Given that f( x ) = x^2 − 6x − 27 g(x)=x-9 find (f-g) (x) and express the result as a polynomial in simplest form.

Answer:

We can use the formula for compound interest to find the balance in Eliana's savings account after 10 years:

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

where A is the balance, P is the principal (initial deposit), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.

Substituting the given values, we get:

A = $700(1 + 0.04/12)^(12*10)

Simplifying, we get:

A = $700(1.0033333)^120

Using a calculator, we get:

A ≈ $1,038.81

Therefore, the balance in Eliana's savings account after 10 years is approximately $1,038.81.

The point on the graph that tells you the amount of sugar you'll use if you don't make any pies is (0, 0).

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship, the variables representing the amount of sugar and time must have the same constant of proportionality:

Constant of proportionality, k = y/x

Constant of proportionality, k = 4/3

Constant of proportionality, k = 12.

Therefore, the required equation is given by:

y = kx

y = 4x/3

When x = 0, the value of y is given by:

y = 4(0)/3

y = 0 pies.

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The statement “For a set of decimals, the longest numeral will belong to the largest number” is false because it doesn't determine the value of a number.

In Mathematics and statistics, a numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In Mathematics and statistics, a numeral simply refer to the symbol and numerical figure that is used for representing or denoting a numerical data (number).

For instance, by using the numerical data (numbers) 8 and 9;

8 is represented as VIII in Roman numerals while 9 is represented as IX in Roman numerals. However, the numeral VIII for 8 is longer than the numeral IX for 9, but IX for the number 9 is greater than VIII for the number 8.

In conclusion, we can logically deduce that the given statement is false.

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Complete Question:

Is the statement “For a set of decimals, the longest numeral will belong to the largest number” true or false?

A 95% confidence interval that the t population mean number of books  is between 9.89 and 11.11 books.

What is confidence interval ?

A confidence interval is a statistical range that provides an estimate of the likely range of values for a population parameter (such as a mean, proportion, or standard deviation) based on a sample of data. It is calculated using a specific level of confidence, which represents the probability that the true population parameter falls within the calculated range.

Confidence intervals are typically expressed as a range of values with a margin of error or standard error. The margin of error represents the amount of random variation that is expected due to sampling error, while the standard error reflects the variability of the sample data.

According to the question:
C. There is 95% confidence that the population mean number of books read is between a lower bound of approximately 9.89 books and an upper bound of approximately 11.11 books.

To construct the confidence interval, we can use the formula:

[tex]CI =\bar x \± z* (s/\sqrt{n})[/tex]

substitute the values, we get:

CI = 10.5 ± 1.96 * (16.6/√1015)

CI = (9.89, 11.11)

This means that we are 95% confident that the  population mean number of books is between 9.89 and 11.11 books.

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Step-by-step explanation:

Semi-annual means an interest period is 1/2 year

    1/2 *8% = 4% = .04

       effective annual interest rate is then

                    (1+ .04)^2  - 1  = .0816   or  8.16    (%)

As x approaches negative infinity (i.e., x → -∞), the term -4x³ dominates the expression and becomes increasingly positive. Therefore, the end behaviour of f(x) as x → -∞ is f(x) → +∞.

The behavior of a function refers to how the function changes or behaves as the input values (usually denoted as x) approach certain values, typically positive infinity, negative infinity, or a critical point.

To determine the end behaviour of the function f(x), we need to examine the highest-degree term of the polynomial, which is -4x³.

As x approaches positive infinity (i.e., x → ∞), the term -4x³ dominates the expression and becomes increasingly negative. Therefore, the end behaviour of f(x) as x → ∞ is f(x) → -∞.

Similarly, as x approaches negative infinity (i.e., x → -∞), the term -4x³ dominates the expression and becomes increasingly positive. Therefore, the end behaviour of f(x) as x → -∞ is f(x) → +∞.

In summary, the end behaviour of f(x) is:

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The factοrs οf the expressiοn is 4x(2xy+3y-4z).

Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.

Here the given expressiοn is ,

=> [tex]8x^2y+12xy-16xz[/tex]

Nοw factοrizing the given expressiοn then,

=> 4×2×x×x×y+4×3×x×y-4×4×x×z

=> 4x(2xy+3y-4z)

Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).

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The fact that Jeri drew a polygon with precisely three sides serves as the representation of this claim.

A polygon is a closed shape made of line segments rather than curves on a two-dimensional plane.

A minimum of three line segments need to be joined end to end to produce a closed figure. As a result, a triangle and a 3-gon are both terms for a polygon with at least three sides.

The polygons are divided into many categories based on the sides and angles, including:

In this instance, Jeri's drawing of a polygon with precisely three sides serves as the symbolic expression of this argument.

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Answer:6^21

Step-by-step explanation:

The equation that represents dividing the rectangle into two equal parts is:

W * L/4 = A/2

Assuming that we want to divide the rectangle into two equal parts by a straight line passing through its center, we can represent the rectangle's dimensions as follows:

Let L be the length of the rectangle, and let W be its width. Then the area of the rectangle is A = L * W.

Therefore, to divide the rectangle into two equal parts, we need to draw a line that passes through the center of the rectangle and divides it into two parts with equal areas.

Let x be the distance of the dividing line from one of the shorter sides of the rectangle. Then, the length of the two parts of the rectangle is equal, which means:

L/2 - x = x

Solving for x, we get:

x = L/4

Therefore, the equation that represents dividing the rectangle into two equal parts is: W * L/4 = A/2

This equation says that if we take the width of the rectangle and multiply it by one-fourth of its length, we get half of the rectangle's area, which represents dividing it into two equal parts.

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Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.

A geometric shape known as an angle is created by two rays or line segments that have a shared termination, or vertex. Angles, which express how much of a turn or rotation there is between two rays or line segments, are measured in degrees or radians. They are frequently employed in physics, engineering, geometry, trigonometry, and other disciplines.

given

The characteristics of parallel lines and transversals allow us to determine that:

Interior angles on the same side of the transversal: 1 + 2 = 180°; 2 + 3 = 180°.

We know that (1) = 147°, thus we can apply the first equation to determine 2:

∠1 + ∠2 = 180°

147° + ∠2 = 180°

∠2 = 33°

We can apply the second equation to determine 3 now that we know 2:

∠2 + ∠3 = 180°

33° + ∠3 = 180°

∠3 = 147°

Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.

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Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36

Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.

Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;

From the information given, we have;

(x² - 4x+9)-(3x² - 6x-9)

First, expand the bracket

x² - 4x + 9 - 3x² + 6x + 27

Now, collect the like terms

x²- 3x² - 4x + 6x + 9 + 27

Add or subtract

-2x² + 2x + 36

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Answer:

40 5/8

Step-by-step explanation:

6 1/2 × 2 1/2

13/2 × 5/2= 65/4

65/4 × 2 1/2

65/4 × 5/2 = 325/8

325/8= 40 5/8

Answer:

40 5/8

Step-by-step explanation:

6 1/2 × 2 1/2

13/2 × 5/2= 65/4

65/4 × 2 1/2

65/4 × 5/2 = 325/8

325/8= 40 5/8

Therefore, it will take about 46.5 minutes for the culture to achieve 10,000 bacteria.

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, x, ÷, etc.) that represents a mathematical quantity or relationship. Expressions can be as simple as a single number or variable, or they can be complex and involve multiple terms and operations. Examples of expressions include 2x + 5, 3y - 7, and (a + b)(c - d).

Here,

We can set up an equation to solve for t:

B(t) = 100 ·[tex]2^{t/20}[/tex]

= 10,000

Dividing both sides by 100, we get:

[tex]2^{t/20}[/tex] = 100

Taking the logarithm of both sides with base 2, we get:

t/20 = log2(100)

t = 20 · log2(100)

Using a calculator, we can simplify this to:

t ≈ 46.5 minutes

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Answer:

When you divide 233 by 6 using long division, you get:

38

---

6|233

 216

 ---

  17

Therefore, 233 ÷ 6 = 38 with a remainder of 17

Answer:

38.83 (the 3 goes on and on)

The linear equation that models the number of pages that he reads is:

y = 56*x

So we know that Mark reads 42 pages every 3/4 of an hour, and we want to write an equation that models the number of pages y that mark reads in x hours, to do so we needto get the unit rate.

Take the quotient between the number of pages and the time above to get:

u = (42 pages)/(3/4 hours) = 56 pages per hour.

Then the number of pages that he can read in x hours is modeled by the linear equation:

y = 56*x

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Answer:

Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.

From the given information, we can form two equations:

2x + 2.5y = 8.55 (Equation 1)

3x + 4y = 13.10 (Equation 2)

To solve for x and y, we can use the method of elimination. Multiplying Equation 1 by 4 and Equation 2 by -2, we get:

8x + 10y = 34.20 (Equation 3)

-6x - 8y = -26.20 (Equation 4)

Adding Equation 3 and Equation 4, we get:

2x + 2y = 8

Simplifying this equation, we get:

x + y = 4 (Equation 5)

Now we have two equations: Equation 2 and Equation 5. We can solve for x and y using substitution or elimination. Here, we will use substitution.

From Equation 5, we can express x in terms of y as:

x = 4 - y

Substituting this expression for x into Equation 2, we get:

3(4 - y) + 4y = 13.10

Simplifying and solving for y, we get:

y = £1.50

Substituting this value for y into Equation 5, we can solve for x:

x + £1.50 = 4

x = £2.50

Therefore, the cost of 1 kg of mushrooms is £2.50 and the cost of 1 kg of turnips is £1.50.

a) The cost of 1 kg of turnips is £1.50.

b) The cost of 1 kg of mushrooms is £2.50.

Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).

A sequence of numbers known as coordinates is used to describe the location of a point or object in space or on a plane. Coordinates in two-dimensional space typically have two values, which are typically written as (x, y), where x denotes the horizontal position and y denotes the vertical position. Coordinates in three dimensions can have three values, denoted as (x, y, z), where x, y, and z stand for the position along the x, y, and z axes, respectively. In many different fields, such as geometry, physics, and computer graphics, coordinates are used.

given

The coordinates of the new origin must be subtracted from the given point in order to translate the point (-8, -6) to the new origin (h, k) = (5, 4).

x' = -8 - 5 = -13

y' = -6 - 4 = -10

Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).

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The diameter of the tin is 2/5D and the circumference of the tin is 0.4πD

Given the the scale factor of dilation is

Container = 2/5 smaller than in reality

This means that

Scale factor = 2/5

So, we have

Diameter = 2/5D where D = diameter in reality

Also, we have

Height = 2/5H where H = height in reality

The circumference is then calculated as

C = πD

So, we have

C = π * 2/5D

Evaluate

C = 0.4πD

Hence, the circumference is 0.4πD

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Complete question

The Ricoffy tin container with no dimensions indicated.The container is 2,5 times smaller than what it is in reality

Diameter of the tin on the picture = ? Height of the tin on the picture = ? Actual weight of coffee = 750 g 1.1 Measure the diameter of the tin in mm and write down the real diameter in mm​

Answer: X=55 and Y=125

Step-by-step explanation:

y is an external angle

so according to external angle property sum of two angles is equal to external angle. two angles are given- 35 and 90

90+35=y

y=125

now with angle sum property

90+35+x=180

125+x=180

x=55

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The probability of the maximum number of black hats that could be present in the group is 2.

Since the probability of selecting a student with a green hat is the highest, it is likely that there are more green hats than any other color. Let's assume that there are 7 green hats. If there are 7 green hats, then there are only 5 hats left for the remaining colors. However, we know that there are only 2 red hats and 1 blue hat, leaving a maximum of 2 hats for the black color. Therefore, the greatest possible number of black hats in the group is 2, which would give a total of 2 red hats, 1 blue hat, 7 green hats, and 2 black hats. In conclusion, if the probability of selecting a student with a green hat is the highest, then the greatest possible number of black hats in the group is 2.

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The cost per ride is $1.50: True.

The situation can be represented by the equation y = 15x + 15: False, it can be be represented by y = 1.5x + 15.

The initial entrance fee was $15: True.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (18 - 15)/(2 - 0)

Slope (m) = 3/2

Slope (m) = 1.50.

At data point (0, 15), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 15 = 1.50(x - 0)

y - 15 = -1.50(x)

y = 1.50(x) + 15

When x = 0, the y-intercept is given by;

y = 1.50(x) + 15

y = 1.50(0) + 15

y = 15.

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Answer:

Step-by-step explanation:

to find the the answer you need to put it on the graph then find the thing you need to do to find out the correct answer

Answer:

Step-by-step explanation:

7xy+3x+3y−3

Answer:

$12.00

Step-by-step explanation:

We know that 1 pound = 16 oz.  Thus, we can create a proportion to find how many ounces (x) is 2.5 pounds:

[tex]\frac{1}{16}=\frac{2.5}{x}\\ x=(2.5*16)\\ x=40[/tex]

Since 2.5 pounds = 40 oz, we can now multiply 40 by 0.30 to find the price of 40 ounces of peacans priced at $0.30/ounce:

40 * 0.30 = $12.00

the total percentage increase in the investor's stock account is 22%.

In mathematics, a ratio or figure that can be expressed as a fraction of 100 is known as a percentage. If we want to calculate a percentage of a number, we should split it by 100 before multiplying it by the original number. Therefore, the percentage relates to a component per 100. The term percent means "per 100". It is represented by the symbol "%". In mathematics, a percentage is a number or ratio that is represented as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most commonly used to denote it. A percentage is a number that has neither measurements nor a defined unit of measurement.

In the given question,

Increase in stock A= 24% of $5150 = 1236

Increase in stock = 20% of $5250 = 1050

The  total percentage increase in the investor's stock account= {(1236+1050)/(5150+5250)* 100=

= 21.98%

≈22%

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