Find the perimeter of the trapezoid.

If we let a = 0, b = 1, and c = 1, then the polynomial

\(x(x-1)(x^2 +\)

Since the polynomial has integer coefficients, if one of the roots is a complex number, then its conjugate must also be a root. Therefore, options A and E cannot be roots of the polynomial, since they have non-real conjugates.

We know that the polynomial has degree 4, so it has four roots in total (counting multiplicities). We also know that two of the roots are integers, so let's call them a and b. Then the polynomial can be written as:

\((x - a)(x - b)(cx^2 + dx + e)\)

where c, d, and e are integers (because they are the coefficients of the quadratic factor). We know that the leading coefficient is 1, so c must be nonzero.

Since the polynomial has two real roots, its discriminant must be nonnegative:

\(d^2 - 4ce > = 0\)

We can use this inequality to rule out some of the answer choices. For example, option C cannot be a root, because if we substitute x = 1/2 + i into the polynomial, we get:

(\((1/2 + i) - a)((1/2 + i) - b)(c((1/2 + i)^2) + d(1/2 + i) + e)\)

The real part of this expression is:

(1/4 - a + 1/4 - b)(c(1/4 - 1) + d/2 + e) = -(a + b - 1/2)(3c/4 + d/2 + e)

If we assume that a and b are integers, then this expression is an integer multiple of 3c/4 + d/2 + e. However, we can choose values of c, d, and e such that 3c/4 + d/2 + e is not an integer (for example, if c = 4, d = 1, and e = 0, then 3c/4 + d/2 + e = 4.5). Therefore, the real part of the expression cannot be zero, and option C cannot be a root.

We can also rule out option D using the same argument. If we substitute x = 1 + i/2, then the real part of the expression is:

((1 + i/2) - a)((1 + i/2) - b)(c((1 + i/2)^2) + d(1 + i/2) + e)

(1 - a + i/2)(1 - b + i/2)(c(5/4 + i) + d(3/2 + i/2) + e)

The real part of this expression is an integer multiple of c(5/4) + d(3/2) + e, which can be non-integer for some choices of c, d, and e.

Therefore, the only possible answer choices are A and B. To determine whether they are roots of the polynomial, we can use the fact that the sum and product of the roots are given by:

a + b + (complex roots) = -d/c

ab(complex roots) = e/c

We know that a and b are integers, so if we can find a polynomial with integer coefficients that has roots a, b, and either A or B, then that root is also a root of the original polynomial.

For option A, we have:

1 + i√11/2 = 2(cos(75°) + i sin(75°))

Therefore, if we let a = 0, b = 1, and c = 1, then the polynomial

\(x(x-1)(x^2 +\)

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Answer:

1/8

Step-by-step explanation:

P(nectarine) = number of nectarines / total

                       =2/16

                        = 1/8

Answer:

The sum of the probabilities of all possible outcomes must equal 1.

Step-by-step explanation:

To solve this problem, we can use the binomial distribution, since we have a fixed number of trials (two children) and each trial has two possible outcomes (boy or girl) with a known probability of success (0.48 for a girl).

Let X be the random variable representing the number of girls born to the family. Then X follows a binomial distribution with parameters n = 2 (the number of trials) and p = 0.48 (the probability of success). The probability mass function (PMF) of X is given by:

P(X = k) = (n choose k) * \(p^{k}\) * \((1 - p)^{(n - k)}\)

where (n choose k) =  \(\frac{n! }{(k! * (n - k)!)}\) is the binomial coefficient.

To find the probability that the family has 0, 1, or 2 girls, we need to calculate the values of P(X = 0), P(X = 1), and P(X = 2):

P(X = 0) = (2 choose 0) * \(0.48^{0}\) * \(0.52^{2}\) = 0.2704

P(X = 1) = (2 choose 1) *  \(0.48^{1}\)  *  \(0.52^{1\\}\) = 0.4992

P(X = 2) = (2 choose 2) *  \(0.48^{2}\)  * \(0.52^{0}\) = 0.2304

Therefore, the probability that the family has 0, 1, or 2 girls is:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2704 + 0.4992 + 0.2304 = 1

Note that the sum of the probabilities of all possible outcomes must equal 1.

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The quadratic equation that represents the solution is F: p(x) = x² - 49.

The term "quadratic" refers to functions where the highest degree of the variable (in this example, x) is 2. A quadratic function's graph is a parabola, which, depending on the sign of the leading coefficient a, can either have a "U" shape or an inverted "U" shape.

Algebra, geometry, physics, engineering, and many other branches of mathematics and science all depend on quadratic functions. They are used to simulate a wide range of phenomena, including population dynamics, projectile motion, and optimisation issues.

Given that the solution of the quadratic function are x = -7 and x = 7 thus we have:

p(x) = (x + 7)(x - 7)

Solving the parentheses we have:

p(x) = x² - 7x + 7x - 49

Cancelling the same terms with opposite sign we have:

p(x) = x² - 49

Hence, the quadratic equation that represents the solution is F: p(x) = x² - 49.

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Answer:

-0.875

Step-by-step explanation:

I got a 100% on my masters test

Answer: it is 9 because 10 - 1 = 9

Step-by-step explanation:

Answer:

Answer 9 because 10-1=9

Step-by-step explanation:

If you have 10  apples and if I stole one from you then it will 9.

Answer:

The percentages are as follows: 1) 16.6%, 2) 12.5%, 3) 200%, 4) 225%, and 5) 1.5%.

Step-by-step explanation:

To find the rate, or percent, for each of the following items, the following calculations must be performed:

1) Base 72; percentage 12 = 12/72 = 0.1666 x 100 = 16.6

2) Percentage 28; base 224 = 28/224 = 0.125 x 100 = 12.5

3) Base 20; percentage 40 = 40/20 = 2 x 100 = 200

4) Base 44; percentage 99 = 99/44 = 2.25 x 100 = 225

5) Percentage 126; base 8400 = 126/8400 = 0.015 x 100 = 1.5

Therefore, the percentages are as follows: 1) 16.6%, 2) 12.5%, 3) 200%, 4) 225%, and 5) 1.5%.

Answer:

Step-by-step explanation:

Answer:

38 cm²

Step-by-step explanation:

The given condition cscx<0 and secx<0 is true in the fourth quadrant.

In trigonometry, the cosecant (csc) of an angle is the reciprocal of the sine, and the secant (sec) of an angle is the reciprocal of the cosine. To determine in which quadrant the given condition cscx<0 and secx<0 is true, we need to analyze the signs of the cosecant and secant functions in each quadrant.

In the first quadrant (0°-90°), both sine and cosine are positive, so their reciprocals, csc and sec, would also be positive.

In the second quadrant (90°-180°), the sine function is positive, but the cosine function is negative. Therefore, csc is positive, but sec is negative. Thus, the given condition is not satisfied in this quadrant.

In the third quadrant (180°-270°), both sine and cosine are negative, resulting in positive values for csc and sec. Therefore, the given condition is not true in this quadrant.

Finally, in the fourth quadrant (270°-360°), the sine function is negative, and the cosine function is also negative. Consequently, both csc and sec would be negative, satisfying the given condition cscx<0 and secx<0.

In conclusion, the condition cscx<0 and secx<0 is true in the fourth quadrant.

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a.  The inequality csc(x) < 0 and sec(x) < 0 is true in the third quadrant (180° to 270°).

b. the arc length is approximately 6.83 cm.

a. To determine in which quadrant the inequality csc(x) < 0 and sec(x) < 0 is true, we need to analyze the signs of the cosecant and secant functions in each quadrant.

Recall the signs of trigonometric functions in different quadrants:

In the first quadrant (0° to 90°), all trigonometric functions are positive.

In the second quadrant (90° to 180°), the sine (sin), cosecant (csc), and tangent (tan) functions are positive.

In the third quadrant (180° to 270°), only the tangent (tan) function is positive.

In the fourth quadrant (270° to 360°), the cosine (cos), secant (sec), and cotangent (cot) functions are positive.

From the given inequality, csc(x) < 0 and sec(x) < 0, we see that both the cosecant and secant functions need to be negative.

Since the cosecant function (csc) is negative in the second and third quadrants, and the secant function (sec) is negative in the third and fourth quadrants, we can conclude that the inequality csc(x) < 0 and sec(x) < 0 is true in the third quadrant (180° to 270°).

b. Regarding the arc length, we can use the formula for the arc length of a sector of a circle:

Arc Length = (central angle / 360°) * (2π * radius)

Given that the central angle is 325° and the radius of the circle is 3 cm, we can calculate the arc length as follows:

Arc Length = (325° / 360°) * (2π * 3 cm)

= (13/ 36) * (2π * 3 cm)

= (13/36) * (6π cm)

= (13/6)π cm

≈ 6.83 cm

Therefore, the arc length is approximately 6.83 cm.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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Answer:

47/100=922/x      hope this helps

Step-by-step explanation:

The proportions could be used to solve this given problem

47/100=922/x.

We have given that,

47% of what number is 922.

We  have to determine,

The following proportions could be used to solve this problem.

Proportion is an equation that defines that the two given ratios are equivalent to each other.

The proportions could be used to solve this given problem

47/100=922/x.

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The volume of the given hollow cylinder to the nearest whole number is 1102 cm³.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.

A cylinder has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

A cylinder that is hollow from the inside out and has a gap between its internal and external radii is referred to as a hollow cylinder. The hollow cylinder's base resembles an annular ring.

Given,

Inner radius r = 5cm

Outer radius R=8cm

Height h = 9 cm

The volume of a hollow cylinder =  π (R² - r²)h

                                                      = 3.14 *(8² - 5²)* 9 = 1102.14cm³

Therefore the volume of the given hollow cylinder to the nearest whole number is 1102 cm³.

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A scatter plot is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables.

A scatter plot is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables. It is a type of mathematical diagram that utilizes Cartesian coordinates to display values for typically two variables for a set of data.

The data is displayed as a collection of points, each with the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. Scatter plots are extremely useful when there are a large number of data points.

Summery:A scatter plot is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables.

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To solve the given boundary-value problem, we first need to find the general solution of the differential equation y'' - y = 0. This can be done by assuming a solution of the form y = e^rx and plugging it into the equation to get the characteristic equation:

r^2 - 1 = 0

This gives us the roots r = 1 and r = -1. Therefore, the general solution of the differential equation is:

y = c1*e^x + c2*e^-x

Now we can use the boundary conditions to find the values of c1 and c2. First, we use the condition y'(0) = 0:

y' = c1*e^x - c2*e^-x

y'(0) = c1 - c2 = 0

c1 = c2

Next, we use the condition y'(/2) = 0:

y'(/2) = c1*e^(/2) - c2*e^(-/2) = 0

c1*e^(/2) = c2*e^(-/2)

c1 = c2*e^(-)

Since c1 = c2, we can substitute c2 for c1 in the above equation to get:

c2 = c2*e^(-)

c2*(1 - e^(-)) = 0

This gives us c2 = 0, and since c1 = c2, we also have c1 = 0. Therefore, the solution to the boundary-value problem is:

y = 0

So the answer is y = 0.

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Answer:

A

Step-by-step explanation:

The particular solution that does not involve any terms from the homogeneous solution is given by:\(Y(t) = C3 + C4te^(-t/2).\)

To find a particular solution of the given differential equation using the method of variation of parameters, we follow these steps:

Solve the associated homogeneous equation: 4y" - 4y + y = 0.

The characteristic equation is:

\(4r^2 - 4r + 1 = 0.\)

Solving the quadratic equation, we find two repeated roots: r = 1/2.

Therefore, the homogeneous solution is given by: y_h(t) = C1\(e^(t/2)\) + C2t\(e^(t/2),\) where C1 and C2 are constants.

Find the particular solution using the variation of parameters.

Let's assume the particular solution has the form:

\(y_p(t) = u1(t)e^(t/2) + u2(t)te^(t/2).\)

To find u1(t) and u2(t), we differentiate this expression:

\(y_p'(t) = u1'(t)e^(t/2) + u1(t)(1/2)e^(t/2) + u2'(t)te^(t/2) + u2(t)e^(t/2) + u2(t)(1/2)te^(t/2).\)

We equate the coefficients of e^(t/2) and te^(t/2) on both sides of the original equation:

\((1/2)(u1(t) + u2(t)t)e^(t/2) = 16e^(t/2).\)

From this, we can deduce that u1(t) + u2(t)t = 32.

Differentiating again:

\(y_p''(t) = u1''(t)e^(t/2) + u1'(t)(1/2)e^(t/2) + u1'(t)(1/2)e^(t/2) + u1(t)(1/4)e^(t/2) + u2''(t)te^(t/2) + u2'(t)e^(t/2) + u2'(t)(1/2)te^(t/2) + u2(t)e^(t/2) + u2(t)(1/2)te^(t/2).\)

Setting the coefficient of \(e^(t/2)\)equal to zero:

\((u1''(t) + u1'(t) + (1/4)u1(t))e^(t/2) = 0.\)

Similarly, setting the coefficient of \(te^(t/2)\)equal to zero:

\((u2''(t) + u2'(t) + (1/2)u2(t))te^(t/2) = 0.\)

These two equations give us a system of differential equations for u1(t) and u2(t):

u1''(t) + u1'(t) + (1/4)u1(t) = 0,

u2''(t) + u2'(t) + (1/2)u2(t) = 0.

Solving these equations, we obtain:

u1(t) = C3\(e^(-t/2)\) + C4t\(e^(-t/2),\)

u2(t) = -4C3\(e^(-t/2)\) - 4C4t\(e^(-t/2).\)

Substitute the values of u1(t) and u2(t) into the assumed particular solution:

\(y_p(t) = (C3e^(-t/2) + C4te^(-t/2))e^(t/2) - 4C3e^(-t/2) - 4C4te^(-t/2).\)

Simplifying further:

\(y_p(t) = C3 + C4te^(-t/2) - 4C3e^(-t/2) - 4C4te^(-t/2).\)

So, the particular solution that does not involve any terms from the homogeneous solution is given by:

\(Y(t) = C3 + C4te^(-t/2).\)

Here, C3 and C4 are arbitrary constants that can be determined using initial conditions or boundary conditions if provided.

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Answer:

x = 9

Step-by-step explanation:

\(2x + 3 = 3x - 6\)

\(3 = x - 6\)

\(x = 9\)

The minimum number is 9 GB to make the unlimited cheaper.

A gigabyte is a specific unit of data that's equal to about 1 billion bytes of data. The term gigabyte is typically used to describe the amount of stored data or the capacity of a storage device. For example, an HDD might offer 500 GB of raw capacity but is currently storing only 200 GB of data.

Given that,

A tablet data provider offers different plans for data usage

The plan Raul chose has a monthly fee of $29.99 per month for 5 GB of data with an additional cost of $10 for each gigabyte over 5.

Assume that he will use n gigabyte per month

The monthly fee is $29.99 for 5 GB

∵ The cost per GB after the first 5 GB is $10

∵ The number of GB whose cost is $10 is (n - 5)

∴ His monthly fees = 29.99 + 10 (n - 5) ⇒ current plan

The fees of the unlimited is $59.99 per month

∵ We need the unlimited cheaper than current plane

Let the current plan greater than the unlimited plan

∴ 29.99 + 10 (n - 5) > 59.99

Subtract both sides by 29.99

∴ 10 (n - 5) > 30

Divide both sides by 30

∴ n - 5 > 3

Add both sides by 5

∴ n > 8

Hence, The minimum number is 9 GB to make the unlimited cheaper.

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h(x) = -7/6x - 25/6.

Given h(-1)=-2 and h(-7)=-9

For linear function h(x), we can use slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept.

To find m, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

h(-1) = -2 is a point on the line, so we can write it as (-1, -2).

h(-7) = -9 is another point on the line, so we can write it as (-7, -9).

Now we can find m using these points: m = (-9 - (-2)) / (-7 - (-1)) = (-9 + 2) / (-7 + 1) = -7/6

Now we can find b using one of the points and m. Let's use (-1, -2):

y = mx + b-2 = (-7/6)(-1) + b-2 = 7/6 + b

b = -25/6

Therefore, the linear function h(x) is:h(x) = -7/6x - 25/6

We can check our answer by plugging in the two given points:

h(-1) = (-7/6)(-1) - 25/6 = -2h(-7) = (-7/6)(-7) - 25/6 = -9

The answer is h(x) = -7/6x - 25/6.

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Out of the 500 teenagers sampled at random, the table presents their preferences in terms of favorite movie genres. To estimate the number of teenagers out of a population of 3,000 who prefer action movies, we can use the proportion of action movie fans from the sample.

Let's say the table shows that "x" out of the 500 sampled teenagers prefer action movies. To find the proportion of action movie fans in the sample, we divide the number of action movie fans by the total number of teenagers in the sample:

Proportion of action movie fans = (x / 500)

Now, we can use this proportion to estimate the number of teenagers who prefer action movies in the entire population of 3,000 teenagers. To do this, multiply the proportion of action movie fans by the total population:

\(Estimated action movie fans = Proportion of action movie fans * Total population\)

Estimated action movie fans = (x / 500) * 3,000

By calculating this value, we can estimate the number of teenagers in the population of 3,000 who will prefer action movies based on the results of the random sample.

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Scale Factor to go from F to G = 3/4

Scale Factor to go from G to F = 4/3

===============================================

Explanation:

Note the sides labeled 4 and 3 are both opposite the angles that have two tickmarks. Therefore, these two sides correspond to one another.

Because of the similar triangles, the corresponding sides are in proportion. The scale factor is 3/4 meaning the smaller triangle has side lengths 3/4 as large compared to the larger triangle.

Put another way, we have a 25% reduction in the side lengths because 3/4 = 75% and 100% - 75% = 25%

So far, all of this applies when figure F is the preimage and G is the image. If we reverse things, then apply the reciprocal to 3/4 to get 4/3. Now G is the preimage and we go from smaller to larger.

------------

Side notes:

The required scale factor for the given transformation is given as 3/4.

Given that,
Two triangles have been shown, is to discuss the transformation and scale factor of the triangle.

The scale factor is defined as the ratio of modified change in length to

Here,
The given figures are similar in shape but not in size,
If the shapes is similar then the ratio of the corresponding sides describes the scale factor between the figures,
So,

Ratio of side = 3 / 4

Thus, the required scale factor for the given transformation is given as 3/4.

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The median of the data set is 5.35.

To find the median, we need to first arrange the data set in order from smallest to largest. In this case, the data set is:

0.53, 5.2, 5.3, 5.35, 5.5, 53.

The median is the middle value of the data set. In this case, there are 6 values, so the median is the average of the 3rd and 4th values. In this case, 5.35 is the average of 5.3 and 5.35, so 5.35 is the median.

Therefore, the answer is 5.35 (Option d).

Median is a measure of central tendency and is used to describe a set of numerical values. It is the middle value when the values are arranged in ascending or descending order. It is the midpoint of a distribution and is often used as a measure of central tendency when the data is skewed or has outliers. The median is less affected by extreme values than the mean, making it a more accurate measure of the central location of the data.

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Answer: 15 minutes

Step-by-step explanation:

60 / 4 = 15

15 * 3 = 45

45 / 3 = 15

Answer:

Step-by-step explanation:

Time spent on jump rope = 1/3 of 3/4

                                           \(= \dfrac{1}{3}*\dfrac{3}{4}=\dfrac{1}{4} \ hour\) or 15 minutes

Answer:

2 quarts .

Step-by-step explanation:

4 quarts make a gallon but two is already added

Answer:

2 quarts

Step-by-step explanation:

The trigonometric identities, for the sum and difference of two angles, which is the addition formula for sine and cosine, indicates that we get;

cos(3·θ) = cos(2·θ)·cosθ - sin(2·θ)·sin(θ)

Trigonometric identities are trigonometric equations that includes trigonometric functions of variables, and which are correct for the possible values of the variables.

The trigonometric function is; cos(2·θ)·cos(θ) - sin(2·θ)·sin(θ)

Trigonometric identities for the addition and subtraction formula for sine and cosine indicates indicates that we get;

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

Therefore, where, A = 2·θ, and B = θ, we get;

Cos(2·θ + θ) = cos(2·θ)·cos(θ) - sin(2·θ)·sin(θ)

2·θ + θ = 3·θ

Therefore; Cos(2·θ + θ) = cos(3·θ) = cos(2·θ)·cos(θ) - sin(2·θ)·sin(θ)

cos(3·θ) = cos(2·θ)·cos(θ) - sin(2·θ)·sin(θ)

The symmetric property indicates that we get;

cos(2·θ)·cos(θ) - sin(2·θ)·sin(θ) = cos(3·θ)

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Answer:  y = 4

Step-by-step explanation: