Solve the following quadratic equation for all values of x in simplest form.

(x + 2)^2 – 46 = 24

Therefore, the solutions to the equation x² - 2x + 17 = 0 are:

x = 1 + 4i and x = 1 - 4i.

To solve the equation x² - 2x + 17 = 0 using the quadratic formula, we can compare the equation to the standard form of a quadratic equation, ax² + bx + c = 0.

In this case, a = 1, b = -2, and c = 17.

The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values from our equation, we get:

x = (-(-2) ± √((-2)² - 4(1)(17))) / (2(1))

x = (2 ± √(4 - 68)) / 2

x = (2 ± √(-64)) / 2

Since we have a negative value inside the square root, √(-64), the equation has complex solutions.

Using the fact that √(-1) = i (the imaginary unit), we can simplify the expression:

x = (2 ± 8i) / 2

Dividing each term by 2, we get:

x = 1 ± 4i

Therefore, the solutions to the equation x² - 2x + 17 = 0 are:

x = 1 + 4i and x = 1 - 4i.

In interval notation, the solution set can be written as:

{(1 + 4i), (1 - 4i)}.

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The set of variables that is most likely to have a cause-and-effect relationship is option C: the weight of a box and the postage rate we have to pay to ship the box to California.

Based on the given sets of variables, the set most likely to have a cause-and-effect relationship is:
B. The height of a person and the weight of a person

This is because there is a general correlation between a person's height and their weight, as taller individuals tend to have higher weights. While this is not an absolute rule, there is a stronger cause-and-effect relationship in this set compared to the other options.

This is because the weight of the box is a likely cause of the postage rate, as the heavier the box, the more postage we will have to pay to ship it. In options A and B, there may be a correlation between the variables, but it is less likely that there is a direct cause-and-effect relationship. In option D, the make of a car is not a likely cause of its mileage, as there are many other factors that can affect a car's mileage.

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You can use the power rule for derivatives for each problem (though you could also use the product rule for the fourth curve).

y = x ² + 6x - 1   ==>   dy/dx = 2x + 6

y = x ² - 5x + 1   ==>   dy/dx = 2x - 5

y = 2 - 4x - x ²   ==>   dy/dx = -4 - 2x

y = (1 + x) (7 - x) = 7 + 6x - x ²   ==>   dy/dx = 6 - 2x

--

or, using the product rule,

dy/dx = (1 + x) (-1) + 1 (7 - x) = -1 - x + 7 - x = 6 - 2x

--

Now, stationary points occur where the derivative is zero. We have

2x + 6 = 0   ==>   x = -3

2x - 5 = 0   ==>   x = 5/2

-4 - 2x = 0   ==>   x = -2

6 - 2x = 0   ==>   x = 3

The quadratic function for the revenue from  the sale of shoes indicates;

The price to be charged to maximize revenue is; 16 dollars

The maximum revenue at the $16 price per shoe is; 256 dollars

A quadratic function is a polynomial function of the form f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are constants.

Whereby the revenue function from the shoes is; h(t) = -t² + 32·t

The maximum revenue can be obtained using the formula for finding the vertex of a quadratic equation, y = a·x² + b·x + c, which indicates that the x-value at the vertex is the point x = -b/(2·a)

The specified revenue function indicates; a = 1, b = 32, and c = 0

x = -32/(2×(-1)) = 16

x = 16

The maximum revenue is therefore; h(t) = -16² + 32×16 256

The maximum revenue when the price per shoe is $16 is $256

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We can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

Now, We can use a bar model to represent the total number of cans and the number of stacks that can be formed.

First, let's find the total number of cans:

7 boxes x 48 cans/box = 336 cans

Now, let's use a bar model to represent this total:

| 336 cans of food  |

Next, we want to find how many stacks of 8 cans we can form. We can use a separate bar model to represent the size of each stack:

| 42 stacks of 8 cans each |

Hence, The number of stacks that can be formed, we need to divide the total number of cans by the number of cans in each stack:

336 cans ÷ 8 cans/stack = 42 stacks

So the final bar model looks like this:

| 336 cans of food  | = | 42 stacks of 8 cans each |

Therefore, we can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

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The probability 3 cars arrive in a second is  0.14037

Let X be a discrete random variable taking non-negative values. Then, X is said to follow the Poisson distribution if its probability mass function is given by:

P(X = x) = \(\frac{e^-^\lambda\lambda^x}{x!}\), x = 0, 1, 2, 3, 4....

where x = number of successes,

λ = mean or expected value of the variable.

This distribution is widely used to predict the likeliness of rare and independent events in a large population.

Now, We have to find the probability 3 cars arrive in a second.

Let X be a random variable denoting the number of cars arriving at a given intersection.

Now,

X is stated to follow a Poisson distribution with a mean rate of 4 per second, i.e. X∼P(λ = 5)

The probability that 3 cars arrive in a given second:

P(X = 3) = \(\frac{e^-^55^3}{3!}\) = 0.14037

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Answer:

$1053

Step-by-step explanation:

If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.

To do this multiplication, we can break 1.62 down  simply into $1.00 +$0.6+$0.02

650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.

When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053

Answer:

Given that the triangle ABC is dilated by a scale factor of 1.25 to form the new triangle PQR, the dimensions of PQR will be as follows;

AB corresponds to PQ, but the length of AB=5 units, the length of PQ will be:

PQ=5*1.25=6.25 units

BC corresponds to QR, but the length if QR=4.2 units, the length of QR will be:

QR=4.2*1.25=5.25 units

lastly,

CA corresponds to RP, but CA=4 units, therefore RP will be:

4*1.25=5 units

Answer:

Geometric sequence

common ratio

5

Step-by-step explanation:

this is multiplying by 5 each time which means that it's a geometric sequence

because it's a geometric sequence that means it's called a common ratio

find the geometirc sequence by dividing the first one by the second

10/2=5

Answer:

28/5

Step-by-step explanation:

Answer:

1.8285714285714285714285714285714 is the answer. Round to the nearest hundredth.

1.83

Step-by-step explanation:

16/5 = 3.2

7/4 = 1.75

3.2/1.75 = 1.8285714285714285714285714285714

#teamtrees #WAP (Water and Plant) #STT (Save the Trees)

Let's isolate y first

\(\\ \rm\Rrightarrow 12x-6y=-36\)

\(\\ \rm\Rrightarrow 6y=12x+36\)

\(\\ \rm\Rrightarrow y=\dfrac{12}{6}x+\dfrac{36}{6}\)

\(\\ \rm\Rrightarrow y=2x+6\)

Compare to y=mx+b

The pair of triangles in option A, C and D are congruent triangles.

What is triangle?

A triangle is a polygon with three edges and three vertices. It's one of the introductory shapes in figure. A triangle with vertices A, B, and C is denoted triangle Alphabet. In Euclidean figure, any three points, whennon-collinear, determine a unique triangle and contemporaneously, a unique aeroplane.

What is congruent triangle?

SSS: When all three sides are equal to each other on both triangles, the triangle is harmonious. AAS: If two angles and anon-included( you can suppose of it as outside) side of one triangle are harmonious to the corresponding corridor of another triangle, also the triangles are harmonious.

A) In the given figure, two angles and one side of the one triangle is equal to two angles and one side of the other triangle

By AAS consonance, two triangles are harmonious.

B) In the given figure, one angle and one side is equal

So, two triangles aren't harmonious

C) Then, two sides and one included angle of the one triangle is equal to two sides and one included angle of the other triangle

D) Then, two angles and one included side of the one triangle is equal to two angles and one included side of the other triangle.

thus, the brace of triangles in option A, C and D are harmonious triangles.

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Answer:

for number 4, i drew it in the picture

for number 6, 5 3/4 is closer

Step-by-step explanation:

give brainliest pls

The combined cost of one pound of pork and one pound of beef is $ 15.5.

The total cost is equal to the sum of the products of unit price and quantity of an article. In this problem we find the sum of the quantities of two products (pork roast, beef roast), whose expression can be described below:

67.50 = (3.25) · (x - 0.50) + (5.5) · x

Where x is the unit cost of the beef roast.

Now we proceed to solve the equation for x:

67.50 = 3.25 · x - 1.625 + 5.5 · x

69.125 = 8.75 · x

x = 7.9

A pound of beef roast costs $ 7.9 and a pound of pork roast costs $ 7.4. Then, the combined cost of one pound of prok and one pound of beef is:

C = 1 · 7.9 + 1 · 7.4

C = 15.5

The combined cost of one pound of pork and one pound of beef is $ 15.5.

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The table of values that represents exponential decay is (c)

From the question, we have the following parameters that can be used in our computation:

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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The equation for the scatter plot will be,y=3x+15. Scatter plots are essential for determining relationships, if any, between the values of observable quantities or occurrences.

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they may demonstrate the degree of connection,

if any, between the values of observed quantities or events, scatter plots are crucial in statistics.

The equation of the trend line for the scatterplot below will be y=3x+15.

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The confidence interval of (3.53, 3.83) hours contains the mean hours that U.S. adults have for leisure time after an average workday.

From the question, we have the following parameters that can be used in our computation:

Sample size, n = 1154

Also, we have

A 95% confidence interval from the 2010 GSS survey for the collected answers is 3.53 to 3.83 hours.

The interpretation of the above confidence interval is that 3.53 to 3.83 hours contains the required mean hours

Hence, the true statement is (c) and others are false

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Question

The General Social Survey (GSS) is a sociological survey used to collect data on demographic characteristics and attitudes of residents of the United States. In 2010, the survey collected responses from 1,154 US residents. The survey is conducted face-to-face with an in-person interview of a randomly selected sample of adults. One of the questions on the survey is “After an average workday, about how many hours do you have to relax or pursue activities that you enjoy?” A 95% confidence interval from the 2010 GSS survey for the collected answers is 3.53 to 3.83 hours.

Identify each of the following statements is true or false. Explain your answers.

1. If the researchers wanted to report a confidence interval with a smaller margin of error based on the same sample of 1,154 Americans, the confidence interval would be larger.

2. We can be 95% confident that the interval (3.53, 3.83) hours contains the mean hours that the sampled adults have for leisure time after an average workday.

3. The confidence interval of (3.53, 3.83) hours contains the mean hours that U.S. adults have for leisure time after an average workday.

If the researchers wanted to report a confidence interval with a smaller margin of error based on the same sample of 1,154 Americans, the confidence interval would be larger.

A confidence interval (CI) is a range of values within which the true population parameter is estimated to lie with a specific level of confidence. The confidence interval is a probability statement that reflects the amount of uncertainty associated with the sample estimate.

The level of confidence that the true population parameter falls within the calculated confidence interval is called the confidence level.

In statistics, a sample is a subset of a population that is used to investigate the properties of the population. The sampling process entails selecting a subset of individuals from a population. As a result, the accuracy of the sample's results in representing the population is critical.

The larger the sample size, the better it represents the population, and the lower the margin of error. When reporting a confidence interval, the larger the margin of error, the larger the range of values in which the true population parameter can lie. When a confidence interval with a smaller margin of error is required, the sample size should be increased to reduce the margin of error and produce a more precise estimation of the true population parameter.

As a result, if the same sample of 1,154 Americans is used, the confidence interval would have to be larger to obtain a smaller margin of error.

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Answer:

A. Radical 12, not a pythagroean triple. B. 5, yes, it is a pythagorean triple.

Step-by-step explanation:

Use the pythagroean theorem ^^

Answer:

300pi

Step-by-step explanation:

that is 3/4 of a circle with the radius of 20. Meaning that the area is 300pi

Punch made with 3 cups: 2 cups of cranberry juice

Divide the proportion's two sides by 5.

Ten glasses of cranberry juice in a 15-cup punch

The ratio has not changed; it has simply been scaled up to produce 15 cups of punch. Cranberry juice and pineapple juice are combined to produce punch by Yuan. He uses 2 cups of cranberry juice for every 3 cups of pineapple juice.

The pineapple juice just makes up the latter portion of the ratio. The appropriate quantity of each juice type is in the box to create 10 cups of yuan's punch.

2 cranberries, 1 pineapple, and 3 cups

10 cranberries, 5 pineapples, and 15 cups

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Answer: 4:6

Step-by-step explanation:

Answer:

i dont know

Step-by-step explanation:

But can you just like it cause im trying get enough points to be able have a hundred points so i could have help with a college essay

please

Answer:

You can solve this by substitution method

substitute the value of Y from 2nd equation in the first thet will give you the value of X and once your find the value of X you can substitute that value in any of the equation and get the answer

Answer:

x = - 27/8 and

y = - 97/8

Step-by-step explanation:

3x-2=y

3x - 2 = 1/3x - 11

3x - 1/3x = -11 + 2

8/3x = - 9

x = (-9) / (8/3)

x = - 27/8

Substitution:

3(-27/8)- 2 = y

81/8 - 2 = y

y = - 97/8

Answer:

2 cans

Step-by-step explanation:

Given that :

Radius of pool = 30 feets

Using the relation for the Area of a circle :

Area = pi*r^2

Thus,

Area of pool = 3.14 * 30^2

Area of pool = 3.14 * 900 = 2826feet²

Paints are sold in cans of 5 gallon

5 gallon of paint = 1500 feet²

Least number of 5 gallon can required :

2826 feet² / 1500 feet² = 1.884 cans

Hence,

Least number of 5 gallon can required = 2 cans

To determine the solutions to the given boundary-value problem, we must first analyze the values of L. If L is greater than 0, then we can use Sturm-Liouville theory to solve the problem.

If L is chosen in such a way that the boundary-value problem has a unique solution, then we have precisely one nontrivial solution. However, if L is chosen so that there are multiple solutions, we have more than one solution.

If L is chosen in such a way that the boundary-value problem has no solution, then there are no solutions, including the trivial solution. The trivial solution is the solution where all the unknowns are set to zero.

Therefore, it is possible to find values of L > 0 so that the given boundary-value problem has precisely one nontrivial solution, more than one solution, no solution, and the trivial solution depending on how L is chosen.

Involving values of L > 0, boundary-value problems, and nontrivial solutions. To determine whether it is possible to find values of L > 0 so that the given boundary-value problem has precisely one nontrivial solution, more than one solution, no solution, and the trivial solution, follow these steps:

1. Identify the boundary-value problem in question. This typically involves a differential equation and boundary conditions.

2. Analyze the boundary conditions and the differential equation to see if there is a possibility of finding values of L > 0 that satisfy the problem.

3. Determine if there is a trivial solution, which typically corresponds to a zero solution, where all the components of the solution are zero.

4. Check for the existence of nontrivial solutions. This may involve solving the differential equation for particular values of L > 0 and applying the boundary conditions.

5. Compare the results from steps 3 and 4 to determine if there is precisely one nontrivial solution, more than one solution, no solution, or only the trivial solution.

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The correct hypothesis relation is  is H₀ : μ ≥ 2,412. and Ha : μ < 2,412

According to the United States Census Bureau, the average area = 2, 412 square feet

Then the null hypothesis is

H₀ :μ ( mean ) area is greater than or equal to 2,412

H₀ : μ ≥ 2,412.

But, according to Jane, in her area, still families want a small home comparison to average.

Alternative hypothesis is that, mean area is less than 2,412 .

Ha : μ < 2,412.

Therefore,  H₀ : μ ≥ 2,412. and Ha : μ < 2,412

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The samples of size n = 2 that can be drawn from this population is 28

From the question, we have the following parameters that can be used in our computation:

Population, N = 8

Sample, n = 2

The samples of size n = 2 that can be drawn from this population is calculated as

Sample = N!/(n! * (N - n)!)

substitute the known values in the above equation, so, we have the following representation

Sample = 8!/(2! * 6!)

Evaluate

Sample = 28

Hence, the number of samples is 28

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Complete question

A finite population consists of 8 elements.

10,10,10,10,10,12,18,40

How many samples of size n = 2 can be drawn this population?

Statistical procedures that summarize and describe a series of observations are called descriptive statistics.

Descriptive statistics involve various techniques and measures that aim to summarize and describe the key features of a dataset. These procedures include measures of central tendency, such as the mean, median, and mode, which provide information about the typical or average value of the data. Measures of dispersion, such as the range, variance, and standard deviation, quantify the spread or variability of the data points.
In addition to these measures, descriptive statistics also involve graphical representations, such as histograms, box plots, and scatter plots, which provide visual summaries of the data distribution and relationships between variables. These graphical tools help in identifying patterns, outliers, and the overall shape of the data.
Descriptive statistics play a crucial role in providing a concise summary of the data, enabling researchers and analysts to gain insights, make comparisons, and draw conclusions. They form the foundation for further statistical analysis and inferential techniques, which involve making inferences about a population based on a sample.

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Answer:

5:16 hope this will help you

have a great day