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The value of ø  in the given equation ø sin(ø-30)=cosø is 60 - 2πn, where n is an integer

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can solve this equation using trigonometric identities.

We know that sin(ø - 30) = cos(90 - (ø - 30)) = cos(120 - ø).

So, the equation becomes:

cos(120 - ø) = cosø

Using the identity cos(A) = cos(B) if and only if A = ±B + 2πn, where n is an integer, we get:

120 - ø = ±ø + 2πn

Simplifying and solving for ø, we get:

ø = 60 ± 2πn

So, the solutions are:

ø = 60 + 2πn, where n is an integer or

ø = 60 - 2πn, where n is an integer

Hence, the value of ø  in the given equation ø sin(ø-30)=cosø is 60 - 2πn, where n is an integer

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Answer:

Step-by-step explanation:

The ratio of fiction books to non-fiction books is 5:2, which means that for every 5 fiction books in the library, there are 2 non-fiction books.

We know that the total number of books in the library is 1421. To figure out how many of those books are fiction, we need to divide the total by the sum of the parts in the ratio (5 + 2 = 7), and then multiply the result by the number of parts that represent fiction books (5).

So, the number of fiction books in the library is:

5/7 x 1421 = 1015

To find out how many non-fiction books there are, we can subtract the number of fiction books from the total:

1421 - 1015 = 406

Finally, to figure out how many more fiction books there are than non-fiction books, we can subtract the number of non-fiction books from the number of fiction books:

1015 - 406 = 609

Therefore, there are 609 more fiction books than non-fiction books in the library.

The derivative of composite functions are listed below:

Case A

Subcase i: y' = 4 · (x³ + 8 · x² - x + 3) · (3 · x² + 16 · x - 1)

Subcase ii: y' = (2 · x - 7)² · [(2 · x + 4) · (2 · x - 7) + 6 · (x² + 4 · x - 2)]

Case B

Subcase i: y' = 5 · (2 · x - 1 / x²) · [(2 · x - 1 / x²) + 2 · x · (2 - 2 / x³)]

Subcase ii: y' = [- (x² + 3 · x - 1) - (2 - x) · (2 · x + 3)] / (x² + 3 · x - 1)²

Chain rule is powerful resource to find the derivative of a composite function, that is, a function of the form:

f ° u (x) = f[u(x)]

And chain rule is now defined:

df[u(x)] / dx = (df / du) · (du / dx)

There are three cases requiring chain rule, now we proceed to determine the derivative for each expression:

Case A

Subcase i

y = (x³ + 8 · x² - x + 3)⁴

y' = 4 · (x³ + 8 · x² - x + 3) · (3 · x² + 16 · x - 1)

Subcase ii

y = (x² + 4 · x - 2) · (2 · x - 7)³

y' = (2 · x + 4) · (2 · x - 7)³ + 6 · (x² + 4 · x - 2) · (2 · x - 7)²

y' = (2 · x - 7)² · [(2 · x + 4) · (2 · x - 7) + 6 · (x² + 4 · x - 2)]

Case B

Subcase i

y = 5 · x · (2 · x - 1 / x²)²

y' = 5 · [(2 · x - 1 / x²)² + 2 · x · (2 · x - 1 / x²) · (2 - 2 / x³)]

y' = 5 · (2 · x - 1 / x²) · [(2 · x - 1 / x²) + 2 · x · (2 - 2 / x³)]

Subcase ii

y = (2 - x) / (x² + 3 · x - 1)

y' = [- (x² + 3 · x - 1) - (2 - x) · (2 · x + 3)] / (x² + 3 · x - 1)²

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We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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The probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb is 9/10 or 0.9 (approximately).

To calculate the probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb, we can use the complementary probability. That is, we can calculate the probability that a 23-watt bulb is obtained within the first 5 selections and then subtract this from 1 to get the probability that at least 6 bulbs must be examined.

The probability of obtaining a 23-watt bulb on the first selection is 1/50. If a 23-watt bulb is not obtained on the first selection, the probability of obtaining one on the second selection is 49/50 x 1/49 = 1/50.

Similarly, the probability of obtaining a 23-watt bulb on the third, fourth, or fifth selection is also 1/50.

Therefore, the probability of obtaining a 23-watt bulb within the first 5 selections is:

P(23-watt bulb in first 5 selections) = P(23-watt bulb on first selection) + P(23-watt bulb on second selection) + P(23-watt bulb on third selection) + P(23-watt bulb on fourth selection) + P(23-watt bulb on fifth selection)

= 1/50 + 1/50 + 1/50 + 1/50 + 1/50

= 1/10

The probability of needing to examine at least 6 bulbs before obtaining a 23-watt bulb is therefore:

P(need to examine at least 6 bulbs) = 1 - P(23-watt bulb in first 5 selections)

= 1 - 1/10

= 9/10

Therefore, the probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb is 9/10 or 0.9 (approximately).

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The intercepts of the parabola are A ( 6 , 0 ) and B ( -2 , 0 ) and the y intercept of the parabola is ( 0 , -12 )

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the equation of the parabola be represented as A

Now , the value of A is

y = x² - 4x - 12   be equation (1)

On simplifying , we get

when y = 0

x² - 4x - 12 = 0

On factorizing the quadratic equation , we get

x² - 6x + 2x - 12 = 0

( x + 2 ) ( x - 6 ) = 0

So , the two values of x are

when ( x + 2 ) = 0

x = -2

And , when ( x - 6 ) = 0

x = 6

So , the x intercepts of the parabola are A ( 6 , 0 ) and B ( -2 , 0 )

The y intercept is when x = 0

So , y = 0 - 0 - 12

y = -12

And , the y intercepts of the parabola are ( 0 , -12 )

Hence , the intercepts of the parabola are solved

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So, in response to the above question, we can state that Due to the use equation of two partial products, 10 x 18 and 2 x 18, Tom is accurate that 12 x 18 equals 216.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Tom is accurate;  

Using partial products, where one of the numbers is divided into smaller pieces and each piece is multiplied by the other number, is an alternate approach. The ultimate result is then calculated by adding the products.

In this instance, Tom has divided 12 into 10 + 2 and is independently multiplying each portion by 18.

10 x 18 = 180

2 x 18 = 36

We only need to combine the two partial products to obtain the outcome:

180 + 36 = 216

Due to the use of two partial products, 10 x 18 and 2 x 18, Tom is accurate that 12 x 18 equals 216.

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Answer:

Step-by-step explanation:

is -2(-12y+5)+4=8(3y+2)-22 a conditional equation an identity or a contradiction

-2(-12y + 5) + 4 - 8(3y - 2) + 22 = 0

24y - 10 + 4 - 24y - 16 + 22 = 0

-6 - 16 + 22

- 22 + 22 = 0

0 = 0   (All real numbers are solutions.)

Answer:

6

Step-by-step explanation:

to be very honest I'm not very good at mathematics but Im here to learn

Answer:

A commonly used fraction that helps you understand a different size or amount is called a ratio.

Step-by-step explanation:

A ratio is a comparison of two or more quantities or measurements, expressed as a fraction or a colon. Ratios are commonly used to express the relationship between different amounts or sizes, and they can be used to help solve problems involving proportions, rates, and percentages. For example, if you are making a recipe that calls for two cups of flour and one cup of sugar, the ratio of flour to sugar is 2:1, or 2/1. Ratios can also be expressed in decimal or percentage form!

In a case whereby teacher gave a reading test to a class of 5th grade students and computed the mean, median, and mode for the test scores. the statements that cannot be an accurate description of the scores is b. The majority of the students had scores above the median.

A data set's mean is its average. The most frequent value in a data set is called the mode. The centre of the group of numbers is known as the median, which implies that the since there could majority of the students had scores above the mode, but ion the case of median, since it is value in the middle of a data set then majority of the the students  can not scores above the median.

The midway number in a set of data is known as the median. The data should first be arranged and ranked from smallest to greatest. Divide the total number of observations by two to get the midway value. The value in that location is the median if there are an odd number of observations; otherwise, round the number up.

Therefore, option B is correct.

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Answer:

To solve this system using elimination, we can add the two equations together to eliminate the y variable:

(5x + 6y) + (10x - 6y) = 26 - 2

Simplifying this equation gives:

15x = 24

Dividing both sides by 15 gives:

x = 24/15 = 8/5

We can substitute this value of x into either of the original equations to solve for y. Let's use the first equation:

5x + 6y = 26

Substituting x = 8/5 gives:

5(8/5) + 6y = 26

Simplifying this equation gives:

y = (26 - 8)/6 = 3

Therefore, the solution to the system is x = 8/5 and y = 3.

The 90% confidence interval for the mean number of books people read is (-16, 38.6).

To construct a 90% confidence interval for the mean number of books people read, we first need to find the critical value (z*) that corresponds to a 90% confidence level. This can be found using a z-table or calculator. The critical value for a 90% confidence level is 1.645.

Next, we need to calculate the margin of error (ME) using the formula ME = z* x SE, where SE is the standard error. In this case, SE = 16.6 books, so ME = 1.645 x 16.6 = 27.3 books.

Finally, we can construct the 90% confidence interval by adding and subtracting the margin of error from the sample mean (x overbar). The confidence interval is:

(x overbar - ME, x overbar + ME) = (11.3 - 27.3, 11.3 + 27.3) = (-16, 38.6)

This means that we are 90% confident that the true mean number of books people read is between -16 and 38.6 books.

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The given algebraic expression (24 - 12w) is equivalent to

6(4 - 2w).

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

4x + 5z

Given is the algebraic expression as -

24 - 12w

We can rewrite the expression above as -

24 - 12w

24 - 12w = 6 x 4 - 6 x 2w

24 - 12w = 6(4 - 2w)

Therefore, the given algebraic expression (24 - 12w) is equivalent to

6(4 - 2w).

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The equivalent expression to -24 - 12w is -6 (4 + 2w).

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

An absolute numerical number is referred to as a constant.

Variable: A symbol without a set value is referred to as a variable.

Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.

Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.

Given:

We have the Expression as -24 - 12w.

So, Prime factorizing

24 = 2 x 2 x 2 x 3

12 = 2 x 2 x 3

So, -24 - 12w.

= - (2 x 2 x 2 x 3) - (2 x 2 x 3)w

= -2  x 3 ( 2 x 2 + 2w)

= -6 (4 + 2w)

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Answer:

Step-by-step explanation:

To find the zeros of F(x), we need to solve the equation F(x) = 0.

F(x) = x^2(x^2+18x+81)

The expression F(x) can be factored as:

F(x) = x^2(x+9)^2

So, the zeros of F(x) are x = 0 and x = -9, with a multiplicity of 2 for both.

The factor x^2 contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = 0 but does not cross it. The factor (x+9)^2 also contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = -9 but does not cross it.

To summarize, the zeros and their multiplicities for F(x) are:

x = 0 (multiplicity 2)

x = -9 (multiplicity 2)

The force exerted by the prism on the floor 245 N.

The physical force applied to an object is referred to as pressure. Per unit area, a perpendicular force is delivered to the surface of the objects. F/A is the fundamental formula for pressure (Force per unit area). Pascals are a unit of pressure (Pa).

Given:

height = 4 m, volume = 28 m³

Pressure = 75 N/m²

Now, Volume of prism = Area of base x height

                              28     = Аrеа х 4

                                Area = 28/4 = 7 m²

Also, Pressure = force / Area

35 = force / 7

Force = 35 x 7

Force = 245 N

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The area of the isosceles trapezoid is 281.25 square cm.

Let's denote the length of the base of the trapezoid as "b".

According to the problem statement, the length of each of the equal sides is one-half the length of the base, which means each equal side has length b/2.

The height of the trapezoid is given as one-fourth the length of the base, so we can write it as h = b/4.

To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

The two parallel sides of length b each contribute b to the perimeter, while the other two sides of length b/2 contribute a total of b to the perimeter.

Therefore, we can write:

Perimeter = 2b + 2(b/2) = 3b

We know that the perimeter of the trapezoid is 45 cm, so we can set up an equation:

3b = 45

Solving for b, we get:

b = 15

Now we can use the formula for the area of a trapezoid to find the area of this isosceles trapezoid. The formula is:

Area = (1/2)h(b1 + b2)

where h is the height, b1 and b2 are the lengths of the two parallel sides. In this case, b1 and b2 are both equal to b (since it's an isosceles trapezoid), and h = b/4.

Substituting these values, we get:

Area = (1/2)(b/4)(b + b) = (1/2)(b/4)(2b) = b^2/8

Substituting b = 15, we get:

Area = 15^2/8 = 281.25 sq cm

Therefore, the area of the isosceles trapezoid is 281.25 square cm.

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In an isosceles trapezoid, the length of the equal sides is one-half the length of the base, while the height is one-fourth the length of the base. If the perimeter of the trapezoid is 45 cm.

Find the areae

The missing side of the prism measures 56 units.

Here we can see that the front face is a triangle with a base of 8 units and a height of 15 units. And x is the length perpendicular to that face, then the volume of the prism is:

V = (15)*(8)*x/2

We know that V = 3,360 cubic units, then:

3,360  = (15)*(8)*x/2

3,360 = 60*x

3,360/60 = x

56 = x

The missing side measures 56 units.

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Answer:

Step-by-step explanation:

We can use proportionality to find out how much Gino will get paid if he has to plow for 40 hours. Since we know that he gets paid $640 for 20 hours of work, we can set up a proportion to find out how much he will get paid for 40 hours of work.

The proportion can be written as:

Payment for 20 hours / 20 hours = Payment for 40 hours / 40 hours

We can simplify this proportion to:

Payment for 20 hours / 20 = Payment for 40 hours / 40

Substituting the given values, we get:

640 / 20 = Payment for 40 hours / 40

Simplifying this equation, we get:

32 = Payment for 40 hours / 40

Multiplying both sides by 40, we get:

Payment for 40 hours = 32 * 40

Payment for 40 hours = 1280

Therefore, Gino will get paid $1,280 if he has to plow for 40 hours. Hence, the correct answer is (D) $1,280.

Answer:

1.280$

because 20hrs=640 so If it's 40hrs it will add additional 640

Statements B , D and E are True.

Statements A and C are False.

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

A. Prism A and C have the same volume. - False

The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.

B. Prism B has a greater volume than Prism C. - True

The volume of Prism B is 8 x 4 x 3 = 96 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.

C. Prism B has the least volume. - False

The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, which is greater than the volume of Prism B.

D. The volume of Prism A is 120 cubic centimeters. - True

As calculated above, the volume of Prism A is 120 cubic cm.

E. The volume of Prism C is less than the volume of Prism A. - True

As calculated above, the volume of Prism C is 105 cubic cm, which is less than the volume of Prism A.

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The collection, description, analysis, and drawing of conclusions from quantitative data are all included in the area of statistics, which is a branch of applied mathematics. Probability theory, linear algebra, and calculus of differential and integrals are some of the core mathematical concepts in statistics.

Descriptive statistics were used in the statement.

Descriptive statistics is a branch of statistics that deals with the collection, presentation, and summary of data. It is used to describe and summarize the main features of a data set, such as measures of central tendency (e.g., mean, median, mode) and measures of dispersion (e.g., range, variance, standard deviation).

In this case, the statement is simply reporting a single value, the average credit card debt for college students in 2008. This is an example of a descriptive statistic because it is a summary measure that describes a characteristic of the population or sample under study.

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Descriptive statistics were used in the statement.

Descriptive statistics is a branch οf statistics that deals with the analysis, descriptiοn, and summarizatiοn οf data. It invοlves the use οf variοus statistical measures, such as measures οf central tendency (mean, median, and mοde), measures οf dispersiοn (standard deviatiοn, variance, range), and graphical representatiοns (histοgrams, bοx plοts, scatter plοts, etc.) tο describe the features οf a dataset.

Descriptive statistics were used in the statement. The statement is simply describing the average credit card debt fοr cοllege students in 2008. Descriptive statistics are used tο describe οr summarize a dataset οr pοpulatiοn, while inferential statistics are used tο draw cοnclusiοns οr make predictiοns abοut a larger pοpulatiοn based οn a sample οf data. Since the statement οnly prοvides infοrmatiοn abοut a specific grοup οf cοllege students in 2008, it dοes nοt invοlve making any inferences οr predictiοns beyοnd this grοup.

Hence, Descriptive statistics were used in the statement.

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So the linear model that describes the growth of the organism over the 5 hour period is: y = 6x + 16, where x is the number of hours and y is the weight of the organism in mg.

A linear model is a mathematical equation that describes a linear relationship between two or more variables. In other words, it is a model that assumes that the relationship between the variables can be represented by a straight line. Linear models are commonly used in various fields, including economics, finance, engineering, and science, to analyze and predict the relationship between variables. They are particularly useful when analyzing data that shows a linear trend, or when making predictions based on historical data. Linear models can be simple or multiple, depending on the number of independent variables involved. They can also be adjusted to fit nonlinear data by transforming the variables or using a different model altogether.

Here,

To find a linear model that describes the growth of the organism over time, we need to determine the rate of growth (change in weight per unit time) and the initial weight.

The rate of growth can be found by taking the difference between the final weight and the initial weight and dividing by the time period:

Rate of growth = (final weight - initial weight) / time period

= (46 mg - 16 mg) / 5 hours

= 6 mg/hour

So the organism is growing at a rate of 6 mg per hour.

The initial weight of the organism is given as 16 mg.

Now we can write the equation of the line as:

y = mx + b

where y is the weight of the organism in mg, x is the time in hours, m is the rate of growth in mg/hour, and b is the initial weight in mg.

Substituting the values we found, we get:

y = 6x + 16

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The value of the variable(s) in the figure is  60°, explaination is given below.

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that function at those values of the considered variables.

We are given that;

The variables; (5y)⁰,(2x)°,120⁰,1080

Now,

The first two expressions are both equal to 1, because any number raised to the power of 0 is always 1.

The third expression, 120°, is an angle measurement in degrees. In a triangle, the sum of the interior angles is always 180°. So, if we let x and y be the other two angles in the triangle, we have:

x + y + 120° = 180°

Simplifying this equation, we get:

x + y = 60°

Therefore, the answer of the given function will be  60°.

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The length of side x is approximately 9.05 cm.

What is law of sines ?

The Law of Sines, also known as the Sine Rule, is a formula used to find unknown angles or sides of a triangle, given some combination of angle and side measurements. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Mathematically, the Law of Sines can be expressed as follows:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides, respectively.

Given by the question:

To find x, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.

Let's use the sine function to find the length of side AB:

sin A / AB = sin C / BC

sin 45 / x = sin 40 / 12

Rearranging and solving for x:

x = sin 45 * 12 / sin 40

x ≈ 9.05 cm

Therefore, the length of side x is approximately 9.05 cm.

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The given function can also be represented as,

[tex]f(x) =3x^2+6x-24[/tex]  

and

[tex]f(x) =3(x+4)(x-2)[/tex]

A relationship between several inputs and outputs is called a function. Simply described, a function is a relation between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for each function. A function is usually referred to as f(x), where x is the input . Typically, a function is written as y = f. (x).

Given function is ,

[tex]f(x) =3(x+1)^2-27[/tex]

This function can also be expressed as,

[tex]f(x) =3(x+1)^2-27\\\\f(x) =3(x^2+1+2x)-27\\\\f(x) =3x^2+3+6x-27\\\\f(x) =3x^2+6x-24\\\\f(x) =3(x^2+2x-8)\\\\f(x) =3(x^2+(4-2)x-8)\\\\f(x) =3(x^2+4x-2x-8)\\\\f(x) =3(x+4)(x-2)[/tex]

So, the given function can also be stated as,

[tex]f(x) =3x^2+6x-24[/tex]  

and

[tex]f(x) =3(x+4)(x-2)[/tex]

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The Mean Value Theorem states that if a function f is continuous on the interval [a,b] and differentiable on (a,b), then there exists at least one c in the interval (a,b) such that


f'(c) = (f(b) - f(a)) / (b - a)

For the function f(x) = x/x+2, we can set
f(a) = a/a+2 and f(b) = b/b+2

Therefore, the equation we need to solve is:
(b/b+2 - a/a+2) / (b - a) = c/(c+2)

After rearranging, we get:
(b-a)c + 2(a-b) = 0

Solving this, we find that c = 2(b-a) / (a-b)

Therefore, the values of c that satisfy the Mean Value Theorem for the given function f(x) = x/x+2 are c = 2(b-a) / (a-b).

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Answer:

y= -6x+5

y= 2x+(-5)

Step-by-step explanation:

This is the equation of the line in point-slope form.
y - 5 = (-5/4)(x + 6)

The equation in slope-intercept form is y = (-5/4)x - 5/4.

And So the equation in standard form is 5x + 4y = -5.

Answer:

A.35°, 114°, 31°.

B.61°,119°,153°,27° and 92°

A. alternates angles are equal;

35°=35°

Vertically opposites angles are equal;

114°=114°

Sum of interior angles of a triangle is 180;

114+35+x=180

x=180-(114+35)

x=31

Picture B.

Corresponding angles are equal;

61°=61°

Sum of angles on a straight line is 180°

61+x=180

x=180-61

x=119°

Corresponding angles are equal;

153°=153°

Sum of angle on straight line is 180;

153+x=180

x=180-153

x=27

Sum of interior angle of a triangle is 180;

27+61+X=180

x=180-(27+61)

x=92

The probability the card is a diamond or a face card is [tex]\frac{11}{26}[/tex].

Probability refers to the likelihood that any random occurrence will occur. This expression refers to estimating the probability that any specific event will take place. For example, when we throw a coin into the air. Possibility: P(A) = f / N, determines the likelihood that an event will occur. Although probability and ratios are linked, the former dictates the latter. The probability of an occurrence must be known before determining its probability.

When we find the probability, we obtain:

There are 52 cards in a standard deck of cards.As there are four suits, there are 12 face cards, which we identify as the Kings, Queens, and Jacks. There are 13 diamonds total, 3 of which are face cards that have previously been counted. There are thus 10 diamonds without faces.

Out of the 52 cards in the deck, 10 diamonds plus 12 face cards equal 22.

P= [tex]\frac{22}{52}[/tex]= [tex]\frac{11}{26}[/tex].

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