ALGEBRA 2 QUESTION You are having a meeting with the CEO of a soda company. You have interpreted the number of cans of soda produced versus profit as the function [tex]P(x) = x^4 - x^3 - 11x^2 + 9x + 18[/tex]. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviours of the graph and where the company will break even (where P(x) = 0). (

The comparisons of the fractions given above is enumerated below.

1) To compare 1/8 and 1/9, I can find a common denominator by multiplying the denominators together. The common denominator is 8 x 9 = 72.

Then, I can convert each fraction to have a denominator of 72 by multiplying the numerator and denominator of each fraction by the appropriate factor. The result is 9/72 and 8/72. Since 9/72 is bigger than 8/72, I know that 1/8 is smaller than 1/9.

2) To compare 7/8 and 8/9, I can find a common numerator by multiplying the numerators together. The common numerator is 56. Then, I can convert each fraction to have a numerator of 56 by multiplying the numerator and denominator of each fraction by the appropriate factor. The result is 49/56 and 64/72. Since 64/72 is bigger than 49/56, I know that 8/9 is bigger than 7/8.

3) To compare 15/38 and 5/13, I can find a common numerator by multiplying the numerators together.

The common numerator is 195. Then, I can convert each fraction to have a numerator of 195 by multiplying the numerator and denominator of each fraction by the appropriate factor.

The result is 75/195 and 75/195. Since the numerators are the same, I can compare the denominators. Since 195 is bigger than 169, I know that 15/38 is smaller than 5/13.

4) To compare 5/9 + 7/12 and 1/2, I can compare each fraction to 1/2 separately.

First, 5/9 is smaller than 1/2 because 9 is bigger than 18, so each ninth is smaller than each half.

Next, 7/12 is also smaller than 1/2 because 12 is bigger than 6, so each twelfth is smaller than each half.

Therefore, both fractions added together (without actually adding them) will be smaller than 1/2.

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Answer:

Step-by-step explanation:

25

The growth rate is - 0.17

a. Growth rate =  (38-55)/100 = -0.17

This shows that it is decreasing

ii. Groth rate = 38-12.5)/(100-250)

= -0.17

This shows that it is decreasing as well

b. The relationship is a linear function. This is because rate of change of price and the number of days are equal

c. formula for game price in terms of days would be:

Price = -0.17*d + 55.

d = days

d. when price is 48.20

48.20 = -0.17d + 55

48.20 - 55 = -0.17d

d = 40

40 days after game was released

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Answer:

[tex]x^4-3x^2-x^2-4[/tex]

Step-by-step explanation:

Given information.

P(x) = R(x) - C(x)

[tex]R(x) = 2x^4-3x^3+2x-1[/tex]  and [tex]C(x) = 2x^4-x^2+2x+3[/tex]

[tex](2x^4-3x^3+2x-1) - (x^4-x^2+2x+3)[/tex]

Distribute the negative then solve by simplying either add or subtracting.

[tex](2x^4-3x^3+2x-1) +(-x^4+x^2-2x-3)\\[/tex]

[tex](2x^4-x^4)-3x^3-x^2+(2x-2x)+(-1-3)\\\\(x^4) -3x^3-x^2+(0x)-4\\\\x^4 -3x^3-x^2-4[/tex]

Answer: Your welcome!

Step-by-step explanation:

N′(−11, −2), M′(−8, −1), O′ (−11, −5)

The image coordinates of N′M′O′ if the preimage is translated 7 units to the left are N′(−11, −2), M′(−8, −1), O′ (−11, −5). This is calculated by subtracting 7 from the x-coordinate of each point in the original triangle NMO. For example, the x-coordinate of point N in the original triangle is -4, so the x-coordinate of point N′ in the translated triangle is -4 - 7 = -11. The y-coordinate of point N does not change, so the y-coordinate of point N′ is also -2.

Answer:

To translate the triangle 7 units to the left, we need to subtract 7 from the x-coordinates of each vertex:

N' = (N_x - 7, N_y) = (-4 - 7, -2) = (-11, -2)

M' = (M_x - 7, M_y) = (-1 - 7, -1) = (-8, -1)

O' = (O_x - 7, O_y) = (-4 - 7, -5) = (-11, -5)

Therefore, the image coordinates of N'M'O' are (-11, -2), (-8, -1), and (-11, -5).

So the answer is N′(−11, −2), M′(−8, −1), O′ (−11, −5).

Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = $200.00

r = 0.09 (9% expressed as a decimal)

n = 1 (compounded annually)

t = 5 years

Plugging these values into the formula, we get:

A = $200.00(1 + 0.09/1)^(1*5)

A = $200.00(1.09)^5

A = $200.00(1.538624)

A = $307.72

Therefore, after 5 years, Megan will have $307.72 in her account.

Step-by-step explanation:

The area of the composite figure is 14.71 square units

The area of the composite figure is found by calculating the sum of the areas of the various parts.

The area of the figure = area of sector + area of triangle + area of trapezium

Area of sector = 135/360 * π * 2²

Area of sector = 4.71 square units

Area of triangle = ¹/₂ * 2 * 1

Area of triangle = 1 square unit

Area of trapezium = ¹/₂ (3 + 6) * 2

Area of trapezium = 9 square units

Therefore, area of composite figure =  (4.71 + 1 + 9) square units

The area of the composite figure = 14.71 square units

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0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves.

In mathematics, a percentage is a quantity or a ratio that is expressed as a fraction of 100. Calculating a percentage involves multiplying a quantity by 100 and dividing it by the total.

To determine "how much" or "how many," utilise the percentage. Calculating the precise quantity or figure that is being discussed is made easier with the use of a percentage. We compare fractions. determining a percentage rise or fall aids in calculating profit and loss margins.

In this case, 0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves for the project.

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True; the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.

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

f(x) = 7.5x

The point is given as

(x, y) = (-1/5, -3/2)

To determine whether the point (-1/5, -3/2) lies on the graph of f(x) = 7.5x, we can substitute x = -1/5 into the equation and see if it gives us y = -3/2.

f(x) = 7.5x

By substitution, we have

f(-1/5) = 7.5(-1/5)

Evaluate

f(-1/5) = -1.5

Express as fraction

f(-1/5) = -3/2

So, the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.

Hence, the statement is false.

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Complete question

True or False. The point (-1/5, -3/2) lies on the graph of f(x).

Where f(x) = 7.5x

The x intercept and the y intercept for 6x - 3y = -12 is x = 0.5y + 2 and y = 2x - 4.

The term “intercept” refers to the location where a line or curve crosses a graph's axis. The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.

The line's steepness is measured by its slope (m). It is the difference between the y-coordinate change and the corresponding x-coordinate change. For 6x - 3y = 12, just enter the above coordinates and solve for m to obtain the slope.

To solve for x, we solve the equation so the variable x is by itself on the left side:

6x - 3y = 12

x = 0.5y + 2

To solve for y, we solve the equation so the variable y is by itself on the left side:

6x - 3y = 12

y = 2x - 4

Therefore, the x = 0.5y + 2 and y = 2x - 4.

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cot (-859°) can be expressed as cot 41° an acute angle which is less than 45°

Trigonometry is used in navigation directions. Estimate the direction you need to place your compass to get a straight line. With the help of a compass and navigation trigonometric functions, it's easy to find a place or find the distance to see the horizon. 

A  Mathematical Statement which contains numbers and variables.

Angle: The two straight lines meeting at the vertex(a common point)

According to the question:

cot (-859) can be expressed as:

cot (-859 + 360x2)= cot (-859 +720)= cot (139)= cot (180 -139)= cot 41°(or)cot(-859) = cot(-859 + 180°x5)= cot (859 +900)= cot (41)°

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Answer:

y = 3/5x - 3

Step-by-step explanation:

slope (m) of line perpendicular to y = -5/3x is 3/5, the negative reciprocal of -5/3

use the point (5, 0) and the point-slope form to find b, the y-intercept:  

y - 0 = 3/5(x - 5)

y = 3/5x - 15/5

y = 3/5x - 3   equation is now in the slope-intercept form

The probability of a false positive test result is approximately 0.267 or 0.267 probability units.

Probability is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1.

For example, the probability of rolling a six on a fair dice is 1/6 or approximately 0.167. It is a fundamental concept in statistics and plays a crucial role in many real-life applications, such as decision-making, risk analysis, and scientific research.

To find the probability of a false positive test result, we need to calculate the proportion of individuals who test positive but do not use drugs out of the total number of individuals. This is represented by the ratio of the number of false positives to the total number of negative test results, which is:

(false positives) / (negative test results) = 8 / 30 = 0.267

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The volume of the top part of the pyramid is 13.4% of the total volume.

The amount of mass that a material has in relation to its volume is measured by its density. By dividing the substance's mass by volume, it is determined. Density is calculated as follows: density = mass/volume

A fundamental idea in physics, density is utilised in many branches of research and engineering, including the construction of effective engines and turbines, calculating the buoyancy of objects in fluids, and forecasting the behaviour of materials under stress.

Given that, average density of the entire pyramid is 4.7g/cm3 and that the bottom part has a mass of 972.8g.

The density is given as:

density = mass/volume

Substituting the value we have:

4.7g/cm3 = 972.8g/volume

volume = 207.23 cubic cm.

For the top part, density of 2.9g/cm3 and a mass of 92.8g. :

density = mass/volume

2.9g/cm3 = 92.8g/volume

volume = 32 cubic cm.

The percent of the top part with respect to total volume is:

percentage = (volume of top part / total volume) x 100

total volume = volume of top part + volume of bottom part

total volume = 32 cm3 + 207.23 cm3

total volume = 239.23 cm3

percentage = (32 cm3 / 239.23 cm3) x 100

percentage = 13.4%

Therefore, the volume of the top part of the pyramid is 13.4% of the total volume.

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(x+4), (3x-1) are the required factors in the given trinomial solution.

The solution provided below has been developed in a clear step by step manner.

Step: 1

Given polynomial is 3x²2² +11x-4

=3x(x+4)-1(x+4)

=(x+4)(3x-1)

Explanation: Please refer to solution in this step.

Step: 2

(x+4), (3x-1) are the required factors

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.

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Answer:27

6574

Step-by-step explanation:

Answer:

2x+12<22

Step-by-step explanation:

Bc I got it correct

The expression that represents Maliq's total points is given as follows:

C. 69x.

The amount of points for each landing is given as follows:

The number of times that Maliq landed on each space is given as follows:

Hence the expression for the total points is given as follows:

21x + 19(2x) + 2(5x) = 21x + 38x + 10x = 69x.

(we multiply the terms and then combine the like terms, as all the terms have the variable x they are like terms).

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By answering the above question, we may infer that We may reduce this equation to: Applying the rule that log base an of ab = b 4 = x Hence, x = 4.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The equation may be changed to read:

x = log base 3 of 81.

81 being equivalent to 3 to the power of 4, we get the following:

x Equals log base 3 of 34.

We may reduce this to: Applying the rule that log base an of ab = b

4 = x

Hence, x = 4.

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One identity that we can write here is:

cos²(θ/2) = - sin²(θ/2) + 1

Here we want to find something that is equal to cos²(θ/2) for every value of theta, that will be an identity.

The general identity for trigonometric functions is:

cos²(θ) + sin²(θ) = 1

So we can rewrite this as:

cos²(θ) = - sin²(θ) + 1

If instead of theta, the argument is theta over two, we could rewrite this as:

cos²(θ/2) = - sin²(θ/2) + 1

That is the identity.

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The ratio for the area and the ratio for the circumferences of the circles are 9 : 1 and 6 : 1 respectively.

What is a circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

If the radius of one circle is three times the radius of another circle, then we can use this information to determine the ratio of the areas of the circles and the ratio of the circumferences of the circles without knowing their actual measurements.

Let's call the radius of the smaller circle "r" and the radius of the larger circle "3r".

Ratio of areas -

The area of a circle is proportional to the square of its radius, so the ratio of the areas of the two circles is -

= (area of larger circle) / (area of smaller circle)

= (π(3r)²) / (πr²)

= 9r²/r²

= 9/1

Therefore, the ratio of the areas of the two circles is 9:1.

Ratio of circumferences -

The circumference of a circle is proportional to its radius, so the ratio of the circumferences of the two circles is -

= (circumference of larger circle) / (circumference of smaller circle)

= 2π(3r) / 2πr

= 6r/r

= 6/1

Therefore, the ratio of the circumferences of the two circles is 6:1.

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Answer:

One solution at (2, -1)

Step-by-step explanation:

You will want to write the equations for both pairs of points:

(-2,-3) and (0,-2)

The slope is the change in y over the change in x.  The first number of the ordered pairs is the x value and the second number in the ordered pair is the y values.  Find the change by subtraction

[tex]\frac{-2 - -3}{0 - -2}[/tex] = [tex]\frac{-2+ 3}{0 + 2}[/tex] = [tex]\frac{1}{2}[/tex]

The slope (m) is 1/2.

The y intercept is when x = 0.  In the point (0,-2) x is 0, so the y-intercept is -2.

The y-intercept (b) is -2.

y = mx + b  Substitute 1/2 for m and -2 for b

y = [tex]\frac{1}{2}[/tex]x - 2

(0,3) and (1,1)

The slope is

[tex]\frac{1-3}{1-0}[/tex] = [tex]\frac{-2}{1}[/tex] = -2

The slope is --2.

The y intercept is 3.

y = mx + b  Substitutes -2 for m and 3 for b.

y = -2x + 3

Set the 2 equation equal to each other and solve for x.

-2x + 3 = 1/2 x -2   Multiply all the way through by 2 to clear the fraction.

-4x + 6 = x - 4   Add 4x to both sides

-4x + 4x + 6 = x + 4x -4

6 = 5x -4  Add 4 to both sides

6 + 4 = 5x - 4 + 4

10 = 5x  Divide both sides by 5

2 = x

Take either of the two original equations and substitute 2 for x and solve for y

y = -2x + 3

y = -2(2) + 3

y = -4 + 3

y = -1

The solution is (2,-1)

Helping in the name of Jesus.

Answer: b-8

Step-by-step explanation:

b-9=b-9

b-9+1=b-8

To find the equation of the perpendicular bisector of PQ, we need to first find the midpoint of PQ, and then determine the slope of the line perpendicular to PQ that passes through this midpoint.

The midpoint of PQ is given by the formula:

((x1 + x2) / 2, (y1 + y2) / 2)

where (x1, y1) = (5, -4) and (x2, y2) = (-1, -2)

So, the midpoint of PQ is:

((5 - 1) / 2, (-4 - 2) / 2) = (2, -3)

Now, the slope of the line PQ can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (5, -4) and (x2, y2) = (-1, -2)

So, the slope of PQ is:

(-2 - (-4)) / (-1 - 5) = 2/3

Since the perpendicular bisector of PQ will have a slope that is the negative reciprocal of the slope of PQ, the slope of the perpendicular bisector is:

-1 / (2/3) = -3/2

Finally, we can use the point-slope form of the equation of a line to find the equation of the perpendicular bisector. We know that the line passes through the point (2, -3), and has a slope of -3/2. So, the equation of the line is:

y - (-3) = (-3/2)(x - 2)

Simplifying this equation, we get:

y + 3 = (-3/2)x + 3

y = (-3/2)x + 0

Hence, the equation of the perpendicular bisector of PQ is y = (-3/2)x.

a. The amplitude of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 4.

b. The period of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 365 days.

c. There are approximately 16 hours of daylight on the longest day of the year.

d. There are approximately 8 hours of daylight on the shortest day of the year.

e. The graph for the function is obtained.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function is given as y = 4 sin [(2π / 365)(x - 79)] + 12.

a. The amplitude of the function is the coefficient of the sine function, which is 4.

Therefore, the amplitude of the function is 4.

b. The period of the function is given by the formula: period = (2π/b), where b is the coefficient of x in the sine function.

In this case, b = (2π/365), so the period is -

period = (2π / (2π/365)) = 365

Therefore, the period value is 365 days.

c. The longest day of the year occurs on the summer solstice, which is around June 21.

On this day, x = 171 (assuming January 1 is x = 1). Plugging x = 171 into the function gives -

y = 4 sin [(2π/365)(171 - 79)] + 12 = 15.998 hours

Therefore, the number of hours for daylight is 16 hours.

d. The shortest day of the year occurs on the winter solstice, which is around December 21.

On this day, x = 355. Plugging x = 355 into the function gives -

y = 4 sin [(2π/365)(355 - 79)] + 12 = 8.002 hours

Therefore, the number of hours for daylight is 8 hours.

e. To graph the function for one period, we need to find the values of y for x ranging from 1 to 365.

We can use a graphing tool or software to plot the function.

The graph is plotted.

The x-axis represents the number of days after January 1, and the y-axis represents the number of hours of daylight.

The function oscillates between 8 and 16 hours of daylight over the course of one year, with the maximum occurring around day 171 and the minimum occurring around day 355.

The graph shows that the function is periodic, with a period of 365 days, as expected.

Therefore, the function is plotted.

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Triangle LMO is congruent to NMO because they are reflections of eachother.

66640 divided by 31 is approximately equal to 2149.68.

Division is a basic arithmetic operation that is used to split a quantity into equal parts or to find out how many times one quantity is contained within another quantity.

When 66640 is divided by 31, the result is:

66640 ÷ 31 =2149.68 (rounded to two decimal places)

Therefore, 66640 divided by 31 is approximately equal to 2149.68.

In general, when we perform division, we are asking the question "how many times does the divisor fit into the dividend?" The dividend is the number being divided, the divisor is the number we are dividing by, and the result is the quotient.,

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The equation can be written as:

(2 + 1/3) + 3*(1/3)

And the solution, writen as a mixed number, is 3 + 1/3.

Here we have a diagram where we can see an addition (its an addition because of the direction of the arrow).

On the leftside we can see two whole squares and a one thid strip.

Then the number is:

2 + 1/3

And to that, we are adding 3 one third strips, then we are adding:

(2 + 1/3) + 3*(1/3)

That should be the equation

We can solve that equation to get:

2 + 1/3 + 3/3

= 2 + 1/3 + 1

= 3 + 1/3

That is the solution written as a mixed number.

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The first five terms of the given sequence are, 12, -9, 30, -51, -72....

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given is the recursive formula, we need to find the first five terms of the  sequence,

1) a₁ = 12, aₙ = 3 and aₙ₋₁-21 :-

a₂ = a₂₋₁ -21

= 12-21

= -9

a₃ = a₃₋₁-21

= -9-21

= -30

a₄ = a₄₋₁-21

= -30-21

= -51

a₅ = a₅₋₁-21

= -51-21

= -72

Hence, the first five terms of the given sequence are, 12, -9, 30, -51, -72....

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Answer: 2.05 repeating

Step-by-step explanation:

18/2= 2
1/2 feet goes into 9 18 times so 1/18 = .055 repeating