Solve the quadratic function by factoring x^2 +10x+9-0

An equation which suggests how the range of skeins of yarn remaining, y, relies upon at the range of hats Anna knits, x is y =6- 1.2x.

An expression is a mathematical equation that is used to reveal the connection present among or extra variables and numerical quantities.

Let y constitute the range of skeins of yarn remaining. Let x constitute the range of hats Anna knits.

Mathematically, an equation which fashions the connection among x and y is given by: Mathematically, an equation which fashions the connection among x and y is given by

Remaining yarn = Total quantity of yarns -

Number of yarns used in keeping with hats

Substituting the given parameters into the formula, we have;

y = 6 - 1.2x

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The pH of the solution of 0.400 M CH3NH2 containing 0.300 M CH3NH3I is approximately 9.17.

pH is a measure of how acidic or basic an aqueous solution is.

The acidity or basicity of an aqueous solution is indicated by the pH value.

pH is defined as the negative logarithm of the hydrogen ion concentration of a solution.PH = - log [H+]

According to the equation, pH is directly proportional to the negative log of hydrogen ion concentration.

As a result, as the concentration of H+ ions decreases, the pH of the solution increases.

Here, the given values are, Concentration of CH3NH2, C1 = 0.400 MConcentration of CH3NH3I, C2 = 0.300 Mkb of CH3NH2 = 4.4 × 10⁻⁴

We know that, The Kb expression is given as: Kb = [CH3NH2][OH-] / [CH3NH3+]

Now we can get [OH-] as follows: [OH-] = Kb [CH3NH3+] / [CH3NH2]

By substituting the given values in the above equation, we get,[OH-] = (4.4 × 10⁻⁴)(0.300) / 0.400 = 3.3 × 10⁻⁴MWe know that, pOH = -log[OH-]

By substituting the given value in the above equation, we get:pOH = -log (3.3 × 10⁻⁴) = 3.48Finally, we can calculate pH by the equation:

pH + pOH = 14pH = 14 - pOH= 14 - 3.48= 10.52 (approx)

Therefore, the pH of the solution of 0.400 M CH3NH2 containing 0.300 M CH3NH3I is approximately 9.17.

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In the context of statistics, a statistic refers to a numerical value that is calculated from a sample of data, while a parameter refers to a numerical value that describes a population.

In the given scenario, the number of birds in different regions can be considered as either a statistic or a parameter depending on the context in which it is used.

If the number of birds is obtained by counting the birds in a specific region and then calculating summary measures such as the mean, median, or standard deviation based on that sample, then it would be considered a statistic. This is because the data is collected from a subset (sample) of the entire population of birds.

On the other hand, if the number of birds represents the total count or an average count across all regions without any sampling involved, then it would be considered a parameter. In this case, the value represents a characteristic of the entire population of birds in different regions.

It is important to note that whether the number of birds is considered a statistic or a parameter depends on how the data is collected and analyzed.

If multiple samples are taken from different regions and statistical inference techniques are used to make inferences about the entire population, then it would be appropriate to consider it as a statistic. However, if the data represents a complete count or an average across all regions without any sampling involved, then it would be considered a parameter.

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Answer:

c. What is your favorite book?

Explanation:

A question is said to be biased when it is asked in such a way that it leads or skews people intentionally to a particular answer.

Looking at the given questions in the options, we can see that three of them have a particular person or thing mentioned in the question. These are examples of biased questions.

But the question, "What is your favorite book?" does not suggest a name of a particular book to the respondent which could influence their responses. This type of question is not biased.

The value of width 'w' of rectangular prism with l = n/a, h = n/a, v = n/a is given by, w = a/n.

We know that the volume of rectangular prism with length L and width W and Height H is given by,

V = L*W*H

Given that the Height of the rectangular prism, h = n/a

Length of the rectangular prism, l = n/a

Volume of the rectangular prism, v = n/a

let the width of the rectangular prism be 'w'.

So from the volume formula we get,

v = lwh

n/a = (n/a)*w*(n/a)

n/a = (n/a)²*w

w = (n/a)/(n/a)² = (n/a)*(a/n)² = a/n

Hence the value of w is a/n.

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Answer:

592 sq. ft.

Step-by-step explanation

area of front and back=2[12×6]+2[1/2×12×8]=144+96=240 ft²

side area=2[(6+10)×11]=2×176=352 ft²

Total surface area=240+352=592 square feet.

Answer:

We can begin by simplifying each equation:

A. 52 = 8n + 4 can be rewritten as 48 = 8n or 6 = n

B. 4(2n + 1) = 52 can be simplified to 8n + 4 = 52 or 8n = 48 or 6 = n

C. 4=52-8n can be rewritten as 8n = 48 or 6 = n

D. 4n = 48 can be simplified to n = 12

Therefore, equations A, B, and C are equivalent, and equation D is not equivalent to the others.

So, the correct answers are A, B, and C.

Answer:

Step-by-step explanation:first you have to multiply then divide then add then subtract and then substitute and then you will get the answer.

The exponent in Sam’s product is -5.

What does a math exponent mean?

Let us first multiply 500 with 3. 625×10-8

3. 625×10-8  × 500 = 1812.5 × 10⁻⁸

Then Sam has reported this answer in scientific notation

The format for writing a number in scientific notation is

(first digit of the number) followed by (the decimal point) and then (all the rest of the digits of the number), times (10 to an appropriate power).

In 1812.5 × 10⁻⁸  we move the decimal 3 times to left side

Since the decimal is moved left side, we multiply by 10³

1812.5 × 10⁻⁸ = 1812.5 × 10⁻⁸ × 10³

1812.5 × 10⁻⁸  = 1812.5 × 10⁻⁵

Exponent is a quantity representing the power to which a given number or expression is to be raised

1812.5 × 10⁻⁵ exponent is -5

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Number of pennies that Betty can have 45

Prime numbers are natural numbers with only the number itself and the number one as their factors. We are aware that a factor is any integer that evenly divides the provided number.

The prime number from 1 to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Here given that

Betty has between 40 and 50 pennies

The set of numbers of pennies that Betty may have is

41, 42, 43, 44, 45, 46, 47, 48, 49.

Given that

Betty arranged all pennies in a rectangular array in 3 different ways

Here,

Number of pennies = Area of the rectangle (in No. of pennies)  

As we know Area of the rectangle = Lenght × Breadth

This means whatever the number of pennies, the number should be a Non-Prime number  

=> The numbers that are non-prime numbers in the given numbers is

42, 44, 45, 46, 48, 49  

It is also given that, after adding 2 pennies she can only arrange the pennies in one way without any gaps or spaces i.e a straight line.

This means after adding 2 pennies the number became a prime number so that she has only one way that she arranged them in a straight line.

Now find which number will be a prime number after adding 2

=>  42 + 2 = 44 - Non-Prime number

=>  44 + 2 = 46 - Non-Prime number

=>  45 + 2 = 47 - Prime number

=>  46 + 2 = 48 - Non-Prime number

=>  48 + 2 = 50 - Non-Prime number

=>  49 + 2 = 52 - Non-Prime number

Therefore,

Number of pennies that Betty can have 45

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Answer:

888

Step-by-step explanation:

let the number be n then divide by 8 , that is \(\frac{n}{8}\)

now add 8 to this

\(\frac{n}{8}\) + 8 and finally multiply this by 8 and equate to 952

8(\(\frac{n}{8}\) + 8) = 952 ( divide both sides by 8 )

\(\frac{n}{8}\) + 8 = 119 ( subtract 8 from both sides )

\(\frac{n}{8}\) = 111 ( multiply both sides by 8 to clear the fraction )

n = 888

the number chosen was 888

The natural breaks, quantile, and equal interval classification schemes are methods used to categorize data for the purpose of creating thematic maps. Each scheme has its own approach and considerations: Natural Breaks, Quantile, Equal Interval.

Natural Breaks (Jenks): This classification scheme aims to identify natural groupings or breakpoints in the data. It seeks to minimize the variance within each group while maximizing the variance between groups. Natural breaks are determined by analyzing the distribution of the data and identifying points where significant gaps or changes occur. This method is useful for data that exhibits distinct clusters or patterns.

Quantile (Equal Count): The quantile classification scheme divides the data into equal-sized classes based on the number of data values. It ensures that an equal number of observations fall into each class. This approach is beneficial when the goal is to have an equal representation of data points in each category. Quantiles are useful for data that is evenly distributed and when maintaining an equal sample size in each class is important.

Equal Interval: In the equal interval classification scheme, the range of the data is divided into equal intervals, and data values are assigned to the corresponding interval. This method is straightforward and creates classes of equal width. It is useful when the range of values is important to represent accurately. However, it may not account for data distribution or variations in density.

In summary, the natural breaks scheme focuses on identifying natural groupings, the quantile scheme ensures an equal representation of data in each class, and the equal interval scheme creates classes of equal width based on the range of values. The choice of classification scheme depends on the nature of the data and the desired representation in the thematic map.

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The dimensions that will minimize the cost of constructing the box are Front width: 7.21 inches, Depth: 7.21 inches and Height: 4.81 inches

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

The volume is calculated as

V = b²h

So, we have

b²h = 250

Make h  the subject

h = 250/b²

The surface area is then calculated as

SA = b² + bh + 3bh

This means that the cost is

Cost = 5b² + 9bh + 2 * 3bh

This gives

Cost = 5b² + 15bh

So, we have

Cost = 5(b² + 3bh)

Recall that

h = 250/b²

So, we have

Cost = 5(b² + 3b * 250/b²)

Evaluate

Cost = 5(b² + 750/b)

Differentiate and set to 0

10b - 3750/b² = 0

This gives

10b = 3750/b²

Cross multiply

10b³ = 3750

Divide by 10

b³ = 375

Take the cube root of both sides

b = 7.21

Next, we have

h = 250/(7.21)²

Evaluate

h = 4.81

Hence, the dimensions are Front width: 7.21 inches, Depth: 7.21 inches and Height: 4.81 inches

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The cost of the plan for the limited talk and text is $50 with an additional cost of $22.99 for each gigabyte of data.

Generally, a mathematical function means a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables. It can take an input from many variables but will  always give the same output, unique to that function.

We are given that "H(g) = 22.99g + 50", where H represents the cost, in dollars, and g represents the number of gigabytes of data. The main answer is based on the given function where the constant term of 50 represents the cost of the plan for limited talk and text, and the coefficient of 22.99 represents the additional cost for each gigabyte of data used.

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Answer:

136.99

Step-by-step explanation:

Đây là một câu hỏi dễ chỉ cần sử dụng máy tính

The image of the transformation is (-5, 11) (-4, 8) (-2, 14)

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

Pre-image: (5, 15) (4, 12) (2, 18)

Transformation: Translate 4 units down, and then reflect over the y-axis.

Mathematically, this can be expressed as

(x, y) = (-x, y - 4)

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

(5, 15) (4, 12) (2, 18) = (-5, 11) (-4, 8) (-2, 14)

Hence, the image is (-5, 11) (-4, 8) (-2, 14)

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The factors of m2 – 6m + 6m – 36 are (m – 2)(m + 18) and (m – 3)(m – 3).

The factors of m2 – 6m + 6m – 36 can be determined using the quadratic formula. The general equation for a quadratic equation is ax2 + bx + c = 0, where a, b, and c are constants and x is the unknown variable.

To find the factors of m2 – 6m + 6m – 36, we can use the quadratic formula to solve for the two factors of the equation. We can start by substituting in the values for a, b, and c: a = 1, b = –6, and c = –36. The quadratic formula for this equation is x = [-b ± √(b2 – 4ac)]/2a.

To solve for the two factors, we can plug in the values for a, b, and c and solve for x. We get x = [6 ± √(62 – 4(1)(–36))]/2(1). After simplifying, we get x = [6 ± √396]/2.

We can then use the positive and negative values of √396 to find the two factors of the equation. The positive value is √396 = m + 18, so the first factor is (m – 2)(m + 18). The negative value is -√396 = m – 3, so the second factor is (m – 3)(m – 3). Therefore, the factors of m2 – 6m + 6m – 36 are (m – 2)(m + 18) and (m – 3)(m – 3).

The factors of m2 – 6m + 6m – 36 are (m – 2)(m + 18) and (m – 3)(m – 3).

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Answer:

x = 13

y = 132

Explanation:

48° and y° are same-side interior angles which means they are supplementary, meaning they have to equal 180° when added.

180 - 48 = 132

So y = 132

48° and (5x - 17)° are alternate exterior angles. So they have to be equal. Meaning when the value of x is substituted into (5x - 17)° it has to give us 48°.

5(13) - 17 = 48

So x = 13

To find the standard error of the sample mean, we use the formula. The standard error of the sample mean derived from a random sample of 12 bowls is approximately 0.0866 inches.

The expected value in this case is simply the mean diameter of the smaller series, which is 7 inches.

To find the standard error of the sample mean, we use the formula:

Standard Error = Standard Deviation / Square Root of Sample Size

Plugging in the given values, we get:

Standard Error = 0.3 / sqrt(12) = 0.086

Therefore, the standard error of the sample mean derived from a random sample of 12 bowls is 0.086 inches.

The expected value is the mean diameter of the bowls. In this case, the mean diameter is already provided, which is 7 inches. So, the expected value is 7 inches.

Now, to find the standard error of the sample mean, we will use the formula:

Standard Error (SE) = (Standard Deviation) / √(Sample Size)

In this case, the standard deviation is 0.3 inch and the sample size is 12 bowls.

SE = 0.3 / √12 ≈ 0.3 / 3.46 ≈ 0.0866 inches

So, the standard error of the sample mean derived from a random sample of 12 bowls is approximately 0.0866 inches.

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You have not provided the contents of any of the drop-down menus, so we cannot say for certain what the answers should be--except in the case of "infinitely many solutions.

2x + 9 + 3x + x = 6x

2x + 9 + 3x + x = 15

2x + 9 + 3x + x = 6x + 9

Based on the given conditions,

(1) No solutions :

There will be no solutions when the left side is inconsistent with the right side:

2x + 9 + 3x + x =  _ x + _

We can sum of difference,

6x + 9 = 6x

Subtract 6x from both sides,

6x - 6x = -9

9 = 0

9 = 0 which is absurd and hence the equation has no solution.

(2) One solutions :

There will be one solution when the left side and right side are not inconsistent and not the same.

2x + 9 + 3x + x = 15

6x + 9 = 15

Subtract 9 from both sides.

6x = 6

Divide both sides by 6.

x = 1 and this is the only solution.

(3) Infinity solutions :

There will be an infinite number of solutions when the equation is true for any value of x. This will be the case when the left side and right side are identical.

2x + 9 + 3x + x = 6x + 9

6x + 9 = 6x + 9

Subtract 6x from both sides,

9 = 9, both sides are balanced which means, the equation has infinitely many solutions.

Therefore,

2x + 9 + 3x + x = 6x

2x + 9 + 3x + x = 15

2x + 9 + 3x + x = 6x + 9

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If all three conditions are met, the function is continuous at x=-8. If any of the conditions fail, the function is discontinuous at x=-8

To determine whether the function is continuous or discontinuous at x=-8, we need to examine the three conditions for continuity:

1. The function must be defined at x=-8.
2. The limit of the function must exist as x approaches -8.
3. The limit of the function as x approaches -8 must equal the function's value at x=-8.

If all three conditions are met, the function is continuous at x=-8. If any of the conditions fail, the function is discontinuous at x=-8.

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The 95% confidence interval for the true population mean textbook weight is (61.68, 66.32) ounces.

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

Confidence Interval = sample mean ± (critical value) * (standard deviation / √sample size)

In this case, the sample mean weight is 64 ounces, and the population standard deviation is 10 ounces. Since the sample size is 31, we need to determine the critical value for a 95% confidence level.

The critical value can be found using a standard normal distribution table or a statistical calculator. For a 95% confidence level, the critical value is approximately 1.96.

Plugging the values into the formula, we have:

Confidence Interval = 64 ± (1.96) * (10 / √31)

Calculating the expression inside the parentheses:

10 / √31 ≈ 1.79

Multiplying 1.96 by 1.79:

1.96 * 1.79 ≈ 3.51

Finally, we can construct the confidence interval:

64 - 3.51 ≈ 61.68

64 + 3.51 ≈ 66.32

Therefore, the 95% confidence interval for the true population mean textbook weight is approximately (61.68, 66.32) ounces.

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Answer:

x=-2 y=-5

x=5 x=2

In conclusion for part A  it would take T - 32.5 minutes to cook a 1.5 kg joint. For part B w is given by the formula w = (T - 25) / (-35). For part C 6.6 kg of beef needs to be cooked for 207 minutes. For part D  5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.

How to solve?

a) To find how long it would take to cook a 1.5 kg joint, we can substitute w = 1.5 into the formula:

T - 35w + 25 = T - 35(1.5) + 25 = T - 32.5

So, it would take T - 32.5 minutes to cook a 1.5 kg joint.

b) To make w the subject of the formula, we need to isolate w on one side of the equation. We can start by subtracting 25 from both sides:

T - 35w = T - 25

Next, we can divide both sides by -35:

w = (T - 25) / (-35)

Therefore, w is given by the formula w = (T - 25) / (-35).

c) To find the weight of beef that needs to be cooked for 207 minutes, we can substitute T = 207 into the original formula:

T - 35w + 25 = 207

Simplifying this equation, we get:

-35w = -232

Dividing both sides by -35, we get:

w = 6.6 kg

Therefore, 6.6 kg of beef needs to be cooked for 207 minutes.

d) To find the weight of beef that needs to be cooked for 3 hours and 48 minutes (which is equivalent to 3 × 60 + 48 = 228 minutes), we can substitute T = 228 into the original formula:

T - 35w + 25 = 228

Simplifying this equation, we get:

-35w = -207

Dividing both sides by -35, we get:

w = 5.91 kg

Therefore, 5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.

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(2+3i)+2i(2+3i) = 1(2+3i) + 2i(2+3i) = (1+2i)(2+3i)

Answer:

|x| = 8

Answer: x = 8, -8

Step-by-step explanation:

| | this symbol represents absolute value. When you remove absolute value it creates a ± sign on the opposite side.

x = ± 8

This means x = 8 and x = -8

The solutions are 8 and -8.

Answer: To determine the marginal cost of the third taco for Jeremy, we need to compare the cost of buying it individually to the cost of buying it as part of the value meal.

Buying two tacos individually:

Buying the value meal with three tacos:

To calculate the marginal cost, we subtract the cost of buying the value meal from the cost of buying two tacos individually:

The negative value indicates that buying the value meal is more cost-effective than buying the third taco individually. Therefore, the marginal cost of the third taco for Jeremy would be $0 (option A).

Answer:

10 x 3 + x 2 -7 x

Step-by-step explanation:

Answer: 10x^3

Step-by-step explanation:

The centerline (X) is 76.2143°F, the upper control limit (UCL) is 76.9063°F, and the lower control limit (LCL) is 74.5223°F.

To find the centerline (X), upper control limit (UCL), and lower control limit (LCL) for the mean temperature, we need to follow these steps:

1. Calculate the overall mean temperature (X) by summing up all the mean temperatures and dividing by the number of days (7).
X = (76.3 + 76.8 + 75.8 + 76.0 + 76.4 + 75.6 + 76.6) / 7 = 76.2143°F

2. Calculate the upper control limit (UCL) using the formula:
UCL = X + (A2 * R), where A2 is a control chart constant (which equals 1.128 for n=10) and R is the mean of the ranges (1.5°F in this case).
UCL = 76.2143 + (1.128 * 1.5) = 76.2143 + 1.692 = 76.9063°F

3. Calculate the lower control limit (LCL) using the formula:
LCL = X - (A2 * R)
LCL = 76.2143 - (1.128 * 1.5) = 76.2143 - 1.692 = 74.5223°F

So, the centerline (X) is 76.2143°F, the upper control limit (UCL) is 76.9063°F, and the lower control limit (LCL) is 74.5223°F.

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The required answer is  the centerline X is 76.2143°F, the UCL is 76.6763°F, and the LCL is 75.7523°F.

To construct a control chart for the process mean, we need to calculate the centerline X, the upper control limit (UCL), and the lower control limit (LCL) using the given information.

First, we calculate the average of the means, which is the centerline X is simply the average of the means of the temperatures for the 7 days. We can calculate it as follows:
X = (76.3 + 76.8 + 75.8 + 76.0 + 76.4 + 75.6 + 76.6) / 7
X = 76.2143
Next, we calculate the control limits. The formula for the UCL and LCL is:
UCL = X + A2(R)
LCL = X - A2(R)
Where A2 is a constant based on the sample size (n = 10 in this case) and R is the average range (given as 1.5°F).
From the table, we can calculate the ranges for each day:
Range on Sun = 76.3 - 76.3 = 0
Range on Mon = 76.8 - 75.8 = 1
Range on Tue = 76.0 - 75.8 = 0.2
Range on Wed = 76.4 - 76.0 = 0.4
Range on Thu = 76.4 - 75.6 = 0.8
Range on Fri = 75.6 - 75.6 = 0
Range on Sat = 76.6 - 75.6 = 1
The average range is:
R = (0 + 1 + 0.2 + 0.4 + 0.8 + 0 + 1) / 7
R = 0.5143
Now we can calculate the control limits:
UCL = 76.2143 + A2(0.5143)
LCL = 76.2143 - A2(0.5143)
From a table of constants, we find that A2 for n = 10 is 0.577.
Substituting the values, we get:
UCL = 76.2143 + 0.577(0.5143) = 76.6763
LCL = 76.2143 - 0.577(0.5143) = 75.7523

Therefore, the centerline X is 76.2143°F, the UCL is 76.6763°F, and the LCL is 75.7523°F.

These values can be used to construct a control chart for the process mean.

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Answer:

42

Step-by-step explanation:

You can find the product of two numbers by adding them. The question says what is the product of the 6th and 2nd square numbers. The first ten square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 so the second square number is 4 and the 6th square number is 36 and 36 + 4 is 42. Hope this helped! Stay safe!

A square number is a number that can be formed when you multiply a number by itself.

a x a = \(a^{2}\)

The product of the 6th square number and the 2nd square number is 144.

Therefore, the product of the 6th square number and the 2nd square number is

= 36 x 4

= 144

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