can you please solve this its urgent

The simplified expression is: cos(13π/35)

Trigonometry is a branch of mathematics that studies the relationships between angles and the sides of triangles. It deals with functions such as sine, cosine, and tangent and their inverses, and is used extensively in fields such as engineering, physics, and astronomy.

We can simplify the given expression using the identity:

cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

We can rewrite the given expression as:

cos(4π/7) cos(π/5) - sin(4π/7) sin(π/5)

= cos(4π/7 - π/5) [using the identity]

To simplify further, we can find a common denominator for 4/7 and 1/5:

4/7 = 20/35 and 1/5 = 7/35

Then, we can write:

4π/7 - π/5 = (20π/35) - (7π/35) = 13π/35

This expression cannot be further simplified using trigonometric identities, and is written only in terms of the cosine function.

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Answer:

b

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Okay, so what you need to do is plug in the 5 for x in all equations. once you do that, then you’ll see if the statement makes sense.

A would be= 2 + 5 = 3 and that would be 7=3 which it doesn’t

B would be 3(5)=15 and that would be 15=15

C would be 5/2=10 and thats not true because that would be 2.5=10

And lastly D would be 5-7=12 and that's nit true because that would be -2=12 and that's not true

√49 is a perfect square and therefore rational.

√50 is also a perfect square and therefore rational.

∛127 is a non perfect cube and therefore irrational.

∛125 is rational because it is equal to a whole number.

It can be expressed as the product of two equal integers. Perfect squares are also known as 'whole squares' or 'complete squares'.

√49 is a perfect square and therefore rational.

This is because the square root of 49 can be expressed as a common fraction 7/7. The square root of 49 = 7, which is a whole number.

√50 is also a perfect square and therefore rational.

The square root of 50 can be expressed as a common fraction 5/5. The square root of 50= 5, which is a whole number.

∛127 is a non perfect cube and therefore irrational.

This is because the cube root of 127 cannot be expressed as a common fraction. The cube root of 127 = approximately 4.9, which is not a whole number.

∛125 is rational because it is equal to a whole number.

The cube root of 125 can be expressed as a common fraction 5/5. The cube root of 125 = 5, which is a whole number.

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Mary has 60/4 = 15$

Nick has 60/5 = 12$

The total amount of money that Mary and Nick have is 15$+12$ = 27$

To find out how much money Jane has, we need to subtract the total amount that Mary and Nick have from the total amount of money they have altogether:

60$ - 27$ = 33$

Therefore, Jane has 33$.

Answer: $33

Step-by-step explanation:

1/5 of $60 is 12. 1/4 of $60 is 15. 15 + 12 = 27. To find out how much money Jane has, simply subtract 60 - 27 to get $33.

We may use the trapezoid area formula to get the areas of trapezoids EJFG, FGHJ, and HJIE. The entire area of polygon EFGHIJ may then be calculated by adding these regions together.

To begin, we must determine the lengths of segments JF, JH, JE, and JI. We can get these lengths using the Pythagorean theorem: JF = (JG2 - FG2) = (122/102) = 44 = 211 cm JH = (JG2 - GH2) = (122) - 82 = √80 = 4√5 cm JE =(JF2 - EF2) =(21112 - 52) =(44 - 25) = 19 cm JI = (JH2 - IH2) = (452 - 32) = (80 - 9) = 71 cm We can now calculate the trapezoidal areas: Trapezoid area EJFG = (JE + JF) * FG / 2 = (211 + 19) * 5 / 2 = 511 + 519 cm2 Trapezoid area FGHJ = (FG + GH + JF) + JH) * HJ / 2 = (10 + 8 + 211 + 45) * 12 / 2 = 120 + 1211 + 245. HJIE = (JI + JE + IH + HE) trapezoid area * JH / 2 = (√71 + √19 + 3 + 3) * 4√5 / 2 = 10√5 + 2√71 cm^2 Lastly, we may sum these areas to calculate the total area of polygon EFGHIJ: E = trapezoid area EJFG + trapezoid area FGHJ + trapezoid area HJIE E = (5√11 + 5√19) + (120 + 12√11 + 24√5) + (10√5 + 2√71) E = 5√11 + 5√19 + 120 + 12√11 + 24√5 + 10√5 + 2√71 E = 120 + 15√11 + 34√5 + 15√19 + 2√71 E ≈ 372.9 cm^2 As a result, the area of polygon EFGHIJ is 372.9 square centimeters.

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Answer: 15x-2 (answer A)

Step-by-step explanation:

To find the total travel time, we need to add the time it takes to travel in the morning and the time it takes to travel in the evening:

Total travel time = (3x - 10) + (12x + 8)

Simplifying the expression by combining like terms, we get:

Total travel time = 15x - 2

Therefore, the total travel time is 15x - 2. So, the answer is (a) 15x - 2.

Answer:

Step-by-step explanation:

The expression 3x − 10 represents the time it takes a commuter to travel in the morning to work. The expression 12x + 8 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?

15x − 2

9x − 2

15x + 2

9x + 2

 the answer is (a) 15x-2 hope that helps :)

Answer:

Helmet = 29, Bell = 10, Lock = 24

Answer:

sin x = d/e, cos x = f/e, tan x = d/f

Step-by-step explanation:

We will use trigonometry and SOH CAH TOA for this problem.

sin x = (opposite/ hypotenuse)

sin x = d/e

cos x = (adjacent / hypotenuse)

cos x = f/e

tan x = (opposite/adjacent)

tan x = d/f

Answer:

C. The areas of the shaded regions are equal

Step-by-step explanation:

The area of a circle of radius r = πr²

The area of the shaded region in the left figure
= Area of outer circle - Area of inner circle
= π(AC)² - π(AB)²

Since RT = AC and RS = AB, substituting for AC and AB gives us
π(AC)² - π(AB)² = π(RT)² - π(RS)²

The expression on the right is the area of the shaded region in the left circle

So the shaded regions of both figures have the same area

Answer
C. The areas of the shaded regions are equal

The graph of inequalities are attached accordingly.

Graphs of inequalities are visual representations of solutions to inequality equations.

These graphs consist of shaded regions on a coordinate plane that indicate all the points that satisfy a given inequality. In real life, graphs of inequalities are used in many areas, including business, finance, and science.

For example, a company may use a graph of inequalities to determine the feasible production and pricing strategies that will maximize profits. Similarly, a biologist may use a graph of inequalities to analyze the optimal conditions for the growth of a particular species. The graphs of inequalities provide a quick and easy way to understand and visualize complex mathematical relationships.

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Answer:

We can use the double angle identity for sine to find sin2θ:

sin2θ = 2sinθcosθ

Since cosθ = √10/8 and 3π/2 < θ < 2π, we know that θ is in the fourth quadrant, where sine is negative. We can use the Pythagorean identity to find the value of sinθ:

sin²θ + cos²θ = 1

sin²θ = 1 - cos²θ

sinθ = -√(1 - cos²θ)

Substituting the value of cosθ, we get:

sinθ = -√(1 - (√10/8)²) = -√(1 - 5/16) = -√(11/16) = -√11/4

Now we can plug in the values of sinθ and cosθ into the double angle identity for sine:

sin2θ = 2sinθcosθ = 2(-√11/4)(√10/8) = -√110/16 = -√(11/4)(10/16) = -√(55/8)

Therefore, sin2θ = -√55/8 when cosθ = √10/8 and 3π/2 < θ < 2π.

The solution of the given problem of expressions comes out to be  ⁶√x⁷*∛x² = [tex]x^{(11/6)[/tex].

Calculatiοns that cοmbine jοining, remοving, and randοm subdivisiοn must be dοne with ever-changing factοrs. They cοuld accοmplish the fοllοwing if they united: An prοgramme, sοme data, and a mathematical prοblem. Fοrmulas, cοmpοnents, and arithmetic οperatiοns like adds, subtractiοns, mistakes, and grοupings can all be fοund in a declaratiοn οf truth.

Here,

Using rational exponents, it is possible to formulate the expression 6x7*x2 more concisely:

=> ⁶√x⁷*∛x² = [tex]x^{(7/6)} \times x^{(2/3)[/tex]

Now, we can include the exponents to further simplify:

=> [tex]x^{(7/6)} * x^{2/3)} = x^{(7/6 + 2/3)[/tex]

We can add 3 and 6 to discover a common denominator of 18 for the numbers 6 and 3. Then, we could type:

=> [tex]x^{(7/6 + 2/3)} = x^{(21/18 + 12/18)}[/tex]

We can now multiply the exponents:

=> [tex]x^{(21/18 + 12/18)} = x^{(33/18)[/tex]

Further reducing the exponent, we can write:

=> [tex]x^{(33/18) }= x^{(11/6)[/tex]

Therefore, in simplified version, ⁶√x⁷*∛x² = [tex]x^{(11/6)[/tex].

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The answers to each question are:

(a) a1 = 3, a2 = 5, a4 = 17 are prime numbers.

(b)  9 is not a prime number,

What are the prime numbers?

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, it can only be divided evenly by 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and so on.

(a) [tex]a_{k} = 2 ^ k + 1[/tex]

[tex]a_{1} = 2^1 + 1 = 3[/tex]

[tex]a_{2} = 2 ^ 2 + 1 = 5[/tex]

[tex]a_{4} = 2 ^ 4 + 1 = 17[/tex]

a1, a2, a4 are prime numbers.

(b) We know when k = 3 an [tex]a_{3} = 2 ^ 3 + 1 = 9[/tex].

9 is not a prime number, it can be divide by 3 * 3 so the Sequence does not always produce a prime number.

Hence, the answers to each question are:

(a) a1 = 3, a2 = 5, a4 = 17 are prime numbers.

(b)  9 is not a prime number,

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Complete question:

It is suggested that the sequence [tex]a_{k} = 2 ^ k + 1[/tex], k...I produces only prime numbers.

(a) Show that a, a, and a, produce prime numbers.

(b) Prove by counter-example that the sequence does not always produce a prime number.

 P - 7 = J is an expression in simplest form that represents the sum of their ages.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.

                               Any mathematical statement made up of numbers, variables, and an operation between them is called an expression or an algebraic expression.

Susie is three times as older as her sister Jenny.

     3S = J

Paula is 7 years younger than Jenny.

        P - 7 = J

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -4}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(-6~~,~~-4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=-6\implies x-4=-12\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3 }{2}=-4\implies y-3=-8\implies \boxed{y=-5}[/tex]

Answer:

Step-by-step explanation:

We can use the information given to find the equation of the line that represents the relationship between the number of bean stalks and the yield. The equation of a line is typically given by the slope-intercept form, y = mx + b, where y is the dependent variable (in this case, the yield), x is the independent variable (the number of bean stalks), m is the slope, and b is the y-intercept.

To find the slope of the line, we can use the formula:

m = (Y2 - Y1) / (n2 - n1)

where (n1, Y1) and (n2, Y2) are two points on the line. We can use the two data points given in the problem to find the slope:

m = (190 - 115) / (8 - 3) = 15

To find the y-intercept, we can use the point-slope form of a line, which is:

y - Y1 = m(x - n1)

where (n1, Y1) is one of the points on the line. We can use the point (3, 115):

y - 115 = 15(x - 3)

Simplifying:

y = 15x - 20

Therefore, the equation that represents the relationship between the number of bean stalks and the yield is:

Y = 15n - 20

This equation tells us that for each additional bean stalk planted, the yield increases by 15 ounces, and the y-intercept of -20 indicates that even if no bean stalks were planted, there would still be a yield of -20 ounces (which doesn't make physical sense in this case, but is a mathematical artifact of the linear regression).

well, the error is 3.06 - 2.955 = 0.105.

now, if we take 3.06(origin amount) to be the 100%, what's  0.105 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 3.06 & 100\\ 0.105& x \end{array} \implies \cfrac{3.06}{0.105}~~=~~\cfrac{100}{x} \\\\\\ 3.06=10.5\implies x=\cfrac{10.5}{3.06}\implies x\approx 3.43[/tex]

There is a moderate negative linear relationship between x and y for the given points.

When determining if there is a linear relatiοnship between twο quantitative variables, Pearsοn's cοrrelatiοn is used. Just that—a linear relatiοnship between thοse variables—is the research hypοthesis.

[tex]\mathrm{r = (n \Sigma xy - \Sigma x\Sigma y) / \sqrt{(n\Sigma x^2- (\Sigma x)^{2)(n\Sigma y)}^2 - (\Sigma y)^2)}}[/tex]

where n is the number οf pοints, Σxy is the sum οf the prοducts οf x and y cοοrdinates, Σx is the sum οf x cοοrdinates, Σy is the sum οf y cοοrdinates, Σx² is the sum οf squares οf x cοοrdinates, and Σy² is the sum οf squares οf y cοοrdinates.

First, we need tο find these values frοm the given pοints. We can use a table tο οrganize οur calculatiοns:

x y xy x² y²

1 6 6 1 36

2 10 20 4 100

3 4 12 9 16

4 4 16 16 16

6 2 12 36 4

7    

The table continues:

|x ||y ||xy ||x² ||y² | |- |- |- |- |- | 1 6 6 1 36

|| || || || || || || || || ||

The table continues:

|x ||y ||xy ||x² ||y² | |- |- |- |- |- | 1 6 6 1 36

|| || || || ||

The table continues:

|x ||y ||xy ||x² ||y² | |- |- |- |- |- | 1 ||6 ||6 ||1 ||36 | 2 ||10 ||20 ||4 ||100 | 3 ||4 ||12 ||9 ||16 | 4 ||4 ||16 ||16 ||16 | 5||8||40||25||64| 6||2||12||36||4| 7||2||14||49||4|

Now we can add up each column to get:

Σx = 28 Σy = 36 Σxy = 120 Σx² = 140 Σy² = 240

Next, we can plug these values into the formula and simplify. Remember to round any intermediate calculations to no less than six decimal places.

r = (7(120) - (28)(36)) / √[(7(140) - [tex](28) ^{* * * * * * * * * *} (240) - (36)^ {* * *}[/tex]

r = (840 - 1008) / √[(980 - 784) (1680 - 1296)]

r = (-168) / √[196(384)]

r = (-168) / (√75264)

r = (-168) / (274.343596)

r ≈ (-0.612487)

Finally, we round our answer to three decimal places.

r ≈ -0.612

This means that there is a moderate negative linear relationship between x and y for the given points.

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Answer:

Value of y is 6

Step-by-step explanation:

Two features of a parallelogram:

1. Opposite angles are equal:

which means:
m∠L = m∠N

∴[tex]14x - 10 = 6x + 22[/tex]

Bring like terms together and make x the subject of the equation:

[tex]14x - 6x = 22 + 10[/tex]

[tex]8x = 32[/tex]

[tex]x = \frac{32}{8}[/tex]

∴x = 4

Substitute this value of x to determine the measurement of ∠N:

   m∠L = [tex]14(4) - 10[/tex]

            = 46°

∴m∠N = 46°

2. Adjacent angles are supplementary:

which means:

m∠M + m∠N = 180°

[tex](23y - 4) + 46 = 180[/tex]

Expand the parenthesis, bring like terms together and make y the subject of the equation:

[tex]23y - 4 + 46 = 180[/tex]

[tex]23y = 180 - 46 + 4[/tex]

[tex]23y = 138[/tex]

[tex]y = \frac{138}{23}[/tex]

∴y = 6

The after-tax rate of return on a taxable bond is calculated by multiplying the pre-tax yield by one minus the tax rate. In this case, it would be 9.1% x (1 - 0.21) = 7.19%. The municipal bond is tax-free, so its after-tax rate of return is equal to its pre-tax yield of 7.35%. Therefore, you should buy the municipal bond as it has a higher after-tax rate of return than the taxable bond.

The value of x in the given triangle is obtained as 4.21. The solution has been obtained by using trigonometry.

What is trigonometry?

A branch of mathematics known as trigonometry is concerned with the study of right-angle triangles, including their sides, angles, and relationships.

We are given perpendicular as 7 and base as x.

We know that tan θ is the ratio of perpendicular to base.

Here, θ = 59°

So,

⇒ Tan 59° = [tex]\frac{7}{x}[/tex]

⇒ 1.66 = [tex]\frac{7}{x}[/tex]

⇒ 1.66x = 7

⇒ x = [tex]\frac{7}{1.66}[/tex]

⇒ x = 4.21

Hence, the value of x in the given triangle is obtained as 4.21.

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a. Length of GK = [tex]\sqrt{34}[/tex]  and Length of adjacent to GK = [tex]\sqrt{34}[/tex]

b. Slope of GK = [tex]\frac{5}{3}[/tex] and Slope of adjacent to RS =  [tex]-\frac{3}{5}[/tex]

c. The parallelogram GHJK is Square.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.

Given in figure GHJK, the vertices are G(-3, 6), H(2, 3), J(-1, -2), K(-6, 1)

a. Length of line = [tex]\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}[/tex]

for points G(-3, 6) and K(-6, 1)

Length of GK = [tex]\sqrt{(-6+3)^{2} + (1-6)^{2} }[/tex] = [tex]\sqrt{34}[/tex]

Length of GK = [tex]\sqrt{34}[/tex]

Length of adjacent side (GH, KJ) to GK =  [tex]\sqrt{(2+3)^{2} + (3-6)^{2} }[/tex] = [tex]\sqrt{34}[/tex]

Length of adjacent to GK = [tex]\sqrt{34}[/tex]

b. [tex]Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}[/tex]

Slope of GK = [tex]\frac{(1 - 6)}{(-6 + 3)}[/tex] = [tex]\frac{5}{3}[/tex]

Slope of GK = [tex]\frac{5}{3}[/tex]

Slope of adjacent side to GK = [tex]\frac{3-6}{2+3}[/tex] = [tex]-\frac{3}{5}[/tex]

Slope of adjacent to RS =  [tex]-\frac{3}{5}[/tex]

c. All sides are equals to [tex]\sqrt{34}[/tex]

So, length of diagonal GJ = [tex]\sqrt{({-3+1))^{2} } + ({6+2})^{2}} = \sqrt{68}[/tex]

and length of diagonal HK = [tex]\sqrt{({2+6))^{2} } + ({3-1})^{2}} = \sqrt{68}[/tex]

All sides and diagonals are equal then parallelogram GHJK is Square.

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Answer: Let's assume that the cost to make one item of clothing is directly proportional to the number of hours it takes to make it. We can use the equation:

Cost = k * Hours

where "Cost" is the cost to make one item of clothing, "Hours" is the number of hours it takes to make one item of clothing, and "k" is the proportionality constant that relates the cost to the number of hours.

In other words, if it takes x hours to make one item of clothing, then the cost to make one item is:

Cost = k * x

The value of k will depend on factors such as the cost of materials, the wages of the workers, and other expenses involved in the production process. The value of k can be determined based on the actual cost and number of hours for a particular item of clothing.

Step-by-step explanation:

I'm pretty sure that this is correct I'm sorry I tried my best

By answering the presented question, we may conclude that Thus function  f(x) = y = (5, 7, 1, 4, 9, 5, 3, 2) and x = (3, 8, 9, 13, 10, 6, 5, 4).

Mathematicians examine numbers and their variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "function" refers to the relationship between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible functions are on functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions.

A. Assume f(x) = (4x - 7). To obtain the inverse of f(x), we must swap x and y in the function and solve for y.

As a result, g(x) = (x + 7)/4 is the inverse of f(x).

B. We must demonstrate that f(g(x)) = x for any x in g's domain.

f(g(x)) = f((x + 7)/4) = 4((x + 7)/4) - 7 = x + 7 - 7 = x + 7 - 7 = x.

As a result, f(g(x)) = x, confirming that g(x) is really the inverse of f. (x).

C. Assuming the function:

| x | 5 8 9 13 10 6 5 4 |\s|—-|—-|—-|—-|—-|—-|—-|—-|\s| f(x) | 3 7 1 4 9 5 3 2 |

Thus f(x) = y = (5, 7, 1, 4, 9, 5, 3, 2) and x = (3, 8, 9, 13, 10, 6, 5, 4).

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Answer:

251 - 77 = 174

Therefore, the range of this sample data is 174.

Step-by-step explanation:

Answer:

Step-by-step explanation:

D) All interior angles are right angles.

To prove that a polygon is a rectangle, you must show that all of its interior angles are right angles. The other properties listed may be true for certain types of rectangles, but they are not sufficient to prove that a polygon is a rectangle.

Therefοre, οnly the cοmparisοns (A and C) are true.

In mathematics, a cοmparisοn is a statement that describes the relatiοnship between twο quantities οr expressiοns. Cοmparisοns can be used tο determine if twο values are equal, if οne value is greater than οr less than anοther value, οr if twο values are prοpοrtiοnal tο each οther.

A. 3.2 > 0.32

This cοmparisοn is true. 3.2 is greater than 0.32 because 3.2 has a whοle number value οf 3, which is greater than the whοle number value οf 0 in 0.32.

B. 4.7 < 4.70

This cοmparisοn is false. 4.7 is nοt less than 4.70 because the extra zerο in 4.70 dοes nοt change its value, and .7 is nοt less than .70.

C. 2.6 > 2.59

This cοmparisοn is true. 2.6 is greater than 2.59 because the extra 9 in 2.59 dοes nοt change its value, and 6 is greater than 5.

Therefοre, οnly the cοmparisοns (A and C) are true.

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