Find the local maximum and minimum values of f using both the first and second derivative tests f(x) = x2 / (x - 1). Summary: The local maximum and minimum values of f(x) = x2 / (x - 1) using both the first and second derivative tests is at x = 0 and x = 2.

The difference of the medians as a multiple of the interquartile range is 0.5,So the correct answer is option (A) 0.5.

The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in numerical order.

For example, consider the data set {3, 5, 2, 6, 1, 4}. When the values are ordered from smallest to largest, we get {1, 2, 3, 4, 5, 6}. The median in this case is the middle value, which is 3.

We can first find the medians and interquartile ranges of the two dot plots.

For Mr. Wilson's class:

Median = 12

Q1 = 10

Q3 = 14

IQR = Q3 - Q1 = 14 - 10 = 4

For Mr. Watson's class:

Median = 10

Q1 = 8

Q3 = 12

IQR = Q3 - Q1 = 12 - 8 = 4

The difference of the medians is |12 - 10| = 2. Therefore, the difference of the medians as a multiple of the interquartile range is:

$$\frac{2}{4} = \boxed{0.5}$$

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Answer:

36.3636364%

or 36.36

Step-by-step explanation:

Answer:

To find the Z-score that has 48.4% of the distribution's area to its left, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look for the closest probability value to 0.484. In the table, we find that the closest probability value is 0.4838, which corresponds to a Z-score of approximately 1.96.

Alternatively, we can use a calculator with a built-in normal distribution function. Using the inverse normal distribution function, also known as the quantile function, we can find the Z-score that corresponds to a given probability. For a probability of 0.484, we get:

To find the Z-score that has 48.4% of the distribution's area to its left, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look for the closest probability value to 0.484. In the table, we find that the closest probability value is 0.4838, which corresponds to a Z-score of approximately 1.96.

Alternatively, we can use a calculator with a built-in normal distribution function. Using the inverse normal distribution function, also known as the quantile function, we can find the Z-score that corresponds to a given probability. For a probability of 0.484, we get:

To find the Z-score that has 48.4% of the distribution's area to its left, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look for the closest probability value to 0.484. In the table, we find that the closest probability value is 0.4838, which corresponds to a Z-score of approximately 1.96.

Alternatively, we can use a calculator with a built-in normal distribution function. Using the inverse normal distribution function, also known as the quantile function, we can find the Z-score that corresponds to a given probability. For a probability of 0.484, we get:

invNorm(0.484)= 1.96

Therefore, the Z-score that has 48.4% of the distribution's area to its left is approximately 1.96.

The expressiοn 5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³). Thus, οptiοn (c) 5x3 is the cοrrect respοnse.

The cοefficients (the numbers in frοnt οf the variables) οf the expressiοn 5x(x²) can be multiplied, and the expοnents οf the variables can be added, tο determine the prοduct.

The first cοefficient we have is 5 times 1, giving us 5. Sο, using the secοnd x², we have x tο the pοwer οf 2 multiplied by x tο the pοwer οf 1 (frοm the first x). Expοnents are added when variables with the same base are multiplied. Sο, x¹ multiplied by x² results in x³.

Cοmbining all οf the parts, the phrase becοmes:

5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³).

Thus, οptiοn (c) 5x³ is the cοrrect respοnse.

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The experimental probability that at least one of the first three customers that walks into the store will make a purchase is 60%.

It is determined by counting the number of times an event occurs in a given experiment and dividing the total number of trials by the number of successful outcomes.

The experimental probability that at least one of the first three customers that walks into the store will make a purchase is calculated by dividing the total number of customers who make a purchase by the total number of customers who enter the store.

In this case, there are 3 trials and 2 customers who make a purchase.

The experimental probability is 3 by 5 which is the total number of trials.

Thus, the experimental probability

=3/5

= 60%.

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Sin 30 =3/x

1/2=3/x

x=6

Answer:

To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.

F1 × F2 can be expanded using the distributive property:

F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3

= 36y^2 + 12y - 54y - 18

= 36y^2 - 42y - 18

Now we can subtract F3 from the result:

F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)

= 36y^2 - 42y - 18 + y + 8

= 36y^2 - 41y - 10

Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.

(please mark my answer as brainliest)

The correct option is D. $18,525.51. is the total profit made in the third as well as fourth quarters by Mr. Brown's store.

In math, addition is the process of adding two or more integers together. The numbers having added are known as addends, while the outcome of the addition process, or the final response, is known as the sum. It is among the most fundamental mathematical operations we employ on a daily basis.

Quarterly profit for Mr. Brown's Goodwill Store in 2012 (in dollars)

1 $9,841.28

2 $8,957.67

3 $7,429.84

4 $11,095.67

Total profit = profit of 3rd quarter + profit of 4th quarter

Total profit = $7,429.84 + $11,095.67

Total profit =  $18,525.51.

Thus, $18,525.51. is the total profit made in the third as well as fourth quarters by Mr. Brown's store.

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Answer:

Yep

Step-by-step explanation:

Yep. Checking this, all of these are correct. Range on parabolas and absolutes will always go to infinity. Nice work

Answer:

●B. The numbers -1,0,1 are zeros of multiplicity 1.

Step-by-step explanation:

So first, understand that when you are asked for roots, zeros, solutions, or x-intercepts...all of these, they are essentially asking for the same thing. Roots ARE solutions ARE zeros ARE x-intercepts. Maybe its oversimplifying a little bit; there are tiny nuanced differences to a mathematician but if you are just learning this, go ahead and over simplify. They are all the same. So you set it equal to 0 and solve.

Yes, literally, change y to a 0 and solve. See image.

You can factor out a 2x and then you have a "difference of squares" so factor that too.

see image.

"multiplicity" is a cool word. It just means how many times a number is the answer. It sort of doesn't even apply here. 0, -1, and 1 are the answer just one time each...so multiplicity 1. Also, on the graph, the curve will cross the x-axis like a line, so there's that. (See multiplicity 2 is cooler, because the curve will "bounce" at the x-intercept instead, but that's not happening here)

Anyway, set the problem equal to 0 and solve. Ta-da! You're done! Hope this helps! See image.

Answer:

(a) Find (f + g)(x)

To find (f + g)(x), we add the two functions f(x) and g(x):

(f + g)(x) = f(x) + g(x) = (4x + 9) + (9x - 5) = 13x + 4

The domain of (f + g)(x) is all real numbers, since there are no restrictions on x that would make (f + g)(x) undefined.

(b) Find (f - g)(x)

To find (f - g)(x), we subtract the function g(x) from f(x):

(f - g)(x) = f(x) - g(x) = (4x + 9) - (9x - 5) = -5x + 14

The domain of (f - g)(x) is all real numbers, since there are no restrictions on x that would make (f - g)(x) undefined.

(c) Find (f * g)(x)

To find (f * g)(x), we multiply the two functions f(x) and g(x):

(f * g)(x) = f(x) * g(x) = (4x + 9)(9x - 5) = 36x^2 + 11x - 45

The domain of (f * g)(x) is all real numbers, since there are no restrictions on x that would make (f * g)(x) undefined.

(d) Find (f / g)(x)

To find (f / g)(x), we divide the function f(x) by g(x):

(f / g)(x) = f(x) / g(x) = (4x + 9) / (9x - 5)

The domain of (f / g)(x) is all real numbers except x = 5/9, since this value would make the denominator of (f / g)(x) equal to zero, resulting in division by zero, which is undefined.

(e) Find f(g(x))

To find f(g(x)), we substitute g(x) into the expression for f(x):

f(g(x)) = 4g(x) + 9

Substituting the expression for g(x), we get:

f(g(x)) = 4(9x - 5) + 9 = 36x - 11

The domain of f(g(x)) is all real numbers, since there are no restrictions on x that would make f(g(x)) undefined.

(f) Find g(f(x))

To find g(f(x)), we substitute f(x) into the expression for g(x):

g(f(x)) = 9f(x) - 5

Substituting the expression for f(x), we get:

g(f(x)) = 9(4x + 9) - 5 = 36x + 76

The domain of g(f(x)) is all real numbers, since there are no restrictions on x that would make g(f(x)) undefined.

(g) Find f(f(x))

To find f(f(x)), we substitute f(x) into the expression for f(x):

f(f(x)) = 4f(x) + 9

Substituting the expression for f(x), we get:

f(f(x)) = 4(4x + 9) + 9 = 16x + 45

The domain of f(f(x)) is all real numbers, since there are no restrictions on x that would make f(f(x)) undefined.

(h) Find g(g(x))

To find g(g(x)), we substitute g(x) into the expression for g(x):

g(g(x)) = 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) Find f(g(x)).

To find f(g(x)), we first need to find g(x) and then substitute it into f(x).

g(x) = 9x - 5

f(g(x)) = f(9x - 5) = 4(9x - 5) + 9 = 36x - 11

Therefore, f(g(x)) = 36x - 11.

(b) Find g(f(x)).

To find g(f(x)), we first need to find f(x) and then substitute it into g(x).

f(x) = 4x + 9

g(f(x)) = g(4x + 9) = 9(4x + 9) - 5 = 36x + 76

Therefore, g(f(x)) = 36x + 76.

(c) Find f(f(x)).

To find f(f(x)), we need to substitute f(x) into f(x).

f(f(x)) = 4(4x + 9) + 9 = 16x + 45

Therefore, f(f(x)) = 16x + 45.

(d) Find g(g(x)).

To find g(g(x)), we need to substitute g(x) into g(x).

g(g(x)) = 9(9x - 5) - 5 = 81x - 50

Therefore, g(g(x)) = 81x - 50.

Domain of f(x) and g(x): Since both f(x) and g(x) are linear functions, their domains are all real numbers.

(e) Find the inverse of f(x).

To find the inverse of f(x), we need to switch the roles of x and f(x) and solve for f(x).

y = 4x + 9

x = 4y + 9

x - 9 = 4y

y = (x - 9) / 4

Therefore, the inverse of f(x) is f^(-1)(x) = (x - 9) / 4.

(f) Find the inverse of g(x).

To find the inverse of g(x), we need to switch the roles of x and g(x) and solve for g(x).

y = 9x - 5

x = 9y - 5

x + 5 = 9y

y = (x + 5) / 9

Therefore, the inverse of g(x) is g^(-1)(x) = (x + 5) / 9.

(g) Find the domain of f^(-1)(x).

The domain of f^(-1)(x) is the range of f(x). Since f(x) is a linear function, its range is all real numbers. Therefore, the domain of f^(-1)(x) is also all real numbers.

(h) Find the domain of g^(-1)(x).

The domain of g^(-1)(x) is the range of g(x). Since g(x) is a linear function, its range is all real numbers. Therefore, the domain of g^(-1)(x) is also all real numbers.

The probability of the union of events A, B, and C is 0.7 where P(A)=0.2, P(B)=0.2 and P(C)=0.3.

In set theory, the union of two or more sets is a set that contains all the distinct elements of the sets being considered. Formally, the union of sets A and B, denoted as A ∪ B, is the set of all elements that are in either set A or set B, or in both.

When A, B, and C are mutually exclusive events, it means that they cannot happen at the same time. Therefore, the probability of the union of these events is equal to the sum of their individual probabilities.

In this case, we are given that:

P(A) = 0.2

P(B) = 0.2

P(C) = 0.3

To find the probability of the union of these events, we need to add their probabilities:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C)

Substituting the given probabilities, we get:

P(A ∪ B ∪ C) = 0.2 + 0.2 + 0.3

P(A ∪ B ∪ C) = 0.7

Therefore, the probability of the union of events A, B, and C is 0.7.

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The question is A, B, and C are mutually exclusive. P(A) = 0.2, P(B) = 0.2, P(C) = 0.3. Find P(A ∪ B ∪ C).

P(A ∪ B ∪ C) = ?

Answer:

8(3/4y - 2) + 6(-1/2x + 4) + 1 can be simplified as:

6(-1/2x) = -3x

8(3/4y) = 6y

8(-2) = -16

6(4) = 24

1 remains as 1.

So the expression becomes:

6y - 3x - 16 + 24 + 1

which simplifies to:

6y - 3x + 9

Therefore, the expressions that are equivalent to 8(3/4y - 2) + 6(-1/2x + 4) + 1 are:

6y - 3x + 9

The quadratic function's zeros are therefore  [tex]x = 1[/tex] and [tex]x = 0.2[/tex] . A degree two polynomial in one or so more variables that is a quadratic function.

Three points are used to determine a quadratic function, which has the form [tex]f(x) = ax2 Plus bx + c.[/tex]

[tex]Sqrt(b2 - 4ac) = [-b sqrt(b)][/tex] Where the quadratic function's coefficients are a, b, and c.

Here,  [tex]a = 20[/tex] , [tex]b = -19[/tex] , & [tex]c = 3[/tex]  . We obtain the quadratic formula by substituting these values: [tex]x = [-(-19) sqrt((-19)2 - 4(20)(3)] / 2(20) (20)[/tex]

When we condense this phrase, we get:

[tex]x = [19 +/- sqrt(361 - 240)] / 40 x = [19 +/- sqrt(121)] / 40\sx = [19 ± 11] / 40[/tex]

Therefore, The zeros of a quadratic equation   [tex]f(x) = 20x2 - 19x + 3[/tex] are as follows: [tex]x = (19 Plus 11) / 40 = 1 and x = (19 − 11) / 40 = 0.2.[/tex]

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Your total grade point average (GPA) for the semester is 2.67.

GPA stands for Grade Point Average. It is a numerical calculation used to measure the academic success of a student. It is calculated by taking the average of all grades received by a student across all courses taken in a given semester or academic year. Each course is assigned a specific number of credit hours, and each grade is assigned a numerical value based on the school’s grading scale. The numerical value of each grade is then multiplied by the number of credit hours for the course, and the total of all courses is added together to determine a student’s GPA.

A higher GPA is generally indicative of higher academic performance while a lower GPA is generally indicative of lower academic performance. A student’s GPA is used by schools, employers, and other organizations to evaluate a student’s academic record.

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This would give you a total of 29.0. Divide this by 10 credit hours and you get a GPA of 2.85 for the semester.

GPA stands for Grade Point Average. It is an academic measure of a student's performance in a course or program of study. It is calculated by dividing the total number of grade points earned by the total number of credit hours taken. A grade point average is typically expressed as a number on a 4.0 scale. A 4.0 GPA is considered to be the highest possible grade point average, while anything below a 2.0 GPA is usually considered to be failing.

This is calculated by adding up the total number of credit hours (10 credit hours) and then multiplying each grade by the respective number of credit hours. A=4.0, B=3.0, C=2.0.
So, you would multiply 4.0 by 3 for FYE 105, 3.0 by 3 for ENG 101, 2.0 by 3 for MAT 150, 2.0 by 3 for BIO 112, and 4.0 by 1 for BIO 113.
This would give you a total of 29.0.
Divide this by 10 credit hours and you get a GPA of 2.85 for the semester.

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Answer:

your answer to the lowest terms

The probability of rolling a sum of 6 with these dice is 1/12.

Yes, there is an analogous ratio between 2:1 and 20:10.

We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.

By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.

As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.

The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:

20 ÷ 10 : 10 ÷ 10

= 2 : 1

As a result, both ratios have the same reduced form, 2:1, making them equal.

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(a) The natural coefficient of variation for one patient is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(b) If the admission times of patients are independent, the mean and variance of admitting a group of 50 emergency patients can be calculated as follows:

mean = n x mean time = 50 x 5 = 250 minutes

variance = n x variance of individual patient / sample size = 50 x (3)^2 / 50 = 9

The coefficient of variation for a group of 50 emergency patients is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(c) The effective mean and coefficient of variation of the admission time for a group of 50 trauma patients can be calculated using the following formula:

te = n x mean time / (1 - p1 x p2)

where p1 is the probability of machine failure and p2 is the probability of repair completion. Assuming the machine can fail at any time, p1 can be calculated as 1 / (mean time between failures / mean admission time) = 1 / (80 x 60 / 5) = 0.001042. Assuming the repair time is also exponentially distributed, p2 can be calculated as 1 / mean repair time = 1 / 4 = 0.25. Therefore, te = 50 x 5 / (1 - 0.001042 x 0.25) = 250.14 minutes. The variance of the admission time can be calculated using the formula:

σe^2 = n x variance of individual patient / (1 - p1 x p2)^2 = 50 x (3)^2 / (1 - 0.001042 x 0.25)^2 = 10.81. The coefficient of variation for a group of 50 trauma patients is the ratio of the standard deviation to the mean, expressed as a percentage:

Ce = (standard deviation / mean) x 100% = (sqrt(10.81) / 250.14) x 100% = 2.60%.

(d) The variability class of the squared coefficients of variation can be determined as follows:

C0² (Part a): (0.6)^2 = 0.36 (low variability)

C0² (Part b): (0.6)^2 = 0.36 (low variability)

Ce² (Part c): (0.026)^2 = 0.000676 (low variability)

(e) The manager of the center can improve the inflated effective admission time in Part c by implementing preventive maintenance measures to reduce the probability of machine failure, such as regular inspection and cleaning of the X-Ray machine, and by improving the repair process to reduce the mean repair time, such as hiring more skilled technicians or improving the repair procedures.

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4775 g968r648 747474874 483892874 23773259635y84b2375789325 7437594365825 4378574937587 49388959365n 98437858746587 32o4iy548569

Answer:

?

Step-by-step explanation:

We can see here that in order to construct a triangle PQR in which angle Q = 30°, angle R=60° and PQ + QR + RP = 10cm​, here is a guide:

A triangle is a geometric shape that is defined as a three-sided polygon, where each side is a line segment connecting two of the vertices, or corners, of the triangle. The interior angles of a triangle always add up to 180 degrees.

Triangles can be classified into different types based on their side lengths and angles, such as equilateral triangles with three equal sides and three equal angles, isosceles triangles with two equal sides and two equal angles, and scalene triangles with no equal sides or angles.

Triangles are used in many areas of mathematics and science, including geometry, trigonometry, and physics.

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The final closed formula answers for each part,

(a) an = n^2 + 1

(b) an = n(n + 1)(n + 2)/6

(c) an = 2n + 6

(d) an = n! + (n-1)! + ... + 2! + 1!

(a) The given sequence can be seen as the sequence of partial sums of the sequence of odd numbers: 1, 3, 5, 7, 9, . . . . That is, the nth term of the given sequence is the sum of the first n odd numbers, which is n^2. Therefore, the closed formula for the given sequence is an = n^2 + 1.

(b) The given sequence can be seen as the sequence of partial sums of the sequence of triangular numbers: 1, 3, 6, 10, 15, . . . . That is, the nth term of the given sequence is the sum of the first n triangular numbers, which is n(n + 1)(n + 2)/6. Therefore, the closed formula for the given sequence is an = n(n + 1)(n + 2)/6.

(c) The given sequence can be seen as the sequence of differences between consecutive squares: 1, 5, 9, 16, 21, . . . . That is, the nth term of the given sequence is the difference between the (n+1)th square and the nth square, which is (n + 1)^2 - n^2 = 2n + 1. Therefore, the closed formula for the given sequence is an = 2n + 6.

(d) The given sequence can be seen as the sequence of partial sums of the sequence defined recursively by a1 = 1 and an+1 = an(n + 1) for n ≥ 1. That is, the nth term of the given sequence is the sum of the first n terms of the recursive sequence. It can be shown that the nth term of the recursive sequence is n! (n factorial), and therefore the nth term of the given sequence is the sum of the first n factorials. That is, an = 1 + 1! + 2! + ... + (n-1)! + n!. Therefore, the closed formula for the given sequence is an = n! + (n-1)! + ... + 2! + 1!.

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Answer: The two positive numbers that satisfy the given requirements are 25 and 50.

Step-by-step explanation:

Let's call the two positive numbers x and y. We want to maximize their product while satisfying the condition that "the sum of the first and twice the second is 100", or mathematically:

x + 2y = 100

We can use algebra to solve for one of the variables in terms of the other:

x = 100 - 2y

Now we want to maximize the product xy:

xy = x(100 - 2y) = 100x - 2xy

Substituting x = 100 - 2y:

xy = (100 - 2y)y = 100y - 2y^2

To find the maximum value of this expression, we can take the derivative with respect to y and set it equal to zero:

d(xy)/dy = 100 - 4y = 0

Solving for y gives:

y = 25

Substituting y = 25 into the equation x + 2y = 100, we get:

x + 2(25) = 100

x = 50

Therefore, the two positive numbers that satisfy the given requirements are x = 50 and y = 25, and their product is:

xy = 50(25) = 1250

Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.

calculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.

Change in temperature on Monday from High to low

=15-10=5°F

Change in temperature on Tuesday from High to low

=8-(-4)=12°F

Change in temperature on Wednesday from High to low

=-2-(-5)=3°F

Change in temperature on Thursday from High to low

=-3-(-7)=4°F

Change in temperature on Friday from High to low

=-1-(-12)=11° F

Days when change in temperature more than 10° F are Tuesday and Friday.

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The Complete question is attached below:

By answering the presented question, we may conclude that Therefore, triangle the length of the base AB is approximately 20.88 centimeters.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

the length of the base AB,

Area = (1/2) * base * height

[tex]CB^2 = CD^2 + BD^2\\9^2 = x^2 + (AB - x)^2\\81 = x^2 + (AB^2 - 2ABx + x^2)\\AB^2 - 2ABx + 2x^2 = 81\\[/tex]

We also know that the area of the triangle is:

[tex]46 = (1/2) * AB * CB\\46 = (1/2) * AB * \sqrt(x^2 + 81)\\Now we can solve for AB in terms of x:AB = (2 * 46) / \sqrt(x^2 + 81)\\AB = 92 / \sqrt(x^2 + 81)\\(92 / \sqrt(x^2 + 81))^2 - 2(92 / \sqrt(x^2 + 81))x + 2x^2 = 81\\[/tex]

[tex]8464 / (x^2 + 81) - (184x) /sqrt(x^2 + 81) + 2x^2 = 81\\8464 - 184x(x^2 + 81) + 2x^2(x^2 + 81) * sqrt(x^2 + 81) = 81(x^2 + 81)\\2x^4 - 181x^2 + 7743 = 0\\x^2 = (181 + \sqrt(181^2 - 427743)) / (2*2)\\x^2 = (181 + sqrt(129961)) / 4\\x^2 = (181 + 361) / 4\\x^2 = 90^2 / 4\\x = 45\sqrt(2) / 2\\[/tex]

[tex]AB = 92 / \sqrt(x^2 + 81)\\AB = 92 / \sqrt((45sqrt(2) / 2)^2 + 81)\\AB = 92 / \sqrt(4050)\\AB ≈ 20.88 cm\\[/tex]

Therefore, the length of the base AB is approximately 20.88 centimeters.

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The concept of Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different theorems and axioms.

The concept of Euclidean geometry as required to be discussed is basically introduced for flat surfaces or plane surfaces. The postulates of the Euclidean geometry are as follows!

1 : A straight line may be drawn from any one point to any other point.

2 :A terminated line can be produced indefinitely.

3 : A circle can be drawn with any centre and any radius.

4 : All right angles are equal to one another (Congruent).

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Answer:

Find f(g(x)) f(x)=7x-8 , g(x)=3x-2. f(x)=7x−8 f ( x ) = 7 x - 8 , g(x)=3x−2 g ( x ) = 3 x - 2. Step 1. Set up the composite result function. f(g(x)) f ( g ...

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The correct option for this question is (d) "No, none of the sides are parallel."

why it is and what is a Quadrilateral?

To determine if quadrilateral CDEF is a trapezoid, we need to check if it has exactly one pair of parallel sides.

We can find the slopes of the line segments CD and EF as follows:

slope of CD = (5 - (-6)) / (-8 - (-1)) = 11 / (-7) = -1.57 (approx.)

slope of EF = (8 - 5) / (3 - 4) = 3 / (-1) = -3

Since the slopes are different, CD and EF are not parallel, and therefore, CDEF is not a trapezoid.

Alternatively, we can also find the slopes of the line segments CF and DE as follows:

slope of CF = (-5 - (-6)) / (4 - (-1)) = 1/5

slope of DE = (8 - 5) / (3 - (-8)) = 3/11

Since the slopes are different, CF and DE are not parallel, and therefore, CDEF is not a trapezoid.

Therefore, the answer is option (d) "No, none of the sides are parallel."

A quadrilateral is a geometric shape that has four straight sides and four vertices (corners). It is a two-dimensional polygon with four sides and four angles. The sum of the interior angles of a quadrilateral is always 360 degrees.

There are many types of quadrilaterals, including squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.

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The actual intake of carbohydrates is 138% as compare to recommended intake.

Recommended intake of carbohydrates or any other nutrient are,

Based on the information provided,

Consumed 159 grams of carbohydrates,

Recommended intake is between 115 and 166 grams.

Calculate the percentage of actual intake compared to the recommended intake, use the following formula,

Percentage = (Actual Intake / Recommended Intake) x 100%

Substituting the values in the formula we have,

⇒Percentage = (159 / 115) x 100%

⇒Percentage ≈ 138.3%

Therefore,  the actual intake of carbohydrates is about 138% of the recommended intake, indicating that consumption of more carbohydrates than recommended.

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The cost of the fat-free cottage cheese required in the recipe is R17.98.

How to determine the cost ?

To determine the cost, we first need to calculate the amount of fat-free cottage cheese required in the recipe. The recipe calls for 250g of fat-free cottage cheese, which can be obtained by using 2 units of 125g each. Knowing the cost of ingredients is important for Mrs Gilfillan to price the cake appropriately to cover her costs and make a profit.

What is the cost of the fat-free cottage cheese required to make the Mixed Berry and Almond Polenta Cake recipe that serves 15 espresso cups at Mrs Gilfillan's coffee shop?

The cost of 1 unit of 125g fat-free cottage cheese is R8.99.

Therefore, the cost of 2 units of 125g is calculated as:

R (2 x 8.99) =R 17.98

Hence, the cost of the fat-free cottage cheese required in the recipe is R 17.98.

This cost is in addition to the cost of the other ingredients, such as butter, sugar, ground almonds, mixed frozen berries, and polenta, as well as the cost of labor, overhead, and other expenses involved in making and selling the cake.

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If a₁ = 5 and an 5an-1 then The value οf a₄ is 625.

An arithmetic sequence is a sequence οf numbers in which each term after the first is fοund by adding a fixed cοnstant number, called the cοmmοn difference, tο the preceding term. Fοr example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a cοmmοn difference οf 3, since each term after the first is fοund by adding 3 tο the preceding term.

The nth term οf an arithmetic sequence can be fοund using the fοrmula:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, and d is the cοmmοn difference. The sum οf the first n terms οf an arithmetic sequence can be fοund using the fοrmula:

Sn = n/2 (a1 + an)

We are given that a₁ = 5, and that the nth term is 5 times the (n-1)th term. We can use this infοrmatiοn tο find the value οf a₄ as fοllοws:

a₂ = 5a₁ = 5(5) = 25

a₃ = 5a₂ = 5(25) = 125

a₄ = 5a₃ = 5(125) = 625

Therefore, the value of a₄ is 625.

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