Given that the polynomial [tex]f(x)[/tex] has 9 turning points, which of the following most accurately describes the degree of [tex]f(x)[/tex]?


A. The degree of F(x) is at most 10.

B. The degree of F(x) is at most 8.

C. The degree of F(x) is at least 10.

D. The degree of F(x) is at most 9.

E. The degree of F(x) is at least 9.

F. The degree of F(x) is at least 8.

Answer:333

Step-by-step explanation:53533535

Answer:

Step-by-step explanation:

Equate whats inside (arguments) \sin with base period of sine function 2\pi and solve for x to get period,

\pi x=2\pi\implies x=2

So the period of the graph of the given function is precisely 2.

Hope this helps :)

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{65}~,~\stackrel{y_1}{149})\qquad (\stackrel{x_2}{105}~,~\stackrel{y_2}{221}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{221}-\stackrel{y1}{149}}}{\underset{\textit{\large run}} {\underset{x_2}{105}-\underset{x_1}{65}}} \implies \cfrac{ 72 }{ 40 } \implies \cfrac{ 9 }{ 5 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{149}=\stackrel{m}{ \cfrac{ 9 }{ 5 }}(x-\stackrel{x_1}{65})\implies y-149=\cfrac{ 9 }{ 5 }x-117 \\\\\\ y=\cfrac{ 9 }{ 5 }x-117+149\implies \boxed{y=\cfrac{ 9 }{ 5 }x+32} \\\\\\ \stackrel{\textit{Celsius is 70, so x = 70}}{y=\cfrac{ 9 }{ 5 }(70)+32}\implies \boxed{y = 158}[/tex]

The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as,

H² = P² + B²

The height of Triangle ΔABC is given as,

17² = h² + 15²

289 = h² + 225

h² = 289 - 225

h² = 64

h = 8 units

The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.

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1. The value of the variable 'x' is 10 that is written as x = 10.

2. The equation is ∠3 + ∠4 = 90°. Then angles ∠3 and ∠4 will be complementary angles.

3. The measure of angle ∠2 is 60° which is an acute angle.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

1.  ∠1 = 6x + 45 and ∠3 = 9x + 15

Angle ∠1 and angle ∠3 are opposite angles. Then the equation is given as,

∠1 = ∠3

9x + 15 = 6x + 45

9x - 6x = 45 - 15

3x = 30

x = 30 / 3

x = 10

2.  Angle ∠2, angle ∠3, and angle ∠4 are supplementary angles. Then the equation is given as,

∠2 + ∠3 + ∠4 = 180°

90° + ∠3 + ∠4 = 180°

∠3 + ∠4 = 90°

3.  Angle ∠1 is 120°, then the measure of angle ∠2 is given as,

∠1 + ∠2 = 180°

120° + ∠2 = 180°

∠2 = 60° (acute)

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This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

Product is an item or service that is created by a business or organization to meet the needs of their customers. It is anything that is offered to a market for sale or trade. Products can be tangible, such as physical goods or intangible, such as services, ideas, or experiences. Companies need to create products that offer value to their customers. This includes making sure that the product meets the customer's needs, is of good quality, and is priced appropriately.

An empty product is a mathematical term that is used to describe a product of two or more numbers, where the result is equal to the product of just one of the numbers. This is because when you multiply any number by zero, the result is zero. Therefore, if a product contains a zero, then the result will be the same as if you only multiplied one of the numbers in the product. For example, if we take the product of 5 and 0, then the result is 0. This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

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Answer:

227.27%

Step-by-step explanation:

From the given options, option 1 depicts a decreasing function. Hence, option 1 is the correct answer for the graph.

Calculus uses a function's derivative to determine whether a function is rising or decreasing at various intervals in a specific domain. Given 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.

We observe that the function of f approaches to 0 as it moves towards infinity. Thus, it is a decreasing function.

From the given options, option 1 depicts a decreasing function. Hence, option 1 is the correct answer.

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[tex]9x^2-6x+1=2 \iff (3x)^2-2(3x)+1=2\\[/tex]

[tex](3x - 1)^2 = 2[/tex]

[tex]3x-1=-\sqrt{2} \iff 3x = 1 - \sqrt{2} \implies x_{1} = \dfrac{1-\sqrt{2} }{3}\\[/tex]

[tex]3x-1=\sqrt{2} \iff 3x = 1 + \sqrt{2} \implies x_{2} = \dfrac{1+\sqrt{2} }{3}\\[/tex]

[tex](-0.14, \ 0.8)[/tex]

Answer:

A. the graph of the function does not form a straight line.

Step-by-step explanation:

The result of simplifying this answer is (x - 1)2 = 16(y - 7) (y - 7) The equation for the parabola is presented here in vertex form.

A parabola is a U-shaped curve in mathematics that is produced by the graph of a quadratic function. It is a particular kind of conic section, which is a circle made when a plane and a cone cross each other. A quadratic function with the following standard form can depict a parabola: Y = ax2+bx+c where are constants a, b, and c. Which way the parabola expands depends on the sign of the coefficient a.

given

We can use the following formula to express the equation of a parabola given a focus and a directrix:

where (h,k) is the parabola's vertex, p is the separation between it and the centre, and the directrix is represented by the horizontal line y = k - p.

The centre in this instance is (1,11), and the directrix is y=3.

We also understand that p is the distance, in this instance 4 units, between the vertex and the focus (since the focus is 4 units above the vertex). Therefore, we can enter the numbers into the formula to obtain:

(x - 1)^2 = 4(4)(y - 7) (y - 7)

The result of simplifying this answer is (x - 1)2 = 16(y - 7) (y - 7) The equation for the parabola is presented here in vertex form.

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Answer:

[tex](r \;\circ\;q)(4) = \boxed{5}\\\\(q \;\circ\;r)(4) = \boxed{13}\\[/tex]

Step-by-step explanation:

We have the following functions

[tex]q(x) = x^2+4\\\\and\\\\r(x) = \sqrt{x+5}\\\\[/tex]

1. To find
[tex](r \;\circ \;q)(4) = r(\;q(4)\;)[/tex]

First find
[tex]q(4) = 4^2 + 4 = 16 + 4 = 20[/tex]

Substitute this value for x in r(x)

[tex]r(20) = \sqrt{20 + 5} = \sqrt{25} = 5[/tex]

So
[tex]\bold{(r \;\circ \;q)(4) = 5}[/tex]

2. To find
[tex](q \;\circ\;r)(4) = q(\;r(4)\;)[/tex]

First find
[tex]r(4) = \sqrt{4 + 5} = \sqrt{9} = 3\\\\[/tex]

Substitute this value for x in q(x)

[tex]q(3) = 3^2 + 4 = 9 + 4 = 13\\\\\bold{(q \;\circ\;r)(4) = 13}[/tex]

The compositions of functions are:

Here we have the two functions:

q(x) = x² + 4

r(x)=  √(x + 5)

We want to find the two compositions:

(r o q)(4) = r(q(4))

First let's find:

q(4) = 4² + 4 = 16 + 4 = 20

Then:

r(q(4)) = r(20) =  √(20 + 5) = 5

And the other composition is:

(q o r)(4) = q(r(4))

First, r(4) = √(4 + 5) = 3

Then:

q(r(4)) = q(3) = 3² + 4 = 9 + 4 = 13

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Answer:

The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

Step-by-step explanation:

Answer:

Ignore my handwriting loll

Step-by-step explanation:

Hope this helps! :)

The length of the radius and diameter are 10.5 and 21 respectively

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

The area of the sector = tetha/360 × πr²

= 72/360 × 3.14 × r²

= 0.628r²

area of the circle = area of the shaded part + area of sector

3.14r² = 277 + 0.628r²

3.14r²-0.628r² = 277

2.512 r² = 277

r² = 277/2.512

r² = 110.3

r = √ 110.3

r = 10.5

d = 2r

d = 10.5 × 2

= 21

therefore the radius and diameter are 10.5 and 21 respectively

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The equation for the function with the described transformations is y(x) = -2f(x+1) + 8.

Starting with the basic function of f(x), we can apply the described transformations in the following order:

Vertical stretching by a factor of 2: We multiply the output of the function by 2. This results in a new function g(x) = 2f(x).

Reflection across the x-axis: We flip the sign of the output of the function. This results in a new function h(x) = -g(x) = -2f(x).

Translation 1 unit left and 8 units up: We shift the graph of the function 1 unit to the left and 8 units up. This can be achieved by replacing x with (x+1) and adding 8 to the output.

This results in a new function y(x) = h(x+1) + 8 = -2f(x+1) + 8.

Putting it all together, the equation for the function with the described transformations is:

y(x) = -2f(x+1) + 8

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The complete question is below:

Write an equation for f(x) when it is vertically stretched by a factor of 2, reflected across the x-axis, then translated 1 unit left and 8 units up.​

Answer:

[tex]310 ^\circ F[/tex]

Step-by-step explanation:

The formula relating surface temperature in °F and time in t minutes after removal from the oven is given as

[tex]S(t)= 72 + 238 (0.97^t)\\\\\text{The initial temperature is when t = 0}\\\\\text{At t = 0}\\\\S(0) = 72 + 238(0.97^0)\\\\0,97^0 = 1 \text{ since any number raised to 0 = 1}\\\\\text{Therefore}\\S(0) = 72 + 238 \cdot 1\\= 72 + 238\\\\= 310 ^\circ F[/tex]

Handheld consoles are the most at risk of being discontinued compared to other types of consoles.

option A.

Handheld consoles have faced tough competition from the rise of mobile gaming on smartphones and tablets, which has impacted their market share and sales.

For example, Nintendo has faced challenges with their handheld consoles, such as the Nintendo DS and 3DS, which experienced a decline in sales due to the emergence of mobile gaming. As a result, Nintendo shifted its focus to the hybrid console, the Nintendo Switch, which can be used as both a handheld and home console.

That being said, it's important to note that the market for handheld consoles is still significant, and there are still popular handheld devices on the market such as the Nintendo Switch Lite and Sony's PlayStation Vita. The entertainment, interactive, and computer console markets also have their own unique challenges and opportunities, and each type of console has its own risks and benefits.

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Answer:

0.0166666666666666666666666666666666666666666667

Step-by-step explanation:

USE CALCULATORRRRRR

The scale factor of the dilation is (d) 1 : 5 reduction

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

The larger rectangle is dilated to form the smaller rectangle

Using the above as a guide, we have the following:

Larger rectangle = 5

Smaller rectangle = 1

So, we have

Scale factor = Smaller rectangle : Larger rectangle

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

Scale factor = 1 : 5

Hence, the scale factor is 1 : 5 reduction

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Answer:

Step-by-step explanation:

We can use the conditional probability formula to find the probability of a student taking a calculus class given that the student takes a statistics class:

P(calculus | statistics) = P(calculus and statistics) / P(statistics)

We are given that P(statistics) = 0.83 and P(calculus and statistics) = 0.66.

Substituting the values we have:

P(calculus | statistics) = 0.66 / 0.83

Simplifying the fraction:

P(calculus | statistics) = 0.795

Therefore, the probability of a student taking a calculus class given that the student takes a statistics class is 0.795. Rounded to three decimal places, the answer is 0.795.

John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. $75 = $15p + A

What is the total of the cost?

Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.

Let the number of people on John's family plan be represented by p.

According to the problem, the family plan cost is $68, and there is an additional cost of $15 for each person on the plan. Therefore, the total cost C of the plan with p people is:

C = $68 + $15p

We know that John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. Therefore, we can write:

$143 = C + A

where A represents any additional charges.

Substituting C into this equation, we get:

$143 = ($68 + $15p) + A

Simplifying, we can write:

$75 = $15p + A

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The constant of proportionality between the side length and the perimeter of the equilateral triangle would be = 3.

The constant of proportionality is defined as the constant value that exists between two variables that are in a direct proportional relationship to each other.

For example, the constant of proportionality (k) between the side lengths and the perimeter of the equilateral triangle= y/X= 15/5= 3 or 24/8 = 3 or 27/9 = 3 or 30/10=3.

Therefore, the constant of proportionality which is the constant value existing between the two variables= 3.

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Answer:

Step-by-step explanation:

We can use the rule of 72 to estimate the time it takes for Arthur's investment to double. The rule of 72 states that the time it takes for an investment to double is approximately 72 divided by the annual rate of return.

To apply this rule, we need to calculate the annual rate of return that Arthur is earning on his investment. We can do this by calculating the percentage increase in his account balance from year to year.

From year 1 to year 2, his account balance increased by (118.81 - 109)/109 = 9.81/109 = 0.09 = 9%.

From year 2 to year 3, his account balance increased by (129.5 - 118.81)/118.81 = 10.69/118.81 = 0.09 = 9%.

So the average annual rate of return over this period is approximately 9%. Using the rule of 72, we can estimate that it will take approximately 72/9 = 8 years for Arthur's investment to double.

Therefore, the closest option among the given responses is option D. It will take about 8.04 years for Arthur's investment to double.

Answer: To simplify the expression, we can apply the exponent rule for powers of powers which states that to raise a power to another power, we multiply the exponents.

So,

(4a^(-2))^(-1/2) = 4a^(-2 * (-1/2)) = 4a^(1) = 4a

Therefore, (4a^-2)^-1/2 simplifies to 4a.

Step-by-step explanation:

The value of x in the figure and given in the task content is; x = 64.

As evident in the task content; the figure is a triangle with angle measures; 63°, 56° and (x - 3)°.

Since the sum of interior angles of a triangle is; 180°.

Therefore, we have;

63° + 56° + (x - 3 )= 180°

open parenthesis

63 + 56 + x - 3 = 180°

x = 180 + 3 - 63 - 56

x = 64°.

Ultimately, the value of variable, x from the triangle is; 64°.

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The solution to the system of inequalities is:

{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.

A linear inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

First, let's graph the line x = -2, which is a vertical line passing through -2 on the x-axis.

Next, let's graph the line x - y = 1, which can be rewritten as y = x - 1. This is a line with a slope of 1 (meaning it goes up 1 unit for every 1 unit it goes to the right) and a y-intercept of -1 (meaning it passes through -1 on the y-axis).

Now, we need to shade in the region that satisfies both inequalities. We know that x has to be greater than or equal to -2, so we shade to the right of the vertical line x = -2. We also know that x - y has to be greater than or equal to 1, so we shade above the line y = x - 1.

The shaded region is the overlapping region that satisfies both inequalities. It is the region above the line y = x - 1 and to the right of the vertical line x = -2.

Therefore, the solution to the system of inequalities is:

{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.

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The complete question is as follows:

What is the solution to the system of inequalities?

x ≥ -2

x - y ≥ 1

Answer:

Step-by-step explanation:

[tex]C=\pi d[/tex]

   [tex]=\pi \times 35[/tex]

   [tex]\approx 109.96 feet[/tex]

Answer:

110. feet approximately

Step-by-step explanation:

circumference means a closed boundary of a curved shape. Mainly known as a circle. To find circumference, use the formula c= π (pie) times diameter.

35 × π ≈ 110

Hope this helps :)