Find the quotient of 6x³-18x²-12x
-6x

-x²-3x-2
x²-18x-12
-x² + 18x-12
-x² + 3x + 2

Answer:

First one worked for 20 hours, second one worked for 5 hours.

Step-by-step explanation:

50 times 5 : 250

45 times 20 :900

250+900 = 1150

Therefore, nine rabbits will need 7.5 sacks of food for one week.

The unitary method is a mathematical technique that involves finding the value of a single unit to determine the value of a given number of units. It is a method of solving mathematical problems that involve proportional relationships between quantities. The unitary method is commonly used in various areas of mathematics, such as algebra, arithmetic, and geometry. It is also used in everyday life to solve problems related to money, time, distance, and other quantities.

Here,

To solve this problem, we can use proportionality. We know that the number of sacks of food needed is directly proportional to the number of rabbits.

Let x be the number of sacks needed for 9 rabbits. Then, we can set up the following proportion:

6/10 = 9/x

Cross-multiplying, we get:

6x = 90

Dividing both sides by 6, we get:

x = 15/2 or 7.5

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Complete question:

If six rabbits need 10 sacks of food per week, how many sacks will nine rabbits need to eat for one week?

The number of CDs that need to be produced by the company in order to break even would be 685 CDs .

To break even, the revenue generated by selling the CDs must equal the total cost of producing them. Let's denote the number of CDs produced and sold as a.

Revenue = Price per CD × Number of CDs = 52a

Total Cost = Fixed Cost + Variable Cost × Number of CDs = 26000 + 14a

To break even, we set Revenue equal to Total Cost:

52a = 26000 + 14a

Now, we can solve for a:

52a - 14a = 26000

38a = 26000

a = 26000 / 38

a = 685 CDs

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Answer:

15.36

Step-by-step explanation:

In this equation, we will be using tangent, which is opposite over adjacent. In this case, the "opposite" will be x, and the "adjacent" will be 12. "θ" means the degrees or measurements of the angle.

To find the missing side of the triangle, we will set up a function. The function is:

Tan (θ) = opposite/adjacent

After plugging in the numbers and variables it will be:

Tan(52) = x/12

Then, we would multiply the 12 to both sides.

12 Tan(52) = x

Then we can plug it into a calculator. We should get 15.3592. We would then round it to the nearest hundredth, which is 15.36.

Answer:

Step-by-step explanation:

0.35 = 35/100

100.00 = 100

100×(35/100) = 35

0.5 = 5/10 = 1/2

150.50 = 1505/10

(1505/10)×(1/2) = 75,25

35+75.25 = 110.25

Answer:

4

Step-by-step explanation:

This is a right triangle, so you can use the Pythagorean Theorem.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]  C has to be the longest side. In this case, that is 5

[tex]a^{2}[/tex] + [tex]3^{2}[/tex] = [tex]5^{2}[/tex]

[tex]a^{2}[/tex] + 9 = 25  Subtract 9 from both sides

[tex]a^{2}[/tex] + 9 - 9 = 25 - 9

[tex]a^{2}[/tex] = 16   Take the square root of both sides.

[tex]\sqrt{a^{2} }[/tex] = [tex]\sqrt{16}[/tex]

a = 4

Helping in the name of Jesus.

Answer: When Lily is 10, Jacob will be 18. When she is 16, he will be 24.

Step-by-step explanation: This is because Jacob is 8 years older than Lily, as seen by subtracting her age from his age (13 - 5 = 8). From there, we just add 8 to Lily's ages from then on. 10 + 8 = 18, and 16 + 8 = 24.

The vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.

A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο parallel bases that are cοngruent circles and a curved lateral surface that cοnnects the bases.

1. The circumference οf the cylinder is given as 13 inches. We knοw that the fοrmula fοr the circumference οf a cylinder is 2πr, where r is the radius οf the cylinder. Sο, we have:

2πr = 13

r = 13/(2π)

Nοw, we can use the fοrmula fοr the vοlume οf a cylinder, which is V = πr²h, where h is the height οf the cylinder:

[tex]V = \pi (13/(2\pi ))^2(9) = 119.8 cubic inches[/tex]

Sο, the approximate vοlume of the cylinder is 119.8 cubic inches.

2. The diameter οf the cylinder is given as 63.5 cm, which means the radius is 31.75 cm (since the radius is half οf the diameter). The height is given as 28 inches.

The formula fοr the vοlume of a cylinder is [tex]V = \pi r^2h[/tex], so we can substitute the values we have tο get:

[tex]V = \pi (31.75)^2(28) = 85816.8 ~cm^3[/tex]

Tο cοnvert this tο cubic inches, we need tο knοw that 1 cubic inch is equal tο 16.3871 cubic centimeters, sο we have:

V = 85816.8/16.3871 ≈ 5235.5 cubic inches

Hence, the vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.

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Answer:

D equilateral triangle.

Step-by-step explanation:

An equilateral triangle has three sides with equal length and three interior angles with the same measure of 60 degrees. Therefore, an equilateral triangle can also be considered as a regular polygon with three sides.

Considering the definition of an equation, the cost for one admission and r rides is Cost= 10 + 2×r

An equation in mathematics is defined as an equality established between two expressions, in which there may be one or more unknowns that must be solved.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a raised equation, means to determine by means of certain procedures the value that satisfies it.

Being "r" the number of rides, and knowing that:

the equation in this case is:

Cost= 10 + 2×r

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In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

To find the annual rate of change between 1992 and 2006, we can use the formula:

r = [tex](V_2/V_1)^{1/n}-1[/tex]

where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.

=>r = -0.0839

Therefore, the rate of change between 1992 and 2006 is -0.0839.

To express the rate of change in percentage form, we can multiply the result from part A by 100:

=>r = -0.0839 x 100

=> r = -8.39%

Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.

To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.

From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:

where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.

=>V = 11792.51

Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).

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Answer: 0

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

0 divided by 1 is 0 similarly to other numbers.

For example 5/1 = 5

Although, 1/0 is undefined as it isn't legal.

The lost annual income from savings on those refunds would be $43,032,000.

o calculate the lost annual income from savings on those refunds, we need to first calculate the total amount of money refunded, and then calculate the lost income from that amount.

The total amount refunded would be:

421,000 people x $3,400 per person = $1,434,400,000

Next, we can calculate the lost income from that amount at an interest rate of 3 percent. To do this, we can use the simple interest formula:

I = P x R x T

Where:

I = interest

P = principal (the amount refunded)

R = interest rate (as a decimal)

T = time (in years)

Substituting the values we have:

I = $1,434,400,000 x 0.03 x 1

I = $43,032,000

Therefore, the lost annual income from savings on those refunds would be $43,032,000.

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The apprοximate cοst per square inch οf the cοοkie cake is $0.50.

A line segment cοnnecting twο pοints οn a circle's perimeter and passing thrοugh its center is said tο be the circle's diameter. It is the furthest pοint οn the circle that can be measured.

The equation A=[tex]\pi r^{2}[/tex],where r is the circle's radius, determines the area οf a prοcess. The radius οf the cοοkie cake is equal tο half οf its diameter, οr 6 inches, οr 3 inches. The cοοkie cake's surface area is as fοllοws:

  A  = [tex]\pi r^{2}[/tex]

       = 3.14 x [tex]3^{2}[/tex]

       = 28.26 square inches

We divide the tοtal cοst by the area tο determine the apprοximate cοst per square inch οf the cοοkie cake:

Cοst per square inch = $14.13 / 28.26

                                   = $0.50

As a result, the cοοkie cake cοsts abοut $0.50 per square inch.

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We can use logical reasoning to conclude that the order is "teenager, little boy, tall man, and woman" as per the explanation below, based on the clues.

Logical reasoning is a process of using rational thinking and deduction to arrive at a conclusion based on available information. In the given problem, logical reasoning is used to analyze the provided clues and determine the order of the four people standing in line.

By carefully examining the clues and using a process of elimination, we can deduce the position of each person in the line. We use logical reasoning to eliminate the possibilities that contradict the given information, and to arrive at the correct sequence that fits all of the provided conditions.

First, we know that the tall man is between the woman and the little boy. So, they can appear in either of the following orders:

However, we are told that the little boy is next to a teenager who is not last. So:

Thus, we can conclude that we have correctly answered this question.

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The equation of the line is y=-4x+9. In order to find the equation of the line, we must first calculate the slope (m) of the line.

Slope is a measure of the steepness of a line on a graph. It is calculated by finding the ratio of the vertical change between two points, divided by the horizontal change between the same two points.

The slope is calculated by dividing the change in y-coordinates (rise) by the change in x-coordinates (run).

In this case, the rise is -5 – (-9) = 4, and the run is 1 – 0 = 1. Therefore, the slope of the line is m = 4/1 = 4.

Next, we plug the slope and a point on the line into the point-slope form of a line equation: y - y1 = m(x - x1).

We can choose any point on the line, so let's use (0, -9).

Plugging in the values, we get:

y - (-9) = 4(x - 0)

Simplifying, we get:

y = 4x - 9

Therefore, the equation of the line is y = 4x - 9.

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Answer:

one solution (6, 2 )

Step-by-step explanation:

x - y = 4 → (1)

x + y = 8 → (2)

add the 2 equations term by term to eliminate y

(x + x) + (y - y) = 8 + 4

2x + 0 = 12

2x = 12 ( divide both sides by 2 )

x = 6

substitute x = 6 into (2) and solve for y

6 + y = 8 ( subtract 6 from both sides )

y = 2

the system has one solution , that is (6, 2 )

The current dimensions of the rectangular soccer field are 45 yards by 100 yards.

What is area of the rectangle?

Area = Length × Width

Here let the width be "w" yards.

Then, according to the problem, the length is 55 yards longer than the width, so the length would be "w + 55" yards.

We can use this information to create an equation for the area of the rectangular field:

Area = (w + 55)w

Area = w² + 55w

Next, the problem tells us that if we increase the width by 5 yards and cut the length in half, we get a square. Let's call the side length of this square "s". We can create another equation for the area of this square:

Area = Side length²

Area = s²

We can use algebra to solve for the current dimensions of the rectangular soccer field. First, we need to find an equation for the side length of the square in terms of the current dimensions of the rectangular field:

s = w + 5 (since we increased the width by 5 yards)

s = (w + 55)/2 (since we cut the length in half)

Setting these two equations equal to each other and solving for "w" gives us:

w + 5 = (w + 55)/2

2w + 10 = w + 55

w = 45

So the width of the rectangular soccer field is 45 yards. Using the equation we created earlier for the length, we can find the length:

Length = Width + 55

Length = 45 + 55

Length = 100

Therefore, the current dimensions of the rectangular soccer field are 45 yards by 100 yards.

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The HCF is 6x^2yz^3

HCF means Highest Common Factor. HCF of two or more numbers is the greatest factor that divides the numbers. It is also the greatest possible number of all their common factors.

To find the HCF of the following,

24x^3yz^4 , 30x^2y^2z^3, 36x^3y^2z^3

To find the HCF among the first value,

24 , 30 and 36

Factors of 24 are 2, 3, 4, 6, 8, 12, 24

Factors of 30 are 2, 3, 5, 6, 10, 15, 30

Factors of 36 are 2, 3, 4, 6, 9, 12, 18, 36.

The highest common factor that it can be divisible with is 6

Among x^3 , x^2 and x^3

The factors of x^3 are x, x^2, x^3

Factors of x^2 are x, x^2

Factors of x^3 are x, x^2, x^3

The highest common factor is x^2

Among y , y^2 and y^2

Factors of y is y

Factors of y^2 are y, y^2

The highest common factor is y

And among z^4 , z^3 and z^3

Factors of z^4 are z, z^2, z^3, z^4

Factors of z^3 are z, z^2, z^3

The highest common factor here is z^3

Therefore, the highest common factor is 6x^2yz^3

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Option b is likely to give the teachers the most accurate data for deciding the end of the year field trip for the 8th graders.

In statistics, a sample is a subset of individuals or observations taken from a larger population. The sample is used to gain insights and make inferences about the population from which it was drawn. Samples are often used when it is not feasible or practical to gather data from every individual in a population, which could be too large or too time-consuming to survey.

Here,

A random sample of 8th graders are directly affected by the decision and are therefore the most appropriate group to survey. Asking a random sample of 6th, 7th, and 8th graders (option a) would include students who are not directly affected by the decision, and may not have the same level of understanding or investment in the trip. Asking the football team (option c) would likely provide biased results, as the football team may have different preferences and priorities than the wider 8th grade class. Asking all the teachers (option d) may also provide biased results, as teachers may have different opinions and preferences than the students. Ultimately, the most accurate data will come from surveying the group of students directly affected by the decision.

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Thus, the surface area of paper is needed to wrap 6 cylindrical mini muffins is 23 and 4 over 7  in².

In geometry, a cylinder is just a three-dimensional shape. A cylinder is cylindrical in shape and has a circle-shaped top and bottom. The top and bottom are both flat and uniform in size. The shape of a cylinder is best described, in my opinion, by picturing a soup can.

Given data:

surface area of 6 cylindrical mini muffins = 6*(π*r²*h)

= 6* (22/7 * 1² * 1.25)

= 23.55 in²

= 23 ⁴/₇ in²

Thus, the surface area of paper is needed to wrap 6 cylindrical mini muffins is 23 and 4 over 7  in².

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Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.

Calculating the exponential growth as well as decay of a given collection of data is done using an exponential function, which is a mathematical function.

Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread. An exponential function has the following form at its most fundamental level.

f(x) = [tex]a^{x}[/tex]

Exponential equation for the amount of Caffeine

C = 80[tex](2)^{-t/6}[/tex]

Amount of caffeine C = 60 mg.

60 = 80[tex](2)^{-t/6}[/tex]

3/4 = [tex](2)^{-t/6}[/tex]

Taking log on both sise:

[tex]log_{2}(3/4) = -t/6[/tex]

Solve the log function using the log calculator:

-t/6 = (-0.41)

t = 0.41 * 6

t = 2.46 hours

Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.

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Correct question:

The biological half-life of caffeine is about 6hr. If one cup of coffee has 80 mg of caffeine, then the amount of caffeine C (in mg) remaining after t hours is given by C = 80[tex](2)^{-t/6}[/tex]

How long will it take for the amount of caffeine to drop below 60 mg?

Step-by-step explanation:

For RIGHT triangles   sin (angle) = opposite LEG / hypotenuse

 for this triangle sin (10) = 500/x

then   x = 500 / sin (10°) = 2879.4 m     Round as necessary

The value of y-intercept = -1 and The value of x-intercept = -4

The value of the vertexes is-

Horizontally vertex: y = -2

Virtically vertex: x = -5

For the y-intercept, you must look at where the graph intersects with the y-axis. In this case, the graph intersects at -1.

For the x-intercept, you must look at where the graph intersects with the x-axis. In this case, the graph intersects at -4.

The horizontal asymptote is a y value the graph approaches but does not pass or touch. In this case, the y value is -2.

The vertical asymptote is an x value the graph approaches but does not pass or touch. In this case, the x value is -5.

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Answer: 85% or 17/20

Step-by-step explanation: Ok, so 17 being what percent of 20 is 17/20. Then, simply divide from there to get 0.85, also known as 85%.

It is obvious that he cannot read an entire page in one minute, meaning D (2/3) is literally the only possible answer.

Answer:

Step-by-step explanation:

first give me a high five

By answering the presented question, we may conclude that Therefore the pattern is that these three fractions are all equal and reflect the same proportion of a whole, which is half.

In mathematics, a fraction is a number that represents a component of a whole or a ratio between two things. It is shown as a top number (numerator) split by a horizontal line, also known as a vinculum, over a bottom number (denominator). For example, the fraction 3/4 indicates three-quarters of a whole split into four equal pieces. A fraction can be expressed using proper fractions, improper fractions, or mixed integers. A appropriate fraction is one with a numerator smaller than the denominator, such as 2/5.

The provided fractions 1/2, 2/4, and 4/8 have the pattern of being comparable fractions.

This indicates that even though they are worded differently, they reflect the same percentage or quantity of a total. Each fraction, in particular, represents half of the whole.

To see that these fractions are comparable, divide the numerator and denominator by the same number. For example, 2/4 may be simplified by dividing both the numerator and denominator by 2, yielding 1/2. Similarly, we may simplify 4/8 by dividing the numerator and denominator by 4, yielding 1/2.

Therefore the pattern is that these three fractions are all equal and reflect the same proportion of a whole, which is half.

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Answer:

A) 2 to 7

Step-by-step explanation:

Step 1: Determine How Many Child Tickets Were Sold

The question is asking about the ratio of the number of child tickets sold to the number of total tickets sold, but we can't find that unless we know how many child tickets were sold, so let's figure that out first.

We are given that 175 tickets were sold. Of those 175 tickets, 125 were adult tickets, and the rest were child tickets. This means that the number of total tickets sold was equal to the sum of the number of child and adult tickets sold. Therefore, there were 175 - 125 = 50 child tickets sold.

Step 2: Determine the Ratio of Child Tickets to Total Tickets

We now know that 50 out of the 175 total tickets sold were child tickets, so we can find the ratio of the two values. Remember that a ratio just represents the relation between numbers, so we can write the current ratio of child tickets to total tickets as 50 to 175. However, since ratios can be written as fractions, we quickly see that this ratio can be simplified.

In fraction form, this ratio is [tex]\frac{50}{175}[/tex]. Simplifying this fraction by dividing both the numerator and denominator by their greatest common factor, which is 25 in this case, gives us [tex]\frac{2}{7}[/tex], so the final ratio is 2 to 7.