O POLYNOMIAL AND RATIONAL FUNCTIONS Finding the asymptotes of a rational function: Constant ovel aph all vertical and horizontal asymptotes of the rational function f(x)=(5)/(3x+6)

The answer is 106993205379072 different ways that the 12 people can order from the 13 items on the menu.

There are a total of 12 people at a Restaurant and each person can order one of the 13 items on the menu. Therefore, the total number of different ways that they can order is 1312 = 106993205379072.

This is because for each of the 12 people, there are 13 choices for what they can order. So for the first person, there are 13 choices, for the second person there are 13 choices, and so on. Multiplying all of these choices together gives us the total number of different ways that they can order:

13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 = 106993205379072

So the answer is 106993205379072 different ways that the 12 people can order from the 13 items on the menu.

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The values of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0 are λ = 1 and λ = 2.

To find the value(s) of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0, we can substitute y = e^(λx) into the differential equation and solve for λ.

First, we need to find the first and second derivatives of y = e^(λx):

y′ = λe^(λx)

y′′ = λ^2e^(λx)

Now, we can substitute these derivatives into the differential equation:

λ^2e^(λx) − 3λe^(λx) + 2e^(λx) = 0

e^(λx)(λ^2 − 3λ + 2) = 0

Since e^(λx) cannot equal 0, we can set the expression in parentheses equal to 0 and solve for λ:

λ^2 − 3λ + 2 = 0

(λ − 1)(λ − 2) = 0

λ = 1 or λ = 2

Therefore, the values of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0 are λ = 1 and λ = 2.

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The simplified ratio of factored polynomials is 18/(6(x-8)).

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial is x^2 + 5x + 6.

The question is asking to simplify the ratio of factored polynomials (18(3x-4))/(6(x-8)(3x-4)). To simplify this ratio, we can divide the numerator and denominator by the common factors.

The numerator and denominator both have the factor of 3x-4, so we can divide both the numerator and denominator by this common factor.


The numerator then becomes 18/(6(x-8)) and the denominator becomes 1.

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Using the statements given for congruency the proof is -

TC ≅ TM                      Given

AT bisects ∠CTM        Given

∠ATC ≅ ∠ATM            Definition of bisect

AT ≅ AT                       Reflexive property

Δ ATC ≅ Δ ATM          SAS theorem

CA ≅ MA                      ≅ Δs → ≅ parts

What is congruency?

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.

A diagram of a diamond ACTM is given.

The line segment TC is equal and congruent to line segment TM.

This statement is already given in the question.

The line segment AT bisects angle CTM.

This statement is already given in the question.

The angle ATC is equal and congruent to angle ATM.

This statement is the definition of bisect.

The line segment AT is equal and congruent to line segment AT.

This statement is true by the reflexive property of the triangles.

Triangle ATC is equal and congruent to triangle ATM.

This statement is true by Side-Angle-Side (SAS) theorem of the triangles.

The line segment CA is equal and congruent to line segment MA.

This statement is true as the triangles are congruent to each other and congruent triangles have congruent parts.

Therefore, the proof is complete.

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Answer:

Below

Step-by-step explanation:

'k' shifts the graph of f(x)   UP   by  ' k'  units     k = 6   ( look how far the y-axis intercepts are shifted UP= 6 units  from -2 to + 4)

1)The completed table is

Yellow paint (quarts) | Red paint (quarts)

5 | 3

6 | 3.6

2) The car travels 98 miles in 14 hours.

3) The orchard can produce 450 liters of olive oil in a year.

What is a ratio?

A ratio is a quantitative comparison between two or more quantities, indicating how many times one quantity contains another. It is expressed as the quotient of the two quantities or in the form of a fraction. Ratios can be represented in various ways, including as decimals, percentages, or fractions.

Complete the table to show the amounts of yellow and red paint needed for different numbers of batches of the same shade of orange paint.

Yellow paint (quarts) | Red paint (quarts)

5 | 3

6 | 3.6

To get the same shade of orange paint, we need to mix yellow and red paint in a certain ratio. This ratio will determine the hue, saturation, and brightness of the final color. In this case, we can see that the ratio of yellow to red paint is 5:3 in the first row of the table, and 6:3.6 (which simplifies to 5:3) in the second row. This means that we need the same amount of yellow and red paint for each batch of orange paint, in a 5:3 ratio.

A car is traveling at a constant speed, as shown by the double number line.

The distance traveled by the car is directly proportional to the amount of time it travels. This means that the ratio of distance to time is constant. From the given double number line, we can see that the car travels 21 miles in 3 hours. Therefore, the ratio of distance to time is 21:3 or 7:1. To find how far the car travels in 14 hours, we can set up a proportion:

distance/time = 7/1

distance/14 = 7/1

distance = 7 x 14

distance = 98 miles

Therefore, the car travels 98 miles in 14 hours.

The olive trees in an orchard produce 3000 pounds of olives per year. It takes 20 pounds of olives to produce 3 liters of olive oil.

To find how many liters of olive oil the orchard can produce in a year, we need to divide the total weight of olives by the amount of olives needed to produce one liter of oil, and then multiply by the conversion factor:

Liters of oil = (Pounds of olives / Pounds per liter) x Conversion factor

Liters of oil = (3000 / 20) x 3

Liters of oil = 150 x 3

Liters of oil = 450

Therefore, the orchard can produce 450 liters of olive oil in a year.

Hence,

1)The completed table is

Yellow paint (quarts) | Red paint (quarts)

5 | 3

6 | 3.6

2) The car travels 98 miles in 14 hours.

3) The orchard can produce 450 liters of olive oil in a year.

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The value of the function at x = 2 is 11.8.

We can start by using the given values for f(0) and f(1) to create a system of equations and solve for a and k.
f(0) = 2 = a + 5ek(0)
f(1) = 9 = a + 5ek(1)
Simplifying the first equation gives us a = 2 - 5ek(0) = 2. Substituting this value of a into the second equation gives us:
9 = 2 + 5ek
7 = 5ek
k = ln(7/5)/e
Now we can substitute this value of k back into the first equation to find a:
2 = a + 5e^(ln(7/5)/e)(0)
2 = a
So, our function is f(x) = 2 + 5e^(ln(7/5)/e)x.
To evaluate f(2), we simply plug in x = 2:
f(2) = 2 + 5e^(ln(7/5)/e)(2)
f(2) = 2 + 5(7/5)^2
f(2) = 2 + 5(49/25)
f(2) = 2 + 9.8
f(2) = 11.8
Therefore, the value of the function at x = 2 is 11.8.

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Shaquille baked 12 vanilla cupcakes and the equation to depict the number of vanilla cookies is 48 = 4x.

The algebraic approach to solving simultaneous linear equations is known as substitution technique. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve. Learn about the graphical approach and the algebraic method before beginning to solve the linear equations using the substitution method.

Let us suppose the number of vanilla cupcakes = x.

The chocolate chip cookies are:

48 = 4x

x = 12

Hence, Shaquille baked 12 vanilla cupcakes and the equation to depict the number of vanilla cookies is 48 = 4x.

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Answer: 10x² + 3x + 4

Step-by-step explanation: I hate math.

Answer:

area=22/7×13=40.85=41 is the nearest whole number

The answer of decimal number that has the specified place values is 964.8.

To write the decimal number, we need to understand the place value of each digit.

The place values are as follows:

- 9 hundreds = 900
- 6 tens = 60
- 4 ones = 4
- 8 tenths = 0.8
- 0 hundredths = 0.00

To write the decimal number, we add the place values together:

900 + 60 + 4 + 0.8 + 0.00 = 964.8

Therefore, the decimal number that has the specified place values is 964.8.

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The inverse function of f(x) = - Vx+1+6 is f^-1(x) = - Vx-7. The domain of f^-1(x) is [-1, ∞), or in interval notation, [-1, ∞).

The inverse function of f(x) = -√x+1 + 6 can be found by following the steps below:

1. Swap the x and y values, so y = -√x+1 + 6 becomes x = -√y+1 + 6
2. Solve for y by isolating it on one side of the equation:
x - 6 = -√y+1
(x - 6)² = y+1
y = (x - 6)² - 1
3. The inverse function is therefore f^-1(x) = (x - 6)² - 1

The domain of f^-1(x) can be found by considering the restrictions on the original function. Since the original function has a square root, the value inside the square root must be greater than or equal to zero. This means that:

x+1 ≥ 0
x ≥ -1

So, the inverse function of f(x) = -√x+1 + 6 is f^-1(x) = (x - 6)² - 1, and the domain of f^-1(x) is [-1, ∞).

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Therefore, the order from least to greatest is:d<f<a<b<c<e

d. 2√2 x √5 ≈ 5.66, f. 3√2 x √3 ≈ 6.00, a. 4√3 = 4 x √(3) ≈ 6.93, b. 3√5 ≈ 6.71, c. 5√2 ≈ 7.07, e. 2√13 ≈ 7.21

To arrange these radicals in order from least to greatest, we need to simplify them and compare the values. We can start by simplifying the radicals using prime factorization.

a. 4√3 = 4 x √(3) = 4 x√(3)

b. 3√5 = 3 x √(5)

c. 5√2 = 5 x√(2)

d. 2√10 = 2 x √(25) = 2 x √(2) x √(5) = 2√2 x√5

e. 2√13 = 2 x √(13)

f. 3√6 = 3 x √(23) = 3 x √(2) x √(3) = 3√2 x √3

Now, we can compare the values of the radicals by comparing their coefficients and the values inside the radical:

a. 4√3 = 4 x √(3) ≈ 6.93

b. 3√5 ≈ 6.71

c. 5√2 ≈ 7.07

d. 2√2 x√5 ≈ 5.66

e. 2√13 ≈ 7.21

f. 3√2 x √3 ≈ 6.00

Therefore, the order from least to greatest is:

d. 2√2 x √5 ≈ 5.66

f. 3√2 x √3 ≈ 6.00

a. 4√3 = 4 x √(3) ≈ 6.93

b. 3√5 ≈ 6.71

c. 5√2 ≈ 7.07

e. 2√13 ≈ 7.21

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The correct answer is sine and cosine.

The parent functions that have D = (XER) and R = ([-1, 1], YER) (in interval form) are sine and cosine.

Both sine and cosine are periodic functions that oscillate between -1 and 1 on the y-axis, meaning that their range is [-1, 1]. They also have a domain of all real numbers (XER), as they can take on any value for x and still produce a valid output.

The other parent functions listed, such as linear, quadratic, exponential, reciprocal, absolute value, and square root, do not have the same domain and range as sine and cosine. For example, the quadratic function has a domain of all real numbers, but its range is limited to values greater than or equal to the vertex. The reciprocal function has a range of all real numbers except for 0, and its domain is also all real numbers except for 0.

Therefore, the correct answer is sine and cosine.

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The coordinates of the pre-images are (-7, 8); (-7, 5); (4, 8), and (2, 5), and the pre-image is given below.

Transformation:

A transformation of a quadrilateral refers to any process that changes the size, position, or shape of a four-sided polygon.

To draw the pre-mage, find the coordinates of the pre-mage as given below and plot the points in a graph

Here we have

The coordinates of the quadrilateral are (-4, 5); (-4, 2); (7, 5), and (5, 2)

Given T < -3, 3 > (x, y)

Hence, the coordinates of the pre-images are

(-4, 5)  => (-4 -3, 5 + 3 ) = (-7, 8)

(-4, 2) => (-4 -3, 2 + 3) = (-7, 5)

(7, 5) => (7 -3, 5 + 3) = (4, 8)

(5, 2) => (5 - 3, 2+3) = (2, 5)  

Therefore,

The coordinates of the pre-images are (-7, 8); (-7, 5); (4, 8), and (2, 5), and the pre-image is given below.

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Answer:

Metallurgy is the science that studies how metals work. It involves the extraction of metals from ores, their purification, and their conversion into useful alloys. Metallurgists also study the physical and chemical properties of metals, as well as their behavior under different conditions such as temperature and pressure.

Step-by-step explanation:

Hello,

the answer is "studies of how metals work."

Reason:

the answer is the science that studies how metals work.

If you need anymore help feel free to ask me!

Hope this helps!

~Matthew1756654

Answer:

X = 20 and Y = √3*20, or about 34.64

Step-by-step explanation:

In a 30-60-90 triangle, the hypotenuse is double the length of the shorter leg. To find the length of the shorter leg with the hypotenuse, just divide the length of the hypotenuse by 2. 40/2=20

In a 30-60-90 triangle, the longer leg is equal to the square root of 3 times the length of the shorter leg. √3(20)=34.6410161514, which can be rounded to 34.64

just a quick addition to the great reply above by "krr2007"

Check the picture below.

Answer: The answer t your question is the second one

Step-by-step explanation:

The height of the kite from the ground is 620.5 feet.

The angle of elevation from your hand to a kite is 65∘ and the distance from your hand to the kite is 287 feet.

Therefore, the height of the kite when your hand is 5 feet from the ground can be found as follows:

The situation forms a right angle triangle. Therefore, the height of the kite can be found using Pythagoras's theorem.

Hence,

tan 65 = opposite / adjacent

tan 65 = h / 287

cross multiply

h = 287 × tan 65

h = 615.473486186

Therefore,

height of the kite = 615.473486186 + 5

height of the kite = 620.5 feet

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The rank of At is the number of linearly independent rows or columns in the matrix. Since At has an inverse for all values of t, the rank of At is 3 for all values of t.

In order to determine the values of t for which At has an inverse, we need to find the determinant of At. If the determinant of At is not equal to 0, then At has an inverse. The determinant of At is given by:

|At| = (1)(5)(-6) + (3)(t)(4) + (2)(2)(7-t) - (4)(5)(2) - (7-t)(t)(1) - (-6)(2)(3)

Simplifying the above expression, we get:

|At| = -30 + 12t + 28 - 14t - 40 - 5t2 + 12

Combining like terms, we get:

|At| = -5t2 - 2t - 30

Setting the determinant equal to 0, we get:

-5t2 - 2t - 30 = 0

Using the quadratic formula, we can find the values of t for which the determinant is equal to 0:

t = (-(-2) ± √((-2)2 - 4(-5)(-30)))/(2(-5))

t = (2 ± √(4 - 600))/(-10)

t = (2 ± √(-596))/(-10)

Since the square root of a negative number is not a real number, there are no real values of t for which the determinant of At is equal to 0. Therefore, At has an inverse for all values of t.

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Total students=1,200

Total number of students whose favorite movie genre is Romance= 10%

So,

10% of total students= 10% of 1,200

Therefore, the Total students who chose romance= 10/100*1200=120

Similarly, 10% of students chose Science fiction, and the total number of students who chose science fiction=10/100*1200=120

Therefore,

Total students who chose romance=120

Total students who chose science fiction=120

The height of the bottom of the hole after the second day is 2579 feet.

Mathematicians employ the action of addition to combine numbers. The sum of the given numbers is the outcome of addition, or the total of the given numbers.

As per the given data:

Drilling on first day = 323 feet.

Drilling on second day = drilling on first day + 1933 feet

Drilling on second day = 323 feet + 1933 feet

= 2256 feet

Total drilling = Drilling on first day + Drilling on second day

= 323 feet + 2256 feet

= 2579 feet

Hence, the height of the bottom of the hole after the second day is 2579 feet.

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Answer: 415

83 = [tex]\frac{y}{5}[/tex]

83(5) = y

415 = y

Answer:

y = 415

Step-by-step explanation:

83 = y/5

83 x 5 = y

415 = y

Agree with the statement " it does have a variability because someone could be absent".

What is meant by variability?

The degree to which the data points in a statistical distribution or data collection deviate from the average value and from one another is virtually by definition the measure of variability. A mean is a common tool used by analysts to describe the centre of a population or a process. Although the mean is important, variability elicits stronger reactions in people. Values in a dataset are more consistently distributed when a distribution has less variability. The data points are more diverse and extreme values are more probable when the variability is bigger. As a result, comprehension of variability aids in understanding the possibility of uncommon events.

Peirce says that there is variability because someone could be absent.

I agree with Peirce's statement.

Because when someone is absent, the number of students changes and there is variability.

Now the range of variability changes with how many students are absent.

If there are only a few students absent, then the variability can be low.' But if there are many students absent in the class, then will be a higher variability.

Therefore there can be variability when someone could be absent.

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The probability of no one getting a hole in one on the sixth hole during the 1989 U.S. Open golf tournament is 0.95431 and the probability of exactly one golfer getting a hole in one on the sixth hole is 0.04478.

The probability of an event occurring is the number of favorable outcomes divided by the number of possible outcomes. In this case, the probability of a professional golfer making a hole in one is 1/3,709.

a. To find the probability that no one gets a hole in one on the sixth hole, we need to find the probability that each of the 174 golfers does not get a hole in one. The probability of not getting a hole in one is 1 - (1/3,709) = 3,708/3,709. The probability that no one gets a hole in one is (3,708/3,709)^174 = 0.95431. Therefore, the probability that no one gets a hole in one on the sixth hole is 0.95431.

b. To find the probability that exactly one golfer gets a hole in one on the sixth hole, we need to find the probability that one golfer gets a hole in one and the rest do not. The probability of one golfer getting a hole in one is 1/3,709 and the probability of the rest not getting a hole in one is (3,708/3,709)^173. There are 174 ways this can happen, so the probability is 174 * (1/3,709) * (3,708/3,709)^173 = 0.04478. Therefore, the probability that exactly one golfer gets a hole in one on the sixth hole is 0.04478.

In conclusion, the probability of no one getting a hole in one on the sixth hole during the 1989 U.S. Open golf tournament is 0.95431 and the probability of exactly one golfer getting a hole in one on the sixth hole is 0.04478.

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Answer:

How are we supposted to do your homework if we dont have a picture or explanation of it??

Step-by-step explanation:

The number of solutions of the polynomial equation, 4x^(5)-8x^(4) +6x^(3)=0 is 5 and the solutions are x=0, x=3/2, and x=1.

The polynomial equation at hand is of degree 5, which means that the highest power of the variable present in any term is 5.

Therefore, we can infer that the equation can be written in the form of ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0, where a, b, c, d, e, and f are constants and x is the variable. To solve this equation, we can try factoring it:

4x^(5)-8x^(4) +6x^(3)=0

2x^(3)(2x^(2)-4x+3)=0

2x^(3)(2x-3)(x-1)=0

The solutions are x=0, x=3/2, and x=1.

Therefore, the number of solutions of the polynomial equation is 5 and the solutions are x=0, x=3/2, and x=1.

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In the given window there are both acute and obtuse angles are shown.

a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space

We have to find the  types of angles are shown by the window-glass shapes

An angle is formed when two straight lines or rays meet at a common endpoint.

As we observe the angles are less than 180 degrees.

Angles between 0 and 90 degrees are called acute angles.

Angles between 90 and 180 degrees are known as obtuse angles.

Hence, In the given window there are both acute and obtuse angles are shown.

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a) f(0) = 3(0)^2 + 3(0) - 3 = -3
b) f(3) = 3(3)^2 + 3(3) - 3 = 33
c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
e)−f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3

We are asked to find the following for the function f(x)=3x^2+3x−3: (a) f(0) (b) f(3) (c) f(−3) (d) f(−x) (e) −f(x) (f) f(x+2) (g) f(3x) (h) f(x+h)

(a) f(0) = 3(0)^2 + 3(0) - 3 = -3
(b) f(3) = 3(3)^2 + 3(3) - 3 = 33
(c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
(d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
(e) −f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
(f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
(g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
(h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3

I hope this helps! Let me know if you have any further questions.

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Step-by-step explanation:

the height is 17 feet and the distance from the wall is 8 feet

using pythogras theorem

[tex] {h}^{2} + {b}^{2} = {hypotenuse}^{2} \\ {h}^{2} + {8}^{2} = {17}^{2} \\ h = \sqrt{( {17}^{2} - {8}^{2} } \\ h = 15[/tex]