If f(x) is a linear function, f(-2)=3, and f(4)=5, find an equation for f(x)

Answer:

Step-by-step explanation:

2=35434567654321-34567887654321=2345678765-cwjbfd3

The value of Sinθ 1/√197, cos θ = 14/√197, csc θ = H/P =√197, sec θ =√197/14, Cot θ = 14

Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilised in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.

Trigonometry employs six fundamental trigonometric functions. These ratios are trigonometric functions. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities.

if triangle is form,

Then Perpendicular(P) = 1 and Base(B) = 14

Then Hypotenuse(H) = √(12 + 142)= √197

Then , sin θ = P/H = 1/√197

cos θ = B/H = 14/√197

csc θ = H/P = √197/1 = √197

sec θ = H/B =√197/14

Cot θ = B/P = 14/1 = 14

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The complete question should be:

use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle, given that tan θ = 1/14 ,

a)The Molecular geometry for AF₃, in above three figures are

i) Trigonal Planar

ii) Trigonal pyramidal

iii) T-shaped

b) NF₃(Nitrogen trifluoride), PF₃(Phosphorus trifluoride).

c) ClF₃(Chlorine trifluoride).

Molecular geometry studies the formulation of 3-D shapes by molecules and how these shapes relate to chemical reactivity and physical properties.

(i) If the central atom A has four valence electrons and three monovalent atom B, then A can form three sigma bond with B and zero free electron left around A, so the molecule is sp² hybridized with three bond pair so it has trigonal planar shape.

ii) If the central atom A has three valence electrons and three monovalent atom B, when there are three bonds and one lone pair on the central atom in the molecule, so the molecule is sp³ hybridized and has trigonal pyramidal.

iii) If the molecule is If the molecule is sp³d hybridized, it has three bond pairs and two lone pair and has T-shaped.

b) Here, we see A have three (+3) valency and F have (-1) valency. In the provide atoms are Atom --> valency : Li --> 1 , B--> 3 , N--> 3 , Al --> 3 , P --> 3 , Cl --> 1. But here AF₃ only possible combinations of metal A and Fluorine, F. So, the required element is NF₃(Nitrogen trifluoride), PF₃(Phosphorus trifluoride).

c) The shape (iii) is T- shaped in nature. After reading the above discussion the molecule which has T -shaped is ClF₃(Chlorine trifluoride).

Hence, the required is ClF₃.

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Complete question:

This figure shows ball-and-stick drawings of three possible shapes of an AF₃ molecule (above figure).

a)For each shape, give the electron-domain geometry on which the molecular geometry

b) Which of the following elements will lead to an AF₃ molecule with the shape in (ii): Li, B, N, Al, P, Cl?

c) Name one of the possible elements A those are expected to lead to the AF₃ structure shown in (iii). Express your answer as a chemicl symbol.

The reasoning based on the information will be:

a) Deductive reasoning.

b) Deductive reasoning.

Deductive reasoning follows a top-down method, whereas inductive reasoning follows a bottom-up method. While deductive thinking involves drawing conclusions by moving from general premises to specific conclusions, inductive reasoning involves moving from the specific to the general.

A specific conclusion is reached by the logical process of inductive reasoning, which combines several premises that are all generally accepted as true or discovered to be true. Applications that involve prediction, forecasting, or behavior use inductive reasoning frequently. In both cases, deductions were made based on the information.

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Answer:

84m²

Step-by-step explanation:

Area if a parallelogram is base×height

base=7m

height=12m

area=7m×12m=84m²

The number of sells she needs to to in order to earn same as fixed monthly salary, 3000

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

First choice, monthly salary of ​$1260 from a company

Second choice, base salary of ​$1200 and a ​2% commission on the amount of furniture she sells during the month.

Let's call the amount of furniture Juliet sells each month "x".

With the second option, Juliet would receive a monthly salary of $1200 + 0.02x,

We want to find the value of x such that this salary is equal to $1260, so we can set up the following equation:

$1200 + 0.02x = 1260

Subtracting $1200 from both sides:

0.02x = 60

Dividing both sides by 0.02:

x = 3000

So, for Juliet to earn the same salary with either option, she would need to sell $3000 worth of furniture each month.

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Answer:

Sera drove 450 miles (y) and his car used 18 gallons (x) of gas. How many gallons of gas will Sera use if she drives 875 miles?

1. Identify x:

2. Identify y:

3. Calculate k using k =y/x:

4. Write an equation for the proportional relationship using y =kx:

5. Solve the problem and show your work: How many gallons of gas will Sera use if she drives 875 miles?

Step-by-step explanation:

Sera drove 450 miles (y) and his car used 18 gallons (x) of gas. How many gallons of gas will Sera use if she drives 875 miles?

1. Identify x:

2. Identify y:

3. Calculate k using k =y/x:

4. Write an equation for the proportional relationship using y =kx:

5. Solve the problem and show your work: How many gallons of gas will Sera use if she drives 875 miles?

The complete equation is,

6x + 4x + 5 = 10x+5.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

We have an equation,

6x + __ = 10x+5.

Let the missing number is y.

Then,

6x + y = 10x+5.

y = 10x - 6x + 5

y = 4x + 5

Therefore, the missing term is  4x + 5.

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20 is 8 less than 28 as 3x-5 is 10 less than 3x-5+10.

Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.

Given that, 20 is to 28 as 3x-5 is to 3x-5+10

We see, 28-20 = 8

That mean, we need to add 8 to 20 or subtract 8 from 28 to make both equal,

Therefore, we can say, 20 is 8 less than 28, or 28 is 8 more than 20,

Similarly,

3x-5 and 3x-5+10

We see, 3x-5+10 - (3x-5)

= 3x+5-3x+5

= 10

That mean, we need to add 10 to 3x-5 or subtract 10 from 3x-5+10 to make both equal,

Therefore, 3x-5 is 10 less than 3x-5+10, or 3x-5+10 is 10 more than 3x-5,

Hence, 20 is 8 less than 28 as 3x-5 is 10 less than 3x-5+10.

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The probability of selecting an 8 is [tex]\frac{4}{52}[/tex] since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to [tex]\frac{1}{13}[/tex]. The probability of selecting a face card is [tex]\frac{12}{52}[/tex] since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to [tex]\frac{3}{13}[/tex].  1 - [tex]\frac{3}{13}[/tex] = [tex]\frac{13}{13}[/tex] - [tex]\frac{3}{13}[/tex] =[tex]\frac{10}{13}[/tex].

There are four suits (hearts, spades, diamonds, and clubs), each with 13 cards from Ace to King, in a conventional 52-card deck of playing cards. As a result, there are four of each potential card.

(A) The probability of selecting an 8 is  [tex]\frac{4}{52}[/tex] since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to [tex]\frac{1}{13}[/tex].

(B) The probability of selecting a face card is [tex]\frac{12}{52}[/tex] since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to [tex]\frac{3}{13}[/tex].

(C) The probability of NOT selecting a face card is [tex]\frac{40}{52}[/tex] since there are 4 of each card from Ace through 10 that are not face cards. This simplifies to 10/13. The solution to part B's question can be used as another way to approach this issue. If the probability of selecting a face card is 3/13, then the probability of NOT selecting a face card has to be 1 - [tex]\frac{3}{13}[/tex] = [tex]\frac{13}{13}[/tex] - [tex]\frac{3}{13}[/tex] =[tex]\frac{10}{13}[/tex]. Recall that you must deduct from 1 since the probability of all conceivable outcomes must add up to 1, or 100%.

Therefore, the probability of selecting an 8 is [tex]\frac{4}{52}[/tex] since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to [tex]\frac{1}{13}[/tex]. The probability of selecting a face card is [tex]\frac{12}{52}[/tex] since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to [tex]\frac{3}{13}[/tex]. the probability of NOT selecting a face card has to be 1 - [tex]\frac{3}{13}[/tex] = [tex]\frac{13}{13}[/tex] - [tex]\frac{3}{13}[/tex] =[tex]\frac{10}{13}[/tex].

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3) The value of function is,  cos² θ

4) The value of function are,

⇒ cos 3π/2 = - 1

⇒ sin 5π/3 = - √3/2

5) The value of k is, 4.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

3) The function is,

⇒ sin θ cos θ / tan θ

Simplify as;

⇒ sin θ cos θ / (sin θ / cos θ)

⇒ cos² θ

4) The value of function are,

⇒ cos 3π/2 = cos (π + π/2)

                  = - cos (π/2)

                  = - 1

⇒ sin 5π/3 = sin (2π - π/3)

                 = - sin π/3

                 = - √3/2

5) The expression is,

⇒ √(2k² + 17) - x = 0

⇒ √2k² + 17 = x

Square both side,

⇒ 2k² + 17 = x²

Substitute x = 7;

⇒ 2k² + 17 = 7²

⇒ 2k² + 17 = 49

⇒ 2k² = 49 - 17

⇒ 2k² = 32

⇒ k² = 16

⇒ k = 4

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The solution for each system of equations is given as follows:

1. (-2,-2).

2. (4,1).

When a system of equations is plotted on graph, the solutions are the intersection points of all the functions that compose the system.

For the first system, the graphs intersect at a x-coordinate of -2 and an y-coordinate of -2, hence the coordinates are given as follows:

(-2,-2).

For the first system, the graphs intersect at a x-coordinate of 4 and an y-coordinate of 1, hence the coordinates are given as follows:

(4,1).

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Answer:

The oldest is 60 years olds.

Step-by-step explanation:

a+b+c+d+e=211

a=3e

b=a-2

c=2e

d=e-3

3e+3e-2+2e+e-3+e-6=211

10e-5=211

211-11=10e

200=10e

e=20

Therefore , the solution of the given problem of linear equation comes out to be monthly amount she applies to it is $550.

Using the formula y=mx+b, a simple regression curve is constructed. The slope is B, and the y-intercept is m. Even if y or y are separate portions, the foregoing sentence is frequently referred to as a "mathematical formula merging many variables." In bivariate linear equations, there are only two variables. Application problems involving linear equations have no known solutions.

Here,

Given :

=> $150 extra in her debt

her debt be x

y be the amount she already pays

=> amount left

=> x - y - 150

=> x- (y+150)

Let x be 1000

y be 300

=> 1000 -(300+150)

=> 1000 -450 = 550

Thus,

monthly amount she applies to it is $550

Therefore , the solution of the given problem of linear equation comes out to be monthly amount she applies to it is $550.

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Answer:

356 i think this is it sorry if its not

Step-by-step explanation:

Answer:

356

Step-by-step explanation:

2 + 2 +2 x2 x2 x2 2x 2 = 356

The correct selling price of an item will be $12.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a  store is instructed by corporate headquarters to put a markup of ​25% on all items. An item costing ​$24 is displayed by the store manager at a selling price of ​$6.

The selling price will be calculated as:-

Selling price = 25% of 24 + $6

Selling price = 6 + 6

Selling price = $12

Hence, the selling price of the item is $12.

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The solution to 2log9(x)=log9+ log9(x-2) is 4.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 2log9(x)=log^9(8)+log9(x-2)

Above equation can be written as below

Log₉x² = log₉8 + log₉(x-2)

Loga+Logb=Log ab from properties of logarithms

Log₉x² = log₉(8×(x-2))

Log₉x² = log₉8x-16

Log₉x² - log₉8x-16 = 0

Loga-logb=log(a/b)

Log₉(x²/(8x-16)) = 0

x²/(8x-16) = 9°

x² = 1 × 8x-16

x²-8x+16 = 0

x²-4x-4x+16 = 0

(x-4)(x-4) =0

x=4

Hence,  the solution to 2log9(x)=log9+ log9(x-2) is 4.

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Answer:

X= ( 14,0)

Y= (0, -2)

The supplementary angles are (a) >AFC and >CFB

The complete question is added as an attachment

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

The figure

As a general rule, supplementary angles are angles that add up to 180 degrees

From the attached figure, we have

AFC + CFB = 180 degrees

This means that these angles are supplementary angles

Hence, the supplementary angles are (a) >AFC and >CFB

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Mean of the set of numbers = 23

Median of the set of numbers = 23

Mode of the set of numbers = 16, 19, 23, 26, 31

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This is what is most often meant by an average. The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Given numbers,

26, 31, 19, 23, 16

Putting in Ascending order

16, 19, 23, 26, 31

No. of elements N = 5

Mean = (26 + 31 + 19 + 23 + 16)/5

Mean = 115/5

Mean = 23

Since N = 5 (Odd)

Median = (N+1)/2th term

            = (5+1)/2th term

            = 6/2th term

            = 3rd term

            = 23

Every element has same frequency,

Mode = 16, 19, 23, 26, 31

Hence, Mean = 23, Median = 23 and Mode = 16, 19, 23, 26, 31

of the set of the numbers.

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The value of 'z' in the equation [tex]25^{(z + 4)} = 125[/tex] is, z = - 2.5.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An exponential equation [tex]25^{(z + 4)} = 125[/tex].

We know, 5² = 25 and 5³ = 125.

Therefore, [tex](5^2)^{(z + 4)} = 5^3[/tex] , Having the same base we can equate the exponents.

2(z + 4) = 3.

2z + 8 = 3.

2z = - 8 + 3.

2z = - 5.

z = - 2.5.

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The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the level of significance.

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is known as the level of significance. The level of significance (α) is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. This is calculated by subtracting the confidence level from 1. For example, if the confidence level is 95%, then the level of significance is 1-0.95 = 0.05. This means there is a 5% chance of making a Type I error.

The confidence level is the probability that the interval will contain the actual value of the population parameter. It is calculated by 1 minus the level of significance. For example, if the level of significance is 0.05, then the confidence level is 1-0.05 = 0.95, which is 95%. This means there is a 95% chance that the interval will contain the actual value of the population parameter.

The confidence coefficient is the width of the interval, which is calculated by subtracting the lower bound from the upper bound of the interval.

The error factor is the difference between the estimated parameter value and the actual parameter value, which is calculated by subtracting the estimated parameter value from the actual parameter value.

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the level of significance.

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The shipping charge of an item on the purchase $56 would be $2.52.

We are Given that, a company charges a shipping fee that is 4.5% of the purchase price for all items at ships.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

The Cost of an item =$56

So, shipping fee = 4.5% of 56

Therefore, we have

= 4.5/100 × 56

= 0.045 × 56

= $2.52

Hence, the shipping charge of an item is $2.52.

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a. The probability that die 1 beats die 2 is 1/4\

b. The probability that die 2 beats die 3 is 2/4 or 1/2

c.  The probability that die 3 beats die 1 is 1/4.

Nothing strange occurred because the probabilities found are all based on the number of sides of each die and their values, which followed the expected outcome for any fair dice.

Probability is described as the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

The probability that die 1 beats die 2 is 1/4 because  die 1 has three sides with the value of 3, and die 2 has only one side with a value which is greater than 3. Hence  there is a 1 in 4 chance that the result of rolling die 1 will be greater than the result of rolling die 2.

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The required value of the x in the given circle is given as,
5. x = 9   6. x = 4  7. x = 5  8. x = 8

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
5.
For the given circle,
The sum of all sections should be equal to 360°.
65 + 34 + 41 + 16 +6x + 150 = 360
x = 9

Similarly,
6. x = 4
7. x = 5
8. x = 8

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The sample mean is 358.54, and the sample median is 365. To keep the median unchanged, we could increase or decrease the largest value by up to 49 seconds. The values of mean and the median in minutes are 5.97 and 6.08.

The sample mean can be calculated as follows:

mean = (sum of all observations) / (number of observations)

mean = (373 + 370 + 364 + 366 + 364 + 325 + 339 + 393 + 356 + 359 + 363 + 375 + 424 + 325 + 394 + 402 + 392 + 369 + 374 + 359 + 356 + 403 + 334 + 397) / 26

mean = 358.54

The median can be calculated by arranging the observations in order and finding the middle value. With 26 observations, we'll find the average of the two middle values.

median = (364 + 366) / 2 = 365

To keep the median unchanged, we need to maintain the same number of observations on either side of the median. In this case, with 26 observations, there are 13 observations on either side of the median. To keep the median unchanged, we need to keep the range of the data the same, which means the difference between the maximum and minimum values should remain the same.

The range of the data is 424 - 325 = 99 seconds.

So, to keep the range the same, the largest value could be increased or decreased by up to half of the range, which is:

99 seconds / 2 = 49 seconds.

To express the observations in minutes, we'll divide each observation by 60.

mean in minutes = 358.54 / 60 = 5.97

median in minutes = 365 / 60 = 6.08

So, the values of mean and the median in minutes are 5.97 and 6.08, respectively.

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Your question is incomplete, but I suppose the question was:

"A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape: 373 370 364 366 364 325 339 393 356 359 363 375 424 325 394 402 392 369 374 359 356 403 334 397

a. Calculate the values of the sample mean and median.

b. By how much could the largest time, currently 424, be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the value of the sample median?

c. What are the values of mean and the median when the observations are re-expressed in minutes?"

The values of x are 13 and 11

Algebraic expressions are expressions having terms, variables, coefficients, constants and factors.

They are also made up of arithmetic operations.

Given that;

(x - 1)²= 50

expand the bracket

x² - x - x + 1 = 50

collect like terns

x² - 2x + 1 = 50

x² - 2x - 49

Factorize the expression

(x² - 13x) + (11x - 49)

Factor the common terms

x(x - 13) + 11(x - 13)

x = 13. x = -11

Hence, the values are 13 and 11

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a) The sample is a systematic sample., b) It may not be representative of all people in line for the roller coaster., c) The sampling frame is all the people who are willing to wait in line for the roller coaster.

a) A systematic sample is a sample where individuals are selected from a larger population at regular intervals or through a set pattern. In this case, the amusement park is selecting every 15th person in line, making it a systematic sample.

b) The sample may not be representative of the population of people in line for the roller coaster because by only including every 15th person, certain groups of people who are similar may be overrepresented or underrepresented in the sample, potentially leading to a biased representation of the opinions of the people waiting in line.

c) The sampling frame for this survey is the population of people waiting in line for the roller coaster. This is the group of individuals from which the sample will be taken. In this case, the sampling frame is not limited to just the patrons of the park, or all the people who go to amusement parks, but is specifically focused on the people waiting in line for the roller coaster.

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