Find the missing value to the nearest hundredth. cos____ = 8/17

1. 0.99 degrees
2. 61.93 degrees
3. 28.07 degrees
4. 25.20 degrees ​

The angles in the triangle are as follows:

A = 32 degrees

B = 58 degrees

The sum of angles in a triangle is 180 degrees. The triangle ABC is a right angle triangle. A right angle triangle has one of its angles as 90 degrees.

Therefore, let's find the angle A and B as follows:

Using trigonometric ratios,

sin A = opposite / hypotenuse

Therefore,

sin A = 8 / 15

A = sin⁻¹ 0.53333333333

A = 32.2286948935

A = 32 degrees

Let's find angle B

B = 180 - 90 - 32(sum of angles in a triangle)

B = 90 - 32

B = 58 degrees

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Angle relationship and algebra are closely related in geometry, as we often use algebraic expressions to represent angle measures and their ratios.

For example, if we are given that angle A and angle B are complementary (meaning that their sum is 90 degrees), we can write an algebraic equation:

Similarly, if we know that angle A is three times larger than angle B, we can write:

We can use algebraic equations to solve for unknown angle measures or to find relationships between angles.

For example, let's say we are given that angle A is complementary to angle B, and that angle B is twice as large as angle C. We can write:

We can substitute the second equation into the first equation to get:

This equation relates the three angles A, B, and C. We can use algebra to solve for any of the unknown angles, given the measures of the others.

Therefore, algebraic equations and expressions are an important tool in understanding and analyzing angle relationships in geometry.

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The amount of fencing, dirt and sod for the baseball field are;

Length of fencing ≈ 1410.5 feet

Area of the sod ≈ 118017.13 ft²

Area of of the field covered with dirt ≈ 7,049.6 ft²

The fencing of a baseball field is the outer enclosure of the field, which typically, is located along the outfield boundary.

The amount of fencing, dirt, and sod can be found using the formula for finding the circumference of a circle and the area of a circle as follows;

Area of a circle = π × r²

Circumference of a circle = 2 × π × r

Where r is the radius of the circle

The area of a quarter of a circle is therefore; Area of a circle ÷ 4

The perimeter of a quarter of a circle is; The perimeter of a circle ÷ 4

Fencing = (1/4) × 2 × π × 380 + 2 × 15 + 2 × 380 + (1/4) × 2 × π × 15

Fencing = 190·π + 790 + 7.5·π = 197.5·π + 790 ≈ 1410.5

Grass = π/4 × (380 - 6)² + 87² - π/4 × (87 + 30)² + 2 × 380 × 15 + π/4 × 15² - (3/4) × π × 10² - 25·π = 31528·π + 18969 ≈ 118017.13

Dirt; π/4 × 380² - π/4 × (380 - 6)² + π/4 × (87 + 30)²- 87² + π·100 = (18613·π - 30276)/4 ≈ 7049.6

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The domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

In mathematics, the range of a function refers to the set of all possible output values (dependent variable) that the function can produce for its corresponding input values (independent variable).

The given function is y = 3x² + 2.

The domain of a function is the set of all possible values of the independent variable (x) for which the function is defined. Since the given function is a polynomial function, it is defined for all real numbers.

Therefore, the domain of the function y = 3x² + 2 is (-∞, ∞), which means that the function is defined for all real values of x.

The range of a function is the set of all possible values of the dependent variable (y) that the function can take. In this case, the function is a quadratic function with a leading coefficient of 3, which means that the parabola opens upwards and its vertex is at the point (0,2).

Since the minimum value of the function is 2, the range of the function is [2, ∞).

Therefore, the domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

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Answer:

Acute or Acute Scalene triangle to be exact

Answer:

13.416407865

Step-by-step explanation:

You wouldn't use soh cah toa

There is no angle given. Instead you should do 6²+12²=180

And then you would square root 180=13.416407865

Therefore the answer is 13.416407865

The correct choice is To control voluntary response bias.

Random assignment helps to control voluntary response bias by icing that individualities are assigned to the treatment and control groups fully arbitrarily, without any input or influence from the individualities themselves.

Voluntary response bias occurs when individuals tone-elect into a particular group, frequently because they have a particular interest or opinion on the content being studied. This can lead to prejudiced results because the individuals who choose to share may not be representative of the larger population.

Random assignment helps to control for voluntary response bias by icing that individualities are assigned to the treatment and control groups fully at arbitrarily, without any input or influence from the individualities themselves. This helps to insure that the groups are representative of the larger population and that any observed differences between the groups are due to the treatment itself, rather than other factors that may be associated with certain individualities or groups.

thus, arbitrary assignment helps to minimize the implicit impact of voluntary response bias on the results of a trial.

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The correct question is given below-

What is the purpose of random assignment in an experiment? Check all that apply.

Group of answer choices

To select a sample that is representative of the population

To create similar treatment groups

To eliminate the effects of the explanatory variable

To control voluntary response bias

Control for confounding variables

The probability of Laura missing 3 free throws before making 12 is approximately 0.0037 or 0.37%.
The basketball free throw.

A success would be considered when Laura makes a free throw.

A failure would be when Laura misses a free throw.
The negative binomial distribution is a probability distribution that calculates the probability of obtaining a certain number of failures before a specified number of successes occur.

The specified number of successes is 12, and the number of failures is represented by the variable x.
To calculate the probability of x failures, we need to know the probability of a single failure.

Since Laura is an 82% free throw shooter, the probability of her missing a free throw is 18%.
We can use the formula for negative binomial distribution to determine how many failures are required before 12 successes are achieved.

The formula is:
[tex]P(X = x) = (r+x-1)C(x) \times p^r \times (1-p)^x[/tex]
Where:
P(X = x) is the probability of having x failures before achieving 12 successes
r is the number of successes required (in this case, 12)
p is the probability of a single success (in this case, 0.82)

[tex](r+x-1)C(x)[/tex]is the combination of r+x-1 choose x

For example, if we want to find the probability of Laura missing 3 free throws before making 12, we will plug in x = 3, r = 12, p = 0.82 into the formula:

[tex]P(X = 3) = (12+3-1)C(3) \times 0.82^1^2\times (1-0.82)^3[/tex]
[tex]P(X = 3) = 14C3 \times 0.082^1^2 \times 0.18^3[/tex]
[tex]P(X = 3) = 364 \times 0.000018 \times 0.005832[/tex]
P(X = 3) = 0.000037
Overall, the trial in this scenario is each individual attempt at a free throw, the success is making a free throw, and 12 successes are required before the shooting session is considered complete.

The negative binomial distribution is used to calculate the probability of obtaining a certain number of failures before achieving the specified number of successes.

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'x' follows a negative binomial distribution with 'r' being 12 successes.

In this scenario, a trial refers to each individual attempt at shooting a free throw. A success is when Laura successfully makes a free throw. To achieve her goal of making 12 free throws, she needs to have 11 successes (since she will miss on the final attempt). Therefore, r = 11.

In this context, a "trial" refers to each individual attempt Laura makes to shoot a basketball free throw. A "success" is when Laura makes a free throw (hits the basket), while a "failure" (not mentioned in the question) would be when Laura misses a free throw. Since Laura keeps shooting free throws until she makes 12, the number of successes required, denoted as 'r', is 12.

Therefore, 'x' follows a negative binomial distribution with 'r' being 12 successes.

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3. The area of the shaded region is 5x² + 2x - 3

4. The area of the shaded region is 18x² + 21x + 6

From the question, we are to determine the area of the shaded region in the given diagrams.

3.

Area of the shaded region = {[(x - 1) + (2x - 1)] × [(x + 1) + (x + 1)]} - (x + 1)(x - 1)

Area of the shaded region = [(x - 1 + 2x - 1) × (x + 1 + x + 1)] - (x + 1)(x - 1)

Area of the shaded region = [(3x - 2) × (2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = [(3x - 2)(2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = (6x² + 6x - 4x - 4) - (x² - x + x -1)

Area of the shaded region = 6x² + 6x - 4x - 4 - x² + x - x + 1

Area of the shaded region = 6x² + 2x - 4 - x² + 1

Area of the shaded region = 6x² - x² + 2x - 4  + 1

Area of the shaded region = 5x² + 2x - 3

4.

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2(1/2(6x +4) × (4x + 2))]

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2((3x + 2)(4x + 2))]

Area of the shaded region = [24x² + 12x + 16x + 8] - [1/2(12x² + 6x + 8x + 4)]

Area of the shaded region = (24x² + 12x + 16x + 8) - (6x² + 3x + 4x + 2)

Area of the shaded region = (24x² + 28x + 8) - (6x² + 7x + 2)

Area of the shaded region = 24x² + 28x + 8 - 6x² - 7x - 2

Area of the shaded region = 24x² - 6x² + 28x - 7x + 8 - 2

Area of the shaded region = 18x² + 21x + 6

Hence, the area is 18x² + 21x + 6

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Answer:

1/x^2 = x^-2

x^4/x^3 = x

(x^2)^2 = x^4

x^3 * x^3 * x^3 = x^9

Step-by-step explanation:

Answer: Problems Involving FractionsIn solving word problems, first, identify what is asked. Then, look for the given facts. Establish the number sentence and the operation/s to be used. Make sure that the operation/s used will bring out the correct answer. Check the answer using the number sentence and see if it will satisfy the given condition.

Step-by-step explanation: Learning Task 2:Answers:16 1/4 square meters₱322,362.50Step-by-step explanation:Solutions:1. Given: 6 1/2 square meters - area which Ruben can paint in an hour

Answer:

Step-by-step explanation:

the inword

When comparing the data from the two locations, the measure of center that should be used to determine which location typically has the cooler temperature is the median.

In Sunny Town, the histogram shows that the shaded bars are skewed to the right, indicating that the distribution is positively skewed. This means that there are a few high temperatures that pull the mean towards the higher end.

However, the median, which represents the middle value when the data is arranged in ascending order, is less affected by extreme values and is a better measure of the center for skewed distributions.In Desert Landing, the histogram shows a symmetric distribution, with the shaded bars evenly distributed around the center.

In this case, both the mean and median can be considered reliable measures of the center.Therefore, to determine which location typically has the cooler temperature, we should use the median.

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Answer: Let's say we want to find out how many red Skittles we need to add to the bag to have the same ratio of red Skittles as in the original bag.

Suppose the original bag contains x red Skittles. Then, the ratio of red Skittles to the total number of Skittles in the bag is x/100.

Let's say we add y red Skittles to the bag, so the total number of red Skittles in the bag becomes x + y. The total number of Skittles in the bag becomes 100 + y, since we only added red Skittles.

For the ratio of red Skittles to be the same as in the original bag, we need:

(x + y) / (100 + y) = x / 100

Cross-multiplying, we get:

100(x + y) = x(100 + y)

Simplifying and rearranging, we get:

y = 100x / (100 - x)

So, we need to add 100x / (100 - x) red Skittles to the bag to have the same ratio of red Skittles as in the original bag. For example, if the original bag has 20 red Skittles, we need to add:

y = 100(20) / (100 - 20) = 25

So, we need to add 25 red Skittles to the bag to have the same ratio of red Skittles as in the original bag.

Step-by-step explanation:

For the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

On a map, scales are frequently present. The scale factor in geography usually applies to how accurately the scale depicted on the map reflects actual distance. Find the corresponding sides upon that two figures before obtaining the scale factor.

Then, divide the new figure's measurement by the old figure's measurement. Your scale factor, i.e., how many times bigger or less than your new image is in comparison to the old, is the consequence.

From the diagram:

coordinate of A = (1,1)

coordinate of A' = (5,5)

Thus, the coordinates of A is multiplied by 5 to get the coordinates of A'

Same applies with the coordinates of B, C and D.

Thus, for the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

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1) The equation (x + 6)² + (y + 4)² = 36 represents a circle centered at the point (-6, -4) with a radius of 6. Therefore, the signal is located at the point (-6, -4).

2) The range of the signal refers to the maximum distance that the signal can travel before it becomes too weak to be detected. In this case, the range of the signal is equal to the radius of the circle, which is 6. This means that any point on the circle (x + 6)² + (y + 4)² = 36 is 6 units away from the signal located at (-6, -4).

To visualize this, imagine the signal as a point source located at (-6, -4), and the range of the signal as a circle centered at the signal with a radius of 6. Any point on this circle represents the farthest distance that the signal can reach and still be detected.

In summary, the signal is located at (-6, -4) and its range is 6 units, as represented by the circle (x + 6)² + (y + 4)² = 36.

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If a quiz has 20 multiple choice questions, then the expected number of correct answers is 5.

For each question, there are 4 possible choices, and only 1 of them is correct.

So, the probability of randomly guessing the "correct-answer" for any  question is = 1/4 = 0.25,

Each question is an independent event, we use the concept of linearity of expectation to calculate the expected number of correct answers for all 20 questions.

The "Expected" number of correct answers for a "single-question" is  probability of guessing it correctly, which is 0.25,

The "Expected-Number" of correct answers for 20 questions is the sum of the expected number of correct answers for each question,

⇒ Expected number of correct answers = (Probability of guessing a single question correctly) × (Number of questions),

Substituting the values,

We get,

⇒ Expected number of correct answers = 0.25 × 20,

⇒ Expected number of correct answers = 5

Therefore, the expected number of correct answers when making "random-guesses" on all 20 multiple choice questions is 5.

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The rejection of the null hypothesis in a hypothesis test that claims the mean gestation period for a fox is more than 48.9 weeks implies there is sufficient evidence to support the claim, indicating a statistically significant difference between the observed sample mean and the hypothesized mean.

If a hypothesis test is performed that rejects the null hypothesis that the mean gestation period for a fox is 48.9 weeks or less, it means that there is sufficient evidence to support the claim that the mean gestation period for a fox is more than 48.9 weeks.

The rejection of the null hypothesis implies that the observed sample mean is significantly different from the hypothesized mean, and this difference is unlikely to have occurred by chance alone. The statistical test used to evaluate the hypothesis would have produced a p-value less than the significance level, indicating that the evidence against the null hypothesis is strong.

Therefore, the scientist can conclude that there is evidence to support their claim that the mean gestation period for a fox is more than 48.9 weeks, and this finding could have important implications for understanding fox reproductive biology and management.

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The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

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The answer is 24. To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

Numbers are often used to measure and compare objects, and they can be used to solve problems and make predictions.

8 1/2% is equal to 0.04.

To calculate the number of poetry books for children, multiply 0.04 by 600.

0.04 x 600 = 24

To find the number of poetry books for children, the decimal equivalent of 8 1/2% needs to be multiplied by the total number of poetry books.

In conclusion, 8 1/2% of 600 poetry books is equal to 24 books.

To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

Then, the decimal needs to be multiplied by the total number of poetry books. This will give the answer, which can be rounded down if necessary.

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The radius of convergence is 4.

To find the radius of convergence, R, of the collection, we can use the ratio test:

[tex]lim_n→∞ |(a_(n+1)/[/tex][tex]a_n)|[/tex]

[tex]lim_n→∞ |(a_{(n+1})/[/tex]

[tex]= lim_n→∞ |(x+8) / 4| * |ln(n+1) / ln(n)|[/tex]

For the series to converge, this limit need to be less than 1. therefore, we've:

[tex]|(x+8) / 4| * lim_n→∞ |ln(n+1) / ln(n)| < 1[/tex]

For the reason that[tex]lim_n→∞ |ln(n+1) / ln(n)| = 1[/tex], we will simplify this to:

|(x+8) / 4| < 1

Taking the absolute cost under consideration, we have cases:

Case 1: (x+8)/4 < 1

In this case, we have x < -4.

Case 2: (x+8)/4 > -1

In this case, we have x > -12.

Consequently, the radius of convergence is the distance from the center of the collection (x = -8) to the closest endpoint of the c language (-12 on the left and -4 at the right):

R = min{8, 4} = 4

So, 4 is the radius of convergence.

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Answer:

6 inches

Step-by-step explanation:

Amy needs 78 inches of fabric for her pants if she follows the given rule.

Define inches ?

An inch is a unit of length that is equal to exactly 2.54 centimeters. It is commonly used in the United States and other countries that use the Imperial system of measurement.

To determine how much fabric Amy needs for her pants, we can use the rule provided to us. The first step is to measure from the waist to the finished length of the pants, which in this case is 35 inches.

Next, we need to double this measurement, which gives us 2 * 35 = 70 inches. This is because we need to account for the fabric that will make up both the front and back of the pants.

Finally, we need to add 8 inches to the doubled measurement, which gives us 70 + 8 = 78 inches. This additional 8 inches is to account for any seams, hems, or other finishing touches that may be required to complete the pants.

Therefore, Amy needs 78 inches of fabric for her pants.

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The density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm³ is 0.5 grams.

Density is a fundamental physical property that measures the amount of matter (mass) packed into a particular space (volume). The mathematical definition of density is simply the mass of an object divided by its volume. Density is typically measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). One crucial aspect of density is that it is an intrinsic property of a substance, meaning it is a characteristic that depends solely on the material and is not affected by the amount of the substance. By using density, we can identify the material a particular object is made of. For example, a piece of gold will have a higher density than a piece of silver because gold is a more dense metal. Additionally, the density of an object can be used to determine its buoyancy in a fluid. Objects with a higher density will sink in a fluid with a lower density, while objects with a lower density will float.

Density is defined as the amount of mass per unit of volume. Mathematically, it can be represented as:

Density = Mass/Volume

Substituting the given values, we get:

Density = 6 grams/12 cm³

Density = 0.5 grams/cm³

Therefore, the density of the sample is 0.5 grams/cm³.

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By using the unitary method, we found that 60 items were sold at $25 each, while 90 items were sold at $5 each at the charity's craft fair.

In this problem, we know the total number of items sold and the total revenue earned. Let's assume that the number of items sold at $5 each is x, and the number of items sold at $25 each is y. Therefore, we can write two equations based on this information:

x + y = 150 (Equation 1)

5x + 25y = 1950 (Equation 2)

Equation 1 represents the total number of items sold, while Equation 2 represents the total revenue earned from the sale. Now, we can use the unitary method to find the value of y, which represents the number of items sold at $25 each.

Let's rearrange Equation 2 to solve for y:

5x + 25y = 1950

25y = 1950 - 5x

y = (1950 - 5x)/25

Now, we can substitute this expression for y into Equation 1:

x + (1950 - 5x)/25 = 150

Simplifying this equation, we get:

25x + 1950 - 5x = 3750

20x = 1800

x = 90

Therefore, we know that 90 items were sold at $5 each. Now, we can use Equation 1 to find the number of items sold at $25 each:

y = 150 - x

y = 150 - 90

y = 60

Hence, 60 items were sold at $25 each.

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Answer:

The answer is 59 ½

Step-by-step explanation:

4×4×4-2×1 ½×1 ½

= 64 - 2× 3/2 × 3/2

= 64 - 9/2

= 128/2 - 9/2

= 119/2

= 59 ½ in3

Hope this helped :)

The answer is: The answers will vary from person to person.

The statement that is true about statistical questions is that the answers will vary from person to person. Statistical questions are questions that can be answered using data and statistics. These questions involve gathering information from a population or a sample of that population, analyzing the data, and making conclusions based on the results. Since different people may have different data and different ways of analyzing that data, the answers to statistical questions can vary. This is why it is important to consider the sample size, the sample method, and the statistical methods used to analyze the data when interpreting the results of statistical questions. A well-designed study can help minimize variability and improve the accuracy of the results, but some degree of variability is still expected due to natural differences in the data collected by different individuals or groups

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The probability of exponential random variables that your job will be ready before 10:01 is approximately 0.0693, or about 6.93%.

We can use the cumulative distribution function (CDF) of the exponential distribution to solve this problem. Let X be the random variable representing the time it takes to print a job. Then, X follows an exponential distribution with parameter λ = 1/12, since the expectation of X is 12 seconds.

The probability that your job will be ready before 10:01 is equal to the probability that the printer finishes the first two jobs in less than 1 minute since your job is third in line.

Let Y be the random variable representing the time it takes to print the first job. Then, Y also follows an exponential distribution with parameter λ = 1/12.

The probability that the first job is finished before 10:01 is given by:

P(Y < 60) = 1 - [tex]$e^{(-\lambda t)}$[/tex] = 1 - [tex]e^{(-(1/12)(60))}[/tex] = 0.3935

Similarly, the probability that the second job is finished before 10:01 is also 0.3935, since it is also an exponential random variable with the same parameter. Therefore, the probability that your job will be ready before 10:01 is:

P(X < 60) = P(Y < 60) × P(Y < 60) × P(X < 60) = 0.3935² × (1 - [tex]$e^{(-\lambda t)}$[/tex]) = 0.0693

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the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).

What is a fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.

To convert these polar coordinates to Cartesian coordinates (x, y), we use the following formulas:

x = r cos(θ)

y = r sin(θ)

Substituting the given values, we get:

x = 6 cos(-π/3) = 6 × (1/2) = 3

y = 6 sin(-π/3) = 6 × (-√3/2) = -3√3

Therefore, the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).

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Answer:

negative

y=-x

y=-2x+6

y=(-1/2)x+1

y=-5x+20

undefined

x=4

x=-3

zero slope

y=2

y=-100