a paint roller has a width of 12 inches and a radius of 3 inches, what is the surface area that can be painted with one complete rotation of the roller

The function obtained after transformation is given as -x³ + 9x²- 27x + 21.

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

For left shifting it is f(x + a).

The function is given as f(x) = x³- 6.

The translation of 3 units towards left can be written as,

f(x + 3) = (x + 3)³ - 6

⇒ x³ + 9x² + 27x + 21

For reflection across y axis replace -x with x as below,

⇒ (-x)³ + 9(-x)² + 27 × -x + 21

⇒ -x³ + 9x²- 27x + 21

Hence, the required form of the transformed function is -x³ + 9x²- 27x + 21.

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The explicit formula of the sequence is aₙ = -10 + 8n

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

The first term and the common difference

These values of the first term and the common difference are given as

First term = -2

Common difference = 8

The interpretation of the above sequence is that the 8 is added to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

aₙ = aₙ₋₁ + 8

When represented explicitly, we have

aₙ = a + (n - 1) * d

Where

a = -2 and d = 8

Substitute the known values in the above equation, so, we have the following representation

aₙ = -2 + (n - 1) * 8

Evaluate the products

aₙ = -2 + 8n - 8

Evaluate the like terms

aₙ = -10 + 8n

Hence, the explicit formula is aₙ = -10 + 8n

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A. 5/10, -6/11, 7/12, -8/13

B. f(n) = n/(n+5)

C. Positive

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.

Here, we have

A. From inspection of the sequence, the pattern is:

Add 1 to the numerator of the previous term.

Add 1 to the denominator of the previous term.

Make every other term negative.

Hence, assuming the pattern continues, the next four terms in the sequence will be:

5/10, -6/11, 7/12, -8/13

B. An explicit formula for an arithmetic sequence allows you to find the [tex]n^{th}[/tex] term of the sequence.

f(1) = 1/6

f(2) = -2/7

We can see that the numerator is the position of the term (n) in the sequence.  So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.

The denominator is 5 more than the position of the term in the sequence.  So when n = 1 the denominator is 1 + 5 = 6, and when n = 2 the denominator is 2 + 5 = 7.

We observe that if the numerator (the value of n) is odd then the term is positive, and if the numerator  (the value of n) is even then the term is negative.

Hence, the rule for the nth term is:

f(n) = n/(n+5)

If n is odd then f(n) is positive.

If n is even then f(n) is negative.

C. 53 is an odd number.

As the function f(n) is positive when n is odd, the sign of f(53) is positive.

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Basic quadratic expression:

[tex]ax^2+bx+c[/tex]

[tex]2x^2+5x-42[/tex]

Factoring a quadratic expression when a ≠ 0

1.  Multiply a and c values (ac=k)

[tex]2(-42) = -84[/tex]

2. Find a factor pair whose sum adds to b and has the product of k

[tex]-7,12[/tex]  

[tex]-7(12)=-84[/tex]           [tex]-7+12=+5[/tex]

3. Replace the middle term (bx) with newfound values

[tex]2x^2 +12x-7x-42[/tex]

4. Factor by grouping

[tex]2x(x+6) -7(x+6)[/tex]

5. Perform the last factorization

[tex](2x-7)(x+6)[/tex]

a. The key features of the exponential function y = 1000(2)^(0.3x) is given as follows:

b. The relevant domain and range are given as follows:

The exponential function for this problem is modeled as follows:

y = 1000(2)^(0.3x).

The features are given as follows:

The domain of the function is the set that composes all input values of the function, and as the exponential function does not have any restrictions such as a fraction or an even root, it is composed by all real values.

However, the relevant domain is x ≥ 0, as the number of days does not assume negative values.

The range is the set containing all output values of the exponential function. As the initial value of the exponential function is of 1000 and the function is increasing, the range is y ≥ 1000.

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The y-intercept of (0,4) is 4.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.

The y-coordinate of the y-intercept is determined by computing  f(0) if the curve in question is supplied as y=f(x), y=f(x), etc. There is no y-intercept for functions that have an  value at x = 0.

The constant term a is the y-coordinate of the y-intercept if the function is linear and is written in slope-intercept form as  f(x)=a+bx"

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Answer:

  2x +3y = 15  or  y = -2/3x +5

Step-by-step explanation:

You want the equation of the line with y-intercept 5 and x-intercept 7.5.

The intercept form equation can be written ...

  x/a +y/b = 1

where 'a' is the x-intercept and 'b' is the y-intercept.

The given intercepts of a=7.5 and b=5 mean we can write the equation as ...

  x/7.5 +y/5 = 1

Multiplying by 15 gives the standard-form equation ...

  2x +3y = 15

Solving for y gives the slope-intercept equation ...

  y = -2/3x +5

If Zoe already has $80 and can save an additional $6 per week using money from her after school job then the total amount of money that Zoe saved after 6 week of saving is $116  and

the expression that represent amount of money Zoe would have saved in w weeks is [tex]80+6w[/tex]  .

The amount that Zoe already saved = $80 ;

the amount that she can additionally save is = $6 per week ,

the amount of money that can be saved after 6 weeks can be written as :

[tex]Amount = \$80+(Amount Saved Per Week)\times(Number Of Weeks)[/tex]

Amount = [tex]80+6\times6[/tex]

= [tex]80+36[/tex]

= $116

and the expression for w weeks will be = [tex]80+6\times w[/tex]

The expression is ⇒ [tex]Amount = 80+6w[/tex].

The given question is incomplete , the complete question is

Zoe is saving up to buy a new bicycle. She already has $80 and can save an additional $6 per week using money from her after school job. How much total money would Zoe have after 6 week of saving ?

Also, write an expression that represent the amount of money Zoe would have saved in w weeks ?

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Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. The scale factor is equal to the ratio of these distances.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

A graph's form is altered by dilations, frequently leading to "movement" in the process. In the figure above, the green curve has been "transformed" into the red curve. It has been three times "dilated" (or stretched) horizontally. A dilatation is an axial stretching or contraction brought on by multiplication or division.

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A. The amplitude of the sinusoidal function 's' would increase.

B. The midline of the sinusoidal curve will upshift.

A function that repeats its values at regular intervals is said to be periodic. For instance, periodic functions include trigonometric functions, which repeat every 2 pi radian. In science, periodic functions are used to describe oscillations, waves, and other periodic events. Aperiodic refers to any nonperiodic function.

We know the moving mechanism of the pendulum can be graphed as a periodic function.

A. If the pendulum is pulled farther away from its resting point it will reach a greater height on both sides this would have an effect of an increase in the amplitude of the sinusoidal curve.

B. If the pendulum is pulled farther away from its resting point the midline of the sinusoidal curve would move up along the y direction as a result of an increase in magnitude.

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Answer:

Step-by-step explanation: Two quarters, 50 pennies: N = 52 (N+1 = 53) One quarter, 75 pennies: N = 76 (N+1 = 77) 100 pennies, N = 100 (N+1 = 101) 6 nickels, 70 pennies: N = 76 (N+1 = 77)

Answer:

2 quarters, 2 dime's, 1 Nickel, 2 penny's

Step-by-step explanation:

Well u well need to quarters because 2 quarters are $25 cent then u well need 2 dimes because when your counting dime's that 10 20 30 40 50 so to dime's and 1 Nickel that makes $75 cents so u need 2 penny's and that makes 77

The plane intercepts on the x,y, z axes are 1, ∞, and 1/2. Hence, the Miller indices for the plane inside the cubic unit cell is (102).

Miller indices are used to specify planes and directions. These planes and directions could be in lattices or crystals. The number of indices will correspond to the size of the lattice or crystal.

In the given graph, the plane intercepts are:

x-intercept : 1

y-intercept : ∞  (since the planes does not intercept y-axes)

z-intercept = 1/2

Take the reciprocal:

1/1 = 1

1/∞ = 0

1/(1/2) = 2

Hence, the miller indices are (102)

The graph in your question is missing. Most likely it was like on the attached picture.

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The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)

An equation is an expression that shows how numbers and variables relate with each other.

A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.

The standard form of a quadratic equation is:

y = ax² + bx + c

where a, b and c are constants.

Given the polynomial:

x² + 3x + 2

Factorizing the polynomial:

x² + 2x + x + 2

= x(x + 2) + 1(x + 2)

= (x + 1)(x + 2)

The factorization gives (x + 1)(x + 2)

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The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} + Base^{2}[/tex]  ;

let the missing side of the right triangle  be the hypotnuse ;

So , missing side can written as :  [tex]Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}[/tex] .

For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10

The length of side "base" is unknown.

So ,  to find length of side b, we put the known values into theorem:

[tex]10^{2} = 6^{2} + Base^{2}[/tex] ;

[tex]base^{2} = 100 - 36[/tex] ;

So , the missing side "base" = 8 ;

Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .

The given question is incomplete , the complete question is

How do you find the missing side of a right triangle without a calculator when the other two sides are given ?

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There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.

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Answer:6 days

Step-by-step explanation:

62-26=36

36/6=

6

4x - 6 = x + 9

4x - x = 9 + 6

3x = 15

[tex]x = \frac{15}{3} \\ [/tex]

x = 5 ...

Answer:

[tex]x =5[/tex]

Step-by-step explanation:

[tex]4x - 6=x+9[/tex]

Subtract x from both sides

[tex]4x -6-x=x+9-x[/tex]

[tex]3x-6=9[/tex]

Add 6 to both sides

[tex]3x-6+6=9+6[/tex]

[tex]3x=15[/tex]

Divide both sides by 3

[tex]\frac{3x}{3} = \frac{15}{3}[/tex]

[tex]x = 5[/tex]

Answer:

d

Step-by-step explanation:

Answer:

$22

Step-by-step explanation:

27.50 20 present off so you get 5.5 substract and u get 22

Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.

Here,

Given :

=>  f(x) = 225(1.29)×

After 10 year number of years x =10

=> f(x) = 225(1.29)¹⁰

=> f(x) = 12.76 * 225

=>  f(x) = 2871 thousands.

Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

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Answer:

SaS

Step-by-step explanation:

In each shape there are 4 wholes hence the answer is yes.

A fraction is referred to as the portion of a whole in mathematics. There are two components to a fraction: a numerator and a denominator. The numerator is the number at the top, and the denominator is the number at the bottom.

13a. There are 4 wholes, hence the answer is yes.

13b. Every whole is divided into 2 parts hence the total number of equal parts is 4 *2 = 8. Hence the answer is yes.

13c. The answer is yes.

13d. No

13e. No

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The measure of ∠Z is 165 degrees to the nearest degree.

In a triangle, the measure of each angle is equal to the sum of the measures of the other two angles subtracted from 180 degrees. This is known as the Triangle Sum Theorem.

Given that x = 5.2 inches, y = 9.8 inches, and z = 7.1 inches in triangle XYZ, we can use the theorem to find the measure of angle Z.

∠Z = 180 - (x+y)

∠Z = 180 - (5.2+9.8)

∠Z = 180 - 15

∠Z = 165

So the measure of ∠Z is 165 degrees to the nearest degree.

Therefore, The measure of ∠Z is 165 degrees to the nearest degree.

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To find the MEAN of Natural numbers, such as  1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, a + b + c3 is the sum of the three numbers a, b, and c. Therefore, 5.5 is the MEAN of the first 10 natural numbers.

Firstly The Given set of numbers Represents Natural numbers,

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc.

Therefore, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

And the mean of three numbers a, b, c is a + b + c3

Then the mean of 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is:-

⇒1+2+3+4+5+6+7+8+9+1010

Adding and dividing we get the value of the above term as,

⇒1+2+3+4+5+6+7+8+9+1010=5510=5.5

Hence, the mean of the first 10 natural numbers is 5.5.

Note: To solve this problem, you must understand that the integers greater than zero are natural numbers and that the mean of the three numbers a, b, and c equals a + b + c3. Knowing how to calculate the average number of elements and being familiar with natural numbers can help you arrive at the correct conclusion.

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The explicit formula for the sequence -28, -31, -34, -37, ..., is aₙ= -28 -3d.

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

-28, -31, -34, -37, ...

The general formula of an arithmetic sequence:

aₙ= a₁ + (n)d,

where a₁ is the first term and d is the common difference.

First, we will find the common difference between consecutive terms.

Here,

a₁ = -28

To find the common difference:

a₂ - a₁ = -31 + 28 = -3

a₃ - a₂ = -34 + 31 = 3

a₄ - a₃ = -37 + 34 = 3

Hence, d = -3.

Substitute the values to the formula,

aₙ= a₁ + (n)d,

aₙ= -28 + (-3)d,

aₙ= -28 -3d

Therefore, aₙ= -28 -3d is the required sequence.

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Answer:

x=-12/5

Step-by-step explanation:

2x-7=7x+5

2x-7x=5-(-7)

-5x=5+7

x=12/-5

x=-12/5

In a triangle, a line is drawn parallel to one side of the triangle. Then it ratio of the two similar triangles will be con

The Basic Proportionality Theorem, often known as the Thales Theorem, was developed by the eminent Greek mathematician Thales. He asserted that the ratio of any two matching sides is constant for any two equiangular triangles. He developed the basic proportionality theorem based on this idea (BPT). Similar triangles have presented this idea. When two triangles resemble one another.

Think about the triangle ΔABC in the given illustration. A line PQ connecting the sides AB and AC of P and Q in this triangle is drawn parallel to the side BC of the triangle.

AP/PB = AQ/QC

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Answer:

2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{2x9}[/tex] - [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex] - [tex]\sqrt{2}[/tex] = 2[tex]\sqrt{2}[/tex]

The two changes that would Karl earn more money are "Karl increases his initial investment" and "Karl deposits more money into the account every year" (options B and D).

In this case, the amount of money Karl can get depends on both the amount of money he invest and the interest rate. Here are some examples:

If he invest $100 and the interest rate is 10% he will get $10

If the invest $1000 and the interst rate is the same (10%) he will get $1000

Moreover, if the interste rate increases he can get more money: If the invest $100 but the interst rate is 12% he gets $12

This means he can get more profit if the investment is higher or the rate increases. Based on this, the two options that would increase his amount of money are increasing the initial investment or depositing more money (option B and D).

Note: This question is incomplete; here is the missing section:

A. The bank decreases the interest rate.

B. Karl increases his initial investment.

C. The bank adds a fee to keep the account active.

D. Karl deposits more money into the account every year.

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A triangle is said to be acute if the sum of the squares of its two shorter sides is greater than the square of its longest side.

Less than 90 degree angles are considered acute. Right angles have a 90 degree angle. Angles that are obtuse exceed 90 degrees.

See samples of various angles and learn about them. If and only if side lengths a, b, and c satisfy a2 + b = c2, a right triangle will be formed. These numbers are referred to as a Pythagorean triple. When the square of a triangle's longest side equals the sum of the squares of its other two sides, the triangle is said to be a right triangle. So, in the ABC equation, if c2=a2+b2, then C is a right triangle, with PQR serving as the right angle.

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