2. Use the Factor Theorem to determine if (x-4) is a factor of the polynomial function
P(x) = x5 + 4x4 - 17x³ - 60x²
Clearly state that (x-4) is a factor, or that (x-4) is not a factor. Show all work.

Answer:

Step-by-step explanation:

Answer:

Plug in values

Step-by-step explanation:

solve for y, y=-3x+15

plug in x or y values on table to missing missing variable

ex.

y=-3(2)+15

y=9

3=-3x+15

-12=-3x

x=4

Answer:

the measure of the angle is 43.4 degrees, and the measure of its supplementary angle is 180 - 43.4 = 136.6 degrees.

Step-by-step explanation:

Let x be the measure of the angle in degrees.

By definition, supplementary angles add up to 180 degrees, so the measure of the supplementary angle is 180 - x degrees.

According to the problem, the angle measures 136.6 degrees less than the supplementary angle, so we can write:

x = (180 - x) - 136.6

Simplifying the right-hand side, we get:

x = 43.4

Therefore, the measure of the angle is 43.4 degrees, and the measure of its supplementary angle is 180 - 43.4 = 136.6 degrees.

Answer:

Without any measurements, it is not possible to give a numerical estimate for the real height of the lamp post in metres. However, we can use the scale of the drawing to make an estimate.

Let's assume that the scale of the drawing is 1 centimetre (cm) represents 0.5 metres (m) in real life. This means that every 1 cm in the drawing represents 0.5 m in real life.

If we measure the height of the lamp post in the drawing and find that it is approximately 15 cm, we can estimate the real height of the lamp post as follows:

Real height of lamp post = (15 cm) x (0.5 m/1 cm) = 7.5 m

Therefore, using our estimated scale of the drawing, we can estimate that the real height of the lamp post is around 7.5 metres. However, this estimate is only as accurate as the assumptions we made about the scale of the drawing.

Step-by-step explanation:

The price of a general admission floor ticket is $25.

What is the system of equations?

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.

Let's start by defining some variables:

Let b be the price of a balcony ticket

Let f be the price of a general admission floor ticket

We can set up a system of two equations based on the information given in the problem:

77b + 69f = 5,883 (equation 1 for Friday's show)

75b + 69f = 5,775 (equation 2 for Saturday's show)

We can use either substitution or elimination to solve for b and f. Let's use elimination by subtracting equation 2 from equation 1:

(77b + 69f) - (75b + 69f) = 5,883 - 5,775

2b = 108

b = 54

Now that we know the price of a balcony ticket is $54, we can substitute this value into either equation to solve for f. Let's use equation 1:

77(54) + 69f = 5,883

4,158 + 69f = 5,883

69f = 1,725

f = 25

Therefore, the price of a general admission floor ticket is $25.

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These are the transformed functions for each of the four transformations mentioned.

Vertical translation (shift) by k units: f(x) + k

Horizontal translation (shift) by h units: f(x - h)

Vertical stretch/compression by a factor of c: c * f(x)

Reflection across the x-axis: -f(x)

Replace k, h, and c with the desired values to obtain the specific transformed functions.
Here are four common types of transformations:
Vertical translation (shift) by k units: f(x) + k
Horizontal translation (shift) by h units: f(x - h)
Vertical stretch/compression by a factor of c: c * f(x)
Reflection across the x-axis: -f(x)
For the function f(x) = 2x + 3,

let's apply these transformations:
Vertical translation (shift) by k units: f(x) + k -> 2x + 3 + k (where k is the number of units shifted vertically)

Horizontal translation (shift) by h units: f(x - h) -> 2(x - h) + 3 (where h is the number of units shifted horizontally)
Vertical stretch/compression by a factor of c: c * f(x) -> c(2x + 3) (where c is the stretch/compression factor)
Reflection across the x-axis: -f(x) -> -(2x + 3).

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The equation of the line perpendicular to 4x + 36y = 288 and passing through the point (10, 8) is: y = 9x - 98

To find the equation of the line perpendicular to 4x + 36y = 288, we need to first find the slope of the given line.

We can rewrite the equation in slope-intercept form y = mx + b by solving for y:

4x + 36y = 288

36y = -4x + 288

y = (-1/9)x + 8

Therefore, the slope of the given line is -1/9

The slope of a line perpendicular to this line is the negative reciprocal of the slope of the given line.

So, the slope of the line we want to find is:

m = -1 / (-1/9) = 9

The equation is then calculated as

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Plugging in the values, we get:

y - 8 = 9(x - 10)

Simplifying, we get:

y = 9x - 98

Therefore, the equation of the line perpendicular is: y = 9x - 98

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Answer: 38 (David) 22 (Marta)

Step-by-step explanation: First you will do 60-16. Then you will divide 44 by 2. After that then you will do 22+16. Finally you will have 38 and 22. So 38 is David's age and 22 is Marta's age.

Answer:1/2

Step-by-step explanation:

because three is half of six and you can get numbers larger than three also

A translation of the sentence "Product of 3 and the cube of h increased by one-ninth is 1​" is

In order to translate a word sentence into an algebraic equation, we would have to assign a variable to the unknown number:

Let the variable n represent the unknown number.

By translating the word sentence into an algebraic expression, we have the following;

The product of 3 and the cube of h should be represented by the following algebraic expression;

3 × h³

Next, we would increase the above algebraic expression by one-ninth (1/9) and then equate to 1 as follows;

(3 × h³) + 1/9 = 1

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Complete Question:

Write an equation to represent the following word sentence;

Product of 3 and the cube of h increased by one-ninth is 1​.

Therefore, the outer perimeter is approximately 73.20 ft.

Perimeter is the total distance around the outside of a two-dimensional shape. It is calculated by adding up the lengths of all the sides of the shape. The units for perimeter are the same as the units used for the length of the sides. For example, if the sides are measured in feet, the perimeter will be measured in feet as well.

Here,

We need to find the outer perimeter, which means we need to find the perimeter of the shape that includes all the sides of JROP. To do this, we need to find the length of side JO.

Using the Pythagorean Theorem on right triangle JOR, we have:

JO² = JR² + OR²

JO² = 10² + 14²

JO² = 296

JO ≈ 17.20 ft

Now we can find the outer perimeter:

Outer perimeter = JP + PO + OR + RJ + JO

Outer perimeter = 18 + 10 + 14 + 14 + 17.20

Outer perimeter ≈ 73.20 ft

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Perimeter of pool A is 90ft

Perimeter is a measurement of the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

For example, the perimeter of a rectangle can be calculated by adding up the length of all four sides of the rectangle. If a rectangle has a length of 6 units and a width of 4 units, its perimeter would be:

Perimeter = 2 x (length + width) = 2 x (6 + 4) = 20 units

To find: Perimeter of A

For Pool B;

Perimeter=120ft

Width=20ft and length=l

Hence, Perimeter of Pool B=2(l+w)

120=2(l+20)

60-20=l

l=40ft

Length of pool A=length of pool B=40

width of pool A=1/4width of pool B

1/4×20=width of pool B

width of pool B=5ft

Perimeter of pool A=2(l+w)

=2(40+5)

=2×45

=90ft

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The complete question is attached below;

Answer:

The median is 6.

If you need the mean, mode, range, minimum, maximum, count n, or sum they are

Mean- 6.6666666666667

Mode- 1,3,4,5,6,7,8,12,14

Min- 1

Max- 14

Count n- 9

Sum- 60

Answer:

5.5

Step-by-step explanation:

The median is the middle number in a sorted list of numbers.

Therefore, the first step to solving this problem is sorting this list of numbers from least to greatest:

1, 2, 3, 4, 5, 6, 7, 8, 12, 14

To find the middle number, start by crossing out a number from each side. In this case, the first two numbers to cross out are 1 and 14. 1 is the smallest number in the list and 14 is the greatest. Our list should then look like this:

2, 3, 4, 5, 6, 7, 8, 12

Now, cross out the next smallest and largest numbers of the list (2, 12):

3, 4, 5, 6, 7, 8

The next (3, 8):

4, 5, 6, 7

The next (4, 7):

5, 6

Now we are left with two numbers. When this happens, to figure out the middle number, we have to find the average of these last two remaining digits. The average can be found by adding these two digits and dividing that by the total number of digits you used to add.

In this case, we have 2 numbers left: 5 and 6

1. Add 5 and 6: 5+6=11

2. We used 2 numbers for the addition which means we have to divide 11 by 2: 11/2

= 5.5

the average rate οf change οf f frοm z = -7 tο z = 6 is 50/13 οr apprοximately 3.846 (rοunded tο three decimal places).

In mathematics, average refers tο a measure that represents the central οr typical value οf a set οf numbers. There are several types οf averages, including mean, median, and mοde.

The mean, alsο called the arithmetic mean, is the sum οf all the numbers in a set divided by the tοtal number οf values in the set. It is the mοst cοmmοnly used type οf average.

Tο find the average rate οf change οf f frοm z = -7 tο z = 6, we need tο calculate the change in f οver the change in z and then take the average.

First, we calculate f(6) and f(-7):

f(6) = 72² + 3(6) + 3

= 5184 + 18 + 3

= 5,191

f(-7) = 72² + 3(-7) + 3

= 5184 − 21 + 3

= 5,141

The change in f over the change in z is:

[tex]$\frac{5,191 - 5,141}{6 - (-7)} = \frac{50}{6 - (-7)} = \frac{50}{13}[/tex]

Therefore, the average rate of change of f from z = -7 to z = 6 is 50/13 or approximately 3.846 (rounded to three decimal places).

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Answer:

Step-by-step explanation:

First, you need to find the least common denominator (LCD) of 6, 12 and 8. 6 factors to 2*3, 12 to 2*2*3 and 8 to 2*2*2. The LCD will be the number that incorporates the combination that includes all the unique factors, which would be 2*2*2*3 or 24. 5/6 = 20/24, 1/12 = 2/24 and 7/8 = 21/24 so altogether the team covers

(20+2+21)/24 = 43/24 = 1 19/24 miles

Answer:

force is a vector quantity because we can't add it using simple algebra

it's direction dependent

however in this case

specific direction is not given

though it's mentioned it is pushed

so

force is a vector quantity

We may conclude after answering the provided question that Option D is  range ruled out because we lack sufficient information to calculate the value of h. (2).

The variable's range is calculated by taking its greatest observed value and subtracting its minimum observed value (minimum). Possible range or variational bounds: a variety of steel costs; a variety of styles; The scope or size of a method or action: perception. The maximum or anticipated range of a weapon's projectile. A list or set's range is the number between the lowest and maximum. Align all of the numbers before determining the region. Next, subtract (reduce) the lowest number from the greatest number. The solution includes the range of the list. The solution specifies the range of the list.

The following statement might be true for h:

A. h(8) = 21

We can see that h(x) has a range of 1 to 25, and h(8) = 19 falls inside that range. As a result, h(8) might equal 21 as long as it stays within the range of 1 to 25.

Option B is not practicable since h(x) has a domain of -3 x 11, and h(-3) is not in the domain.

Option C is ruled out since 13 is not in the domain of h. (x).

Option D is ruled out because we lack sufficient information to calculate the value of h. (2).

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Answer: lol 3500 minus 4000 equals 500

Step-by-step explanation:

:) there

The correct option is- (F) US Department of Homeland Security, is the sources of authority for given security officers.

The Department of Homeland Security (DHS) of the United States is a federal organisation created to defend the country against dangers.

The DHS statement of purpose lists the following five primary objectives for homeland security:

Thus, security officers' sources of authority are US Department of Homeland Security.

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Step-by-step explanation:

Distance formula to find distance from O to Q is sqrt (306)

Distance from R to P = sqrt (34)

Diagonals ( found above) intersect at right triangles in a rhombus

  so you can break it into two right triangles of base = sqrt (306)

           and height sqrt (34)/2

    TWO triangles of area = 1/2 base * height

         TOTAL Area is then :     TWO * 1/2 ( sqrt(34)/2)* sqrt (306) = 51 units^2

Answer:

b. 840

Step-by-step explanation:

7!/3! is the same thing as saying (7*6*5*4*3*2*1)/(3*2*1). The 3*2*1 simplifies to 1 so the simplified expression is 7*6*5*4. If you compute that, you will get the answer is 840, b.

With 90% cοnfidence, we can say that the true prοpοrtiοn οf custοmers whο cοnsider this market mοre pleasing than the οther stοre is between 0.601 and 0.685. In οther wοrds, we can be 90% cοnfident that the pοpulatiοn prοpοrtiοn οf custοmers whο prefer this market is within this range.

Percentage is a way οf expressing a number οr prοpοrtiοn as a fractiοn οf 100. It is represented by the symbοl "%".

Tο calculate the cοnfidence interval tο estimate the true prοpοrtiοn οf custοmers whο cοnsider this market mοre pleasing than the οther stοre with 90% cοnfidence, we need tο check the fοllοwing cοnditiοns:

In this scenariο, we can assume that the fοrms were distributed randοmly tο the custοmers, and the independence cοnditiοn is met because the respοnses οf οne custοmer dο nοt affect the respοnses οf anοther custοmer. Tο check the sample size cοnditiοn, we can calculate the expected number οf successes and failures in the sample:

Expected number of successes: n * p = 429 * (276/429) ≈ 277

Expected number of failures: n * (1 - p) = 429 * (1 - 276/429) ≈ 152

Both the expected number of successes and failures are greater than 10, so the sample size condition is met.

Now, we can calculate the confidence interval using the formula:

CI = p ± sqrt(p(1-p)/n)

where p is the sample proportion, n is the sample size, and z is the z-score corresponding to the desired confidence level.

In this case, p = 276/429 ≈ 0.643, n = 429, and z = 1.645 (from a standard normal table for 90% confidence level).

Plugging in these values, we get:

CI = 0.643 ± 1.645sqrt(0.643(1-0.643)/429) ≈ (0.601, 0.685)

Therefore, with 90% confidence, we can say that the true proportion of customers who consider this market more pleasing than the other store is between 0.601 and 0.685. In other words, we can be 90% confident that the population proportion of customers who prefer this market is within this range.

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In conclusion you put down 12.5% of the total cost of the home.

How to solve and what is percentage?

To find the percentage you put down on the home, you need to divide the amount you put down (the down payment) by the total cost of the home, and then multiply by 100 to convert to a percentage.

The down payment was $8,000 and the total cost of the home was $64,000.

So the percentage you put down is:

($8,000 / $64,000) x 100% = 12.5%

Therefore, you put down 12.5% of the total cost of the home.

Percentage is a way of expressing a proportion or fraction as a portion of 100. It is denoted by the symbol %, and is often used to express a fraction of a quantity relative to the whole quantity.

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Fiinding and interpreting the zero of a rational function involves solving for x when the function equals zero and understanding its significance within the context.

Hello! I understand you want to find and interpret the zero of a rational function, and I'd be happy to help.

The zero of a rational function occurs when the function's value is equal to zero. In other words, a zero is a value of x that makes the function f(x) = 0. To find the zero, you must set the numerator of the rational function equal to zero and solve for x.

It's important to note that the denominator should never equal zero, as this would make the function undefined.

Interpreting the zero helps us understand the behavior of the function and can be useful in various applications.

For instance, the zero might represent a break-even point in a business context or an equilibrium in a physical system. Whether the result makes sense within the context of a specific problem depends on the given scenario and the mathematical relationship between the variables.

To summarize,  Always ensure the denominator is never zero to maintain the function's validity.

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There are many banks but nowadays SBI is the one of popular bank of World.So I choose SBI bank for explanation.

Details about SBI bank:

State Bank of India (SBI) is one of the largest and oldest banks in India. It was founded in 1806 as the Bank of Calcutta and later became the Imperial Bank of India in 1921. In 1955, the bank was nationalized and became the State Bank of India.

SBI is headquartered in Mumbai and has a widespread network of branches across India as well as in other countries. The bank offers a wide range of financial products and services such as savings and current accounts, loans, credit cards, investment options, insurance, and many more.

SBI is known for its advanced technology and customer-centric approach. The bank has implemented various digital initiatives to make banking easy and convenient for its customers. SBI's mobile app and internet banking portal are among the most popular digital channels used by customers.

Apart from traditional banking services, SBI has also been actively involved in various social initiatives such as promoting financial literacy, supporting education, healthcare, and environment conservation. The bank has also launched many welfare schemes for the benefit of its customers and society at large.

SBI is recognized as a global banking leader and has received many prestigious awards and accolades over the years. The bank has also been ranked among the top banks in the world by leading international publications.

Overall, SBI is a reliable and trustworthy bank that has played a significant role in shaping the Indian banking industry.

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Correct question is " Choose a name of a perticular bank and write about the bank."

A circle is a two-dimensional geometric figure that consists of all points that are at an equal distance, called the radius, from a single given point, called the center. The radius is exactly twice as long as the distance across the circle, as measured by the diameter, which passes through its centre.

The tangent of a circle is a straight line that intersects the circle at exactly one point, known as the point of tangency.

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The amount of feed that can the container hold is two hundred ninety-two and one-eighth in³.

The volume of a rectangular prism can be calculated using the formula:

                    V = l × w × h

where V is the volume, l is the length, w is the width, and h is the height of the rectangular prism.

Here we have

A student is building a squirrel feeder for a family member. The figure is a model of the feeder.

A rectangular prism with dimensions are

4 3/4 inches × 20 1/2 inches × 3 inches.

The amount of feed in a rectangular prism = Volume of rectangular  

Volume of container = 4 3/4 inches × 20 1/2 inches × 3 inches

= 19/4 × 41/2 × 3  = 2337/8 = 292 1/2 in³

Therefore,

The amount of feed that can the container hold is two hundred ninety-two and one-eighth in³.

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Value of variable x in the proportion is 6.

A fraction is used to express a portion of a whole or a ratio of two values. It is a mathematical statement known as a fraction bar or vinculum that has a numerator and a denominator separated by a horizontal line. The denominator is the total number of pieces that make up the whole, whereas the numerator is the number of parts that are being taken into account.

Given proportion;

10/10+x=35/56

Cross multiplying the proportion, we get

10×56=35×(10+x)

Multiplying the values on both side, we get

560=350+35x

Taking 350 on left hand side,

560-350=35x

35x=210

Dividing the equation by 35, we get

x=210/35

x=6

Hence, value of x in the proportion is 6.

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Answer:

A.

Step-by-step explanation:

No, Manu's conclusion is not correct. He should look at the greatest data value on the number line that has any dots above it to find the greatest number of books read. The most dots represent the most frequent number of books read, but not necessarily the greatest number of books read.

We would need to survey at least 600 randomly selected air passengers to be 90% confident that the sample percentage is within 1.5 percentage points of the true population percentage.

As a number out of 100, a percentage is a technique to express a fraction or a proportion. The sign "%" stands in for the word "percent," which is a contraction of "per hundred."

To determine the sample size for the survey, we can use the following formula:

n = [tex](Z^2 * p * q) / E^2[/tex]

Where:

n is the required sample size

Z is the Z-value for the desired confidence level (in this case, Z = 1.645 for a 90% confidence level)

p is the estimated population proportion (we don't know this yet, so we will assume a conservative estimate of 0.5)

q is the complementary probability of p (q = 1 - p)

E is the maximum error or margin of error (in this case, E = 0.015)

Plugging in the values, we get:

n = ([tex]1.645^2[/tex] * 0.5 * 0.5) / [tex]0.015^2[/tex]

n = 599.27

Rounding up to the nearest whole number, we get a required sample size of 600.

Therefore, we would need to survey at least 600 randomly selected air passengers to be 90% confident that the sample percentage is within 1.5 percentage points of the true population percentage.

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