need ur help guys!

1. _____ of the graph of a rational function are the points of intersection of its graph and an axis.

2. _____ of a function are the values of x which make the function zero. The numbered zeroes are also ______ of the graph of the function.

3. ______of the graph of a rational function r(x) , if it exists, occurs at the zeros of the denominators. To find _____ equate the function to ____.

4. _____ of the graph of a rational function r(x) if it exists, occurs at r(0), provided that r(x) is defined at x = 0. To find ________ simply evaluate the function at x = ______.

5. An_______is an imaginary line to which a graph gets closer and closer as the x or y increases or decreases its value without limit.

6. To find ________ of a rational function, first reduce the given function to simplest form then find the zeroes of the denominator that are not zeros of the numerator.

7. To determine the_______ of a rational function, compare the degree of the numerator n and the degree of the denominator d.

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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Answer:

(4, 120)

Step-by-step explanation:

I could be wrong tho.

Multiply total serves by percentage:

120 x 0.45 = 54

Answer: 54

Answer:

54 Im sure of it. I revised this question by wacthing a video.

Step-by-step explanation:

When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

a. p = 63/200 = 0.315

b. the 90% confidence interval to estimate the population proportion p is (0.26, 0.37).

c. based on the sample data, we can estimate that the proportion of all Americans who get their driver's license before turning 18 falls within this interval with a 90% confidence level.

a. The point estimate for the proportion p of Americans who get their driver's license before they turn 18 can be calculated by dividing the number of Americans in the sample who received their driver's license before their 18th birthday (63) by the total sample size (200).

p = 63/200 = 0.315

b. To find a 90% confidence interval for the population proportion p, we can use the formula:

CI = p ± Z * sqrt((p * (1 - p)) / n)

where:

CI is the confidence interval,

Z is the Z-score corresponding to the desired confidence level (90% in this case),

sqrt denotes the square root,

p is the point estimate,

and n is the sample size.

First, we need to find the Z-score for a 90% confidence level. Using a standard normal distribution table or calculator, we find that the Z-score for a 90% confidence level is approximately 1.645.

Substituting the values into the formula:

CI = 0.315 ± 1.645 * sqrt((0.315 * (1 - 0.315)) / 200)

Calculating the values:

CI = 0.315 ± 1.645 * sqrt(0.2205 / 200)

CI = 0.315 ± 1.645 * 0.03128

CI = 0.315 ± 0.05149

Rounding to two decimal places:

CI = (0.26, 0.37)

Therefore, the 90% confidence interval to estimate the population proportion p is (0.26, 0.37).

c. The confidence interval (0.26, 0.37) indicates that we are 90% confident that the true proportion of Americans who get their driver's license before turning 18 lies between 0.26 and 0.37.

This means that, based on the sample data, we can estimate that the proportion of all Americans who get their driver's license before turning 18 falls within this interval with a 90% confidence level.

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The value of opposite side of angle θ would be,

⇒ EF

Since, A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that,

A right triangle EFD is shown in figure.

And, At angle E, right angle is shown.

We know that;

The Opposite side of a angle is called perpendicular side.

Hence, The value of opposite side of angle θ would be,

⇒ EF

Thus, Option A is true.

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All of these statements are correct.

When describing categorical data, several methods can be used to provide meaningful insights and summarize the data.

Counts and proportions: Counting the number of observations in each category can provide information about the distribution and frequency of different categories. Proportions, also known as percentages, can be calculated by dividing the count in each category by the total count, allowing for a comparison of the relative frequencies of different categories.

Measures of center, spread, and shape: Although measures of center, spread, and shape are commonly associated with numerical data, they can also be used to describe certain aspects of categorical data. For example, the mode represents the most frequent category, which can be considered a measure of center. Measures of spread, such as the range or interquartile range, may not be applicable to categorical data. However, bar graphs and pie charts can visually depict the distribution and shape of categorical variables.

Box plots: Box plots are graphical representations primarily used for numerical data. They display the median, quartiles, and any potential outliers. While box plots are not commonly used for categorical data, they can be adapted by representing the frequency or proportion of categories instead of numerical values.

In summary, when describing categorical data, counts and proportions are commonly used to present the frequency and relative frequency of categories. Measures of center, such as the mode, can provide insights into the most frequent category. Measures of spread and shape may not be applicable, but graphical representations like bar graphs and pie charts can be used to visualize the distribution and shape of the categorical data. Box plots are not typically used for categorical data, as they are more suitable for numerical variables.

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In problem 10, the solution to the initial value problem behaves as t approaches 0. In problem 11, the behavior of the solution as t approaches 0 depends on the specific values given.

In problem 10, we are given the initial value problem x' = (3 - 7)*, x(0) = (-3). The behavior of the solution as t approaches 0 can be determined by solving the differential equation and evaluating the initial condition. The specific solution will reveal how the system evolves near t = 0.

In problem 11, we are given x' = (1) + x(0) = (2). The behavior of the solution as t approaches 0 depends on the values of the initial condition x(0). By solving the differential equation and incorporating the initial condition, we can examine how the system behaves near t = 0 for different initial values.

To fully describe the behavior of the solution as t approaches 0 in both problems, it is necessary to solve the initial value problems and analyze the resulting solutions.

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Given the functions f(x) = 6x 11 and g(x) = x 6, So now the following functions  f[g(x)]  which represented correctly by the expression f[g(x)] = 6x2 + 17.

To find the composition of two functions, first we substitute the expression for g(x) into f(x). And then the function g(x) = x - 6 is substituted into f(x) = 6x + 11. Replacing x in f(x) with g(x), we have f[g(x)] = 6(g(x)) + 11. Substituting g(x) = x - 6, we get f[g(x)] = 6(x - 6) + 11. Simplifying the expression, we have f[g(x)] = 6x - 36 + 11. And finally combining like terms, we get f[g(x)] = 6x - 25, which can be rewritten as f[g(x)] = 6x2 + 17.

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The answer to the problem 18 + pi is an irrational number.

The sum of 18 and pi, 18 + pi, will result in an irrational number.

To understand why the result is irrational, let's first clarify the definitions of rational and irrational numbers.

A rational number is any number that can be expressed as the ratio of two integers, while an irrational number cannot be expressed as such and has an infinite non-repeating decimal expansion.

In this case, 18 is a rational number since it can be expressed as 18/1. However, pi (π) is an irrational number.

Pi is a mathematical constant representing the ratio of a circle's circumference to its diameter, and its decimal representation goes on infinitely without repeating.

It is approximately equal to 3.14159.

When we add a rational number (18) to an irrational number (pi), the result is always an irrational number.

This is because adding a rational number to an irrational number does not change the irrational nature of the latter.

The irrationality "overrides" the rationality, resulting in an irrational sum.

Therefore, the answer to the problem 18 + pi is an irrational number.

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Question : Determine whether each of the following problems will have a rational or an irrational answer. Your answer should be either the word “rational” or “irrational.” 18 + pi

Answer:

irrational number.

Step-by-step explanation:

Therefore , the solution of the given problem of integral comes out to be 8ln2 is solution for the integral expression.

The region beneath a curve among two set limits is referred to as a definite integral. The representation of the definite integral for such a function of two variables), defined to reference to the x-axis, is ∫ baf(x)dx a b f (x) d x, where an is the lower bound and b is the upper bound.

Here,

Given :

\(\int\limits \int\limitsa_R\) 3xy²/x²+ 1 dA

=> R = {(x, y) | 0 ≤ x ≤ 3, −2 ≤ y ≤ 2} ·

So,

=>  \(\int\limits^1_{x=0} \int\limits^2_{y=-2}\) 3xy²/x²+ 1  dxdy

=> \(\int\limits^1_{x=0}\) 3x / x²+ 1  \(\int\limits^2_{y=-2}\) y²

=>\(\int\limits^1_{x=0}\) 3x / x²+ 1 ( y³/2)²dx

=>   \(\int\limits^1_{x=0}\) 3x / x²+ 1 (8 + 8 /3) dx

=> \(\int\limits^1_{x=0}\) 16x/x²+ 1

=> 8 [ln(x²+ 1) ]

=>  8 [ln2 -ln1 ]

=>8ln2

Therefore , the solution of the given problem of integral comes out to be

8ln2 is solution for the integral expression.

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Answer: 54

Step-by-step explanation:

Total votes: 240

Votes for the winner: x

Votes for candidate 1: x - 8

Votes for candidate 2: x - 13

Votes for candidate 3: x - 15

Equation to find the amount of votes of the winner (x) is:

240 = x +  x - 8 + x - 13 + x - 15

Combine x and x to get 2x.

240=2x−8+x−13+x−15

Combine 2x and x to get 3x.

240=3x−8−13+x−15

Subtract 13 from −8 to get −21.

240=3x−21+x−15

Combine 3x and x to get 4x.

240=4x−21−15

Subtract 15 from −21 to get −36.

240=4x−36

Swap sides so that all variable terms are on the left hand side.

4x−36=240

Add 36 to both sides.

4x=240+36

Add 240 and 36 to get 276.

4x=276

Divide both sides by 4.

x= 4/276  

Divide 276 by 4 to get 69.

x=69

Votes for the winner: 69

Votes for candidate 1: 69 - 8 = 61

Votes for candidate 2: 69 - 13 = 56

Votes for candidate 3: 69 - 15 = 54

The candidate that had the lowest number of votes received 54 votes.

Answer:

M2+m3=90

Step-by-step explanation:

Angle 1 already is equal to 90. A triangle can only go up to 180 wo the other two angles have to add up to 90.

The interval of convergence is (-111/16, -15/16), and the radius of convergence is R = 15/16.

To find the interval of convergence and radius of convergence of the power series ∑n=1[infinity](−4)nn‾√(x 7)n, we can use the ratio test:

|(-4)nn‾√(x 7)n+1 / (-4)nn‾√(x 7)n| = 4√(x 7) → as n → infinity

The ratio test tells us that the series converges if 4√(x 7) < 1, and diverges if 4√(x 7) > 1. Solving for x, we get:

4√(x 7) < 1
√(x 7) < 1/4
x 7 < 1/16
x < -111/16

and

4√(x 7) > 1
√(x 7) > 1/4
x 7 > 1/16
x > -15/16

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The nature of the solution to the system of linear equations is a unique solution.

To determine the nature of the solution to each system of linear equations, we need to examine the slopes of the two equations.

For the first equation, y = (-1/4)x + 1, the slope is -1/4.

For the second equation, y = (2/3)x + 4, the slope is 2/3.

Now let's analyze the nature of the solutions:

1. If the slopes of the two equations are different, the system has a unique solution. This means the lines represented by the equations intersect at a single point.

2. If the slopes of the two equations are the same and the y-intercepts are different, the system has no solution. This means the lines represented by the equations are parallel and do not intersect.

3. If the slopes of the two equations are the same and the y-intercepts are the same, the system has infinitely many solutions. This means the lines represented by the equations are identical and overlap.

In this case, the slope of the first equation (-1/4) is different from the slope of the second equation (2/3). Therefore, the system has a unique solution, and the lines represented by the equations intersect at a single point.

The nature of the solution to the system of linear equations is a unique solution.

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Answer:

m = 3.625

Step-by-step explanation:

1.2m + 0.65 = 5

~Subtract 0.65 to both sides

1.2m = 4.35

~Divide 1.2 to both sides

m = 3.625

Best of Luck!

1/2 gallons of water rush down the slide each seconds.

For the given question-

Rate of running water = 1 half gallon every 3 seconds.

Rate of running water = 1 1/2 = 3/2 gallon every 3 seconds.

It means-

In every 3 seconds ----> 3/2 gallons water flows.

Thus for 1 sec, divide both side by 3.

1 seconds ----> 1/2 gallons water flows.

Therefore, 1/2 gallons of water rush down the slide each seconds.

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Answer:

0.25 or 1/4

Step-by-step explanation:

Answer: 1/4

Step-by-step explanation:

Answer:

4 degrees Fahrenheit

Step-by-step explanation:

Answer:

negative four

Step-by-step explanation:

Answer:

= 12x + -15/2

Step-by-step explanation:

4x + 1/4 + 8x + -31/4

(4x+8x) + (1/4 + -31/4)

=12x+ -15/2

Answer:

12x - 15/2

Step-by-step explanation:

(4x + 1/4) + (8x - 31/4)

4x + 1/4 + 8x - 31/4

4x + 8x

12x + 1/4 - 31/4

1/4 - 31/4

12x -15/2

Correct option is A,  f(x) -2 has changed the parent function f(x) = (0.5)x to its new appearance.

The parent function f(x) = log5x has been modified by reflecting it over the x-axis, extending it vertically by a factor of three, and moving it down by three units.

In the picture below you can see the blue line is the graph of the function

f(x) = log(5x) and the green line is the graph of the function

g(x) = log[5(x + 4)] - 2

Since the function f passes at point (2, 1), we must reduce it by 2 units to ensure that it also passes at position (-2, -1). To do this, we add 2 to the function f.

We only need to add 4 to the variable x to have the function go left when we obtain log(5x) - 2.

The function shifts to the left when you add a number to x;

The function moves to the right when you remove a number from x;

The function increases when you add a number to it;

The function decreases when you take a number away from it.

Then we get a function g(x) = log[5 (x + 4)] - 2.

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Answer:

288 degrees celcius

Step-by-step explanation:

48 x 6 is 288

Answer:

The total change in temperature was 288* degrees.

Step-by-step explanation:

6 x 48 = 288

9514 1404 393

Answer:

  D: {-4, 1, 5, 9}

  R: {-8, 0, 1, 5}

Step-by-step explanation:

The domain is the list of first numbers of the ordered pairs: {-4, 1, 5, 9}.

The range is the list of second numbers of the ordered pairs: {-8, 0, 1, 5}.

A substitute is a good or service that buyers can quickly swap out for another. For instance, a one-dollar bill can be used in place of another dollar bill.

In business and economics, a replacement, or substitutable good, is a good or service that consumers perceive as just being substantially the same as or reasonably similar to some other good. Consumers are given options and alternatives through substitutes, which also spur competition and lower prices in the market.

Here are a few examples of replacement goods:

1. A $1 bill can be exchanged for four quarters.

2. Coke against Pepsi

3. Regular vs. premium gas

4. Butter and lard

5. Tea and coffee

6. Apples and oranges

7. Comparing driving a car to riding a bike

8. Books in general and e-books

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Answer: 10

Step-by-step explanation:

For a survey to put an estimate the proportion of voters who support gun control, the minimum sample size is 752 that is minimum 752 people need to be included in the sample.

We have a survey which is planned to estimate the proportion of voters who support gun control. Margin of error, MOE = 3% = 0.03

Confidence level = 90% = 0.90

No information about the proportion of the voters that is p,so let's assume, p= 0.5

Level of significance, α = 1 - CI

= 1 - 0.90 = 0.10

We have to determine the sample size of people. Using the following formula for computes minimum sample size required to estimate population proportion within the required margin of error, \(n ≥ p( 1-p) (\frac{z_c}{MOE})²\)

where, n --> sample size

\(z_c\)--> critical value of z

using the Z-distribution table, the value of z for 90% confidence interval is 1.64.

Substitute all known values in above formula, \(n ≥ 0.5( 1- 0.5) (\frac{1.64}{0.03})²\)

= 751.54 ~ 752( people must be a integer no.)

Hence, required minimum sample size is 752.

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Answer:

276

Step-by-step explanation:

The minus reverses the negative too a positive then you subtract

Answer:

Step-by-step explanation:here is a example:Recall that the volume of a regular prism is given by the area of the base times the height.

Given that the base of the prism is a regular pentagon with an apothem of 2.8 centimeters.

The pentagon consist of 5 isosceles triangles with the apothem as the height and the side of the pentagon as the base.

Recall that the are of a triangle is given by 1/2 base times height.

Thus the area of of the pentagon base of the prism is given by

Therefore, the volume of the prism is given by volume=7x(2x+1)=14x2+7x

Answer:

Its D

Step-by-step explanation:

Using substitution method, the cost of hotel per night is $ 85

Let hotel cost per night = x

Let car rental per day = y

4x + 2y = 500 ____(1)

4x + 5y = 740 ____(2)

Solving for x in the equation

Equation (1) - (2)

-3y = - 240

y = 80

Substitute the value of y in (1)

4x + 2(80) = 500

4x + 160 = 500

4x = 500-160

4x = 340

x = $85

Therefore, hotel cost per night is $85

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