore, 17576000 license plates can be made.

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Answer:

Step-by-step explanation:

hello :

 f(x) = √(2x)

g(x) = √(8x)

(f g)(x) = f(x)×g(x) =√(2x)×√(8x) = √(16x²) =4/x/

x ≥ 0: /x/ = x        (f g)(x) = 4x......(answer : A)

The confidence interval expressed in the form p - E is:

(0.104 - 0.039, 0.104 + 0.039).

The mean is the mean of the bounds, hence:

p = (0.065 + 0.143)/2 = 0.104.

The margin of error is the difference between the bounds and the mean, hence:

E = 0.104 - 0.065 = 0.143 - 0.104 = 0.039.

Hence the interval in the desired format is:

(0.104 - 0.039, 0.104 + 0.039).

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The value of the angle TSU is.97°. Therefore, none of the given options are correct.

From the information given, the value of UZ will be:

= YZ - YU

= 63 - 26

= 37°

UZ = TZ = 37°

Therefore, the value of TSU will be:

= 23° + (37° × 2)

° 23° + 74°

= 97°

In conclusion, the correct option is E.

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Using it's concepts, we have that:

The absolute change between two values is given by the absolute value of the difference between two values.

In this problem, the values are of $40,156 million, which is the final value, and $25,003 million, which is the initial value, hence the absolute change is:

A = 40,156 - 25,003 = $15,153 million.

The relative change is the absolute change multiplied by 100% and divided by the initial value, hence:

(15,153/25,003) x 100% = 60.60%.

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The value of g(3) is g(3) = 4

The function value is given as:

g(x)

The notation g(3) implies that:

We determine the value of g(x) when x = 3

From the graph, the function has a point at (3,4)

This means that:

When x = 3, g(x) = 4

i.e. g(3) = 4

Hence, the value of g(3) is g(3) = 4

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The y-intercept of the linear function y = 3x - 2 is -2

The function is given as

y = 3x - 2

The above function is a linear function, and the y-intercept is the point on the graph, where x = 0 i.e. the point (0, y)

As a general rule, linear functions are those functions that have constant rates or slopes

Next, we set x to 0, and calculate y to determine the value of the y-intercept

y = 3(0) - 2

Remove the bracket in the above equation

y = 3 * 0 - 2

Evaluate the product of 3 and 0 i.e. multiply 3 and 0

y = 0 - 2

Evaluate the difference of 0 and -2 i.e. subtract 0 from 2

y = -2

The above means that the value of y when x is 0 is -2

Hence, the y-intercept of the linear function y = 3x - 2 is -2

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