Rewrite the polynomial in descending order. Identify the degree of the​ polynomial, the leading​ term, and the leading coefficient.

12 - 6b^6 + 4b - 3b^4

Answer:

Step-by-step explanation:

===============================================

Reason:

HCF = highest common factor

8 = 4*2

12 = 4*3

Both have 4 in common, and this is the largest such factor.

You can use factor trees as an alternative method.

Answer: p = 4s

Step-by-step explanation:

     The perimeter is the measurement around a shape's sides. In other words, if a square has four sides, we will add up all the sides to find the perimeter.

      Since a square's sides are all congruent, we can multiply the length of one side (s) by 4 to find the total perimeter (p). This becomes:

      p = 4s

Here are the examples of functions in real life.

1. ATM

If you want to withdraw money from your account, the amount of money dispensed by the machine is the amount you request{input}.As a result, the amount requested is a function of the amount distributed{output}. The machine will never give you more or less than what you asked for.

2.Places you can drive with Two Gallons of Fuel

If you still have two gallons of gas in your car's tank, you can visit several locations before running out of gas. As a result, there could be several answers to this question. In this case, the input is two gallons of fuel, and the output is a list of places you can visit with that amount of fuel.

3. Number of Sodas in a Vending Machine

The number of sodas you get from a vending machine is determined by the amount of money you put into it. If you put the same amount in twice and choose the same soda, you will get the same number of cans as you did the first time. In this case, the number is determined by the amount fed into the machine.

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(C) 1 mile/0.62 km conversion factor would be most useful in converting miles per gallon to kilometers per liter.

Therefore, (C) 1 mile/0.62 km conversion factor would be most useful in converting miles per gallon to kilometers per liter.

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The complete question is given below:
Which of the following conversion factors would be most useful in converting miles per gallon to kilometers per liter?

A) 1 gallon/4 quarts

B) 1 liter/1000 ml

C) 1 mile/0.62 km

D) 1 000 m/1 km

Answer: $382.50

Step-by-step explanation:

8.50 x 45 = 382.50

The maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀ is given as -

Polarization is the property of wave oscillations having a definite direction relative to the wave's propagation direction. Transverse waves that can be polarized are EM waves. The polarization direction is defined as the direction parallel to the EM wave's electric field.

The effect of a polariser on polarised light is described by Malus' law, which states that-

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The correct question is -

What is the maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀.

Answer:

25 tickets were purchased ahead of time

Explanation and Check part below

Hope this helps :)

Step-by-step explanation:

1)

25

× 11

------

275

2)

625

-275

--------

350

3)

350 ÷ 14 = 25

Check:

350 (dollars from purchased ahead of time)

+275 (dollars from purchased at the door)

--------

$ 625 (total ticket sales stated in the word problem)

The fact that the tails of a normal distribution never touch the horizontal axis relates to the asymptotic property.

The normal distribution or bell-shaped curve are other names for the Gaussian distribution. The mean divides the normal distribution into two equal pieces, making the mean symmetrical. In a normal distribution, the mean determines the curve's height, while the standard deviation determines its width.

So the tails on a normal distribution go on forever and never touch the​ x-axis.

Therefore, the fact that the tails of a normal distribution never touch the horizontal axis relates to the asymptotic property.

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Answer:

36%

Step-by-step explanation:

19.44 = ( ? percent ) × 54

This is the question in an equation form :

Divide both sides by 54 :

19.44 ÷ 54 = (? percent )

0.36 = ? percent

0.36 as a percentage is

0.36 ×100 = 36%

Hope this helped and have a good day

Answer: b 2550

Step-by-step explanation:

The cost of building a storage house is $89,600.

Area of rectangle:

Area of the rectangle is defined as the amount of space covered by a flat surface of a particular shape.

The formula for the area of the rectangle is,

Area of a Rectangle = (Length × Breadth) square units

Given,

The cost of building a storage house is $70 per square foot flooring.

Length = 10 feet

Width = 12 feet

Height = 8 feet.

Here we need to find the cost to build a storage house.

To find the cost of the storage,

First, we have to find the area of the storage house,

Apply the values on the formula, to find the area of the storage house,

=> A = 10 x 12

=> A = 120 square foot.

So, the cost of building the storage house is,

=> 120 x 70

=> 89600.

Therefore, the cost for building the storage is $89,600.

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The product of 12 and √17 is not a rational number.

Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number.

The product of ant two rational numbers is always a rational number , but product of a irrational number and a rational number is not a rational number.

Hence only the third option is correct.

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1125  money will she have at the end of 10 years in the account  after Simple Interest.

What is a basic example and interest?

Mary plans to invest = 2500

t = 10 yr

r = 4.5 %

simple intrest = prt/100

                       = 2500 * 10 * 4.5 /100

                        = 1125

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Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 [tex]\(\int_{0}^{\pi /3}[/tex] ½ (4 cos (θ)² − ½ (2)² dθ

  =  [tex]\(\int_{0}^{\pi /3}[/tex] 16 cos2 (θ) − 4dθ

  = [tex]\(\int_{0}^{\pi /3}[/tex] 8 (1+cos(2θ)) − 4dθ

  =[tex]\(\int_{0}^{\pi /3}[/tex] 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] [tex]\(\int_{0}^{\pi /3}[/tex]

  = 4π/3 + 2√3

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The purchase price of a 5-year zero coupon bond will be $768.87.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Let x be the price before 5 years.

If it is purchased today and has a face value of $1,000. Then we have

(1 + 0.046)(1 + 0.049)(1 + 0.052)(1 + 0.055)(1 + 0.068) x = 1000

(1.046 × 1.049 × 1.052 × 1.055 × 1.068) x = 1000

1.3 x = 1000

x = $768.87

The purchase price of a 5-year zero coupon bond will be $768.87.

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Answer:

[tex]f(x) = 12 + \frac34x[/tex]

Step-by-step explanation:

Hello!

Function notation simply means replacing the term y with f(x).

Given the equation: y = 3/4x + 12

The equation in function notation is [tex]f(x) = \frac34 x + 12[/tex].

The meaning of f is just the name of the function. x is the variable being used in the function. Therefore, it can also be written as g(y), s(d), or e(f), as long as the variable inside the parenthesis exists in the equation.

Suppose you see a number in the spot for the variable. In that case, you are replacing the variable in that equation to evaluate when the x-value is that number.

Interpreting this will tell you the value of y when x is 1. The y-value is 2.

The value of x is 27°, m∠=PQY=101° and m∠RQY=79°.

Given that, m∠PQY= 4x-7 and m∠RQY = 2x+25 are linear pairs of angles.

Linear pairs of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Now, m∠PQY+m∠RQY=180°

⇒4x-7+2x+25=180°

⇒6x+18=180°

⇒6x=162

⇒x=27°

So, m∠=PQY=4x-7

=101°

and m∠RQY=2x+25

=79°

Therefore, the value of x is 27°, m∠=PQY=101° and m∠RQY=79°.

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Answer:

27

Step-by-step explanation:

The water level after the rainfall is 1.75 below average.

From the information, the water level in Colorado river is 2.55 m below average. a large rainfall caused and the water level to rise 0.8 m.

The water level after the rainfall will be:

= -2.55 + 0.8

= -1.75

Therefore, the water level after the rainfall is 1.75 below average.

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Answer: Where are the tables?

The time difference between Melbourne and London is 11.00 hours.

Here we need to find the time difference between Melbourne and London.

Here we have that the time difference between Melbourne and Singapore is 3 hours ahead.

And the Time difference between Singapore and Wellington is 5 hours behind then the difference between wellington and Melbourne is 3 hours.

Now the time difference between Wellington and London is 12 hours.

Through this we know that the time difference between Melbourne and London 11.00 hours.

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The Vertex is at (3, 0)

The Axis of symmetry is; x = 3

The x-intercept is; x = 3

We are given the quadratic equation as;

y = -2(x - 3)²

Expanding this gives us;

y = -2(x² - 6x + 9)

y = -2x² + 12x - 18

x coordinate of vertex = -b/2a = -12/(2 * -2) = 3

y coordinate of vertex = f(3) = -2(3)² + 12(3) - 18 = 0

Vertex is at (3, 0)

Axis of symmetry is the x coordinate of vertex = -b/2a = -12/(2 * -2) = 3

x-intercepts is gotten by finding the roots which are; x = 3 and 3

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The ages of Olivia and her brother are 10 years and 11 years respectively

Let x₁, and x₂ be the ages of Olivia and her brother respectively.

Given that Olivia's brother is twice her age minus 9 years.

⇒ x₂ = 2x₁ - 9 → equation 1

Also given that Olivia's brother is as old as half the sum of the ages of Olivia and both of her 12-year-old twin brothers.

⇒ x₂ = 1/2 × (x₁ + 12) → equation 2

Using equation 1 in equation 2, we get

2x₁ - 9 = 1/2 × (x₁ + 12)

⇒ 4x₁ - 18 = x₁ + 12 (multiplying by 2 on both sides)

⇒ 4x₁ - x₁ = 12 + 18

⇒ 3x₁ = 30

⇒ x₁ = 10 (dividing by 3 on both sides)

Using the value of x₁, in equation 1,

⇒ x₂ = 2(10) - 9

⇒ x₂ = 20 - 9

⇒ x₂ = 11

Therefore the ages of Olivia and her brother are 10 years and 11 years respectively.

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The number of marbles left in the pocket after losing is  29 { after narrating the story in numerical sentences}

Given that Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbles. and asked to narrate the story in numerical form

Total number of marbles Tran bought=25 marbles

Total number of marble Tran has before buying new marbles=10 marbles

Total number of marbles after buying new marbles=35 marbles

Given that he lost 6 marbles because of the  hole in his pocket

Therefore, the Total number of marbles left=35-6

The total number of marbles left=29 marbles.

Therefore, The number of marbles left in the pocket after losing is  29 { after narrating the story in numerical sentences}

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154mm

we know that  1cm = 10 mm

 therefore      15cm= 10*15 mm

                               =  150 mm

and 4 mm

we get total mm= 15cm +4mm

                          = 150mm+4mm

                           = 154 mm                  

mm stands for millimeters and cm stand for centimeters

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The fraction of a pizza Matt gave Stuart is 4/8 or 2/4 or 1/2.

Given that, Matt sliced a pizza into 8 equal parts and gave 4 slices to Stuart.

We need to find the fraction of a pizza Matt gave Stuart.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.

Now, the fraction=4/8

=2/4 =1/2

Therefore, the fraction of a pizza Matt gave Stuart is 4/8 or 2/4 or 1/2.

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