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The classification , symmetry , maximum r-values and the zeroes of the function are solved

Given data ,

a)

Let the function be represented as A

Now , the value of A is

r² = 25 sin( 2θ )

The equation represents a cardioid

It is symmetric about the polar axis.

The maximum values of r occur at θ = (π/4) + kπ/2, and the maximum value of r is 5.

The equation has zeroes at θ = kπ/2, and the corresponding values of r are given by r = 0

b)

The equation represents a limaçon.

It is symmetric about the polar axis.

The maximum value of r is 7.

The equation has zeroes at θ = arccos(1/3) + 2kπ or θ = -arccos(1/3) + 2kπ, and the corresponding values of r can be found by substituting into the equation r = 4 - 3cos(θ).

c)

The equation represents an Archimedean spiral.

It does not possess any symmetry.

There is no maximum r value.

The equation has a zero at θ = 1/2.

Hence , the zeroes of the function are solved

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For the function y = 3sin[2(θ-90°)] + 2, the amplitude is 3, the period is π, the phase shift is -45° and the vertical shift is 2 units up.

The amplitude of a sine function represents the maximum displacement from the midline.

The coefficient in front of the sine function is 3, so the amplitude is 3.

The period of a sine function is the length of one complete cycle. It can be calculated using the formula T = 2π/b, where b is the coefficient of θ inside the sine function brackets.

Here, b = 2, so the period is T = 2π/2 = π.

The phase shift of a sine function indicates a horizontal shift to the left or right.

In this case, c = 90°, so the phase shift is θ = 0° - 90°/2 = -45°.

The vertical shift indicates a shift up or down on the y-axis.

The constant term outside the sine function is 2, so the vertical shift is 2 units up.

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Answer:

The correct answer:

(B) SAS Similarity

Answer:

16x+4y=2

Step by step explanation

The required exact value of cos(-10π/3) or cos(2π/3) is -1/2.

To find the exact value of the expression cos(-10π/3), we can use the periodicity and symmetry properties of the cosine function.

In this case, we have cos(-10π/3). Since -10π/3 is equivalent to 2π/3 radians (because it completes a full revolution plus an additional 2π), we can rewrite the expression as cos(2π/3).

Now, let's find the exact value of cos(2π/3).

In the unit circle, an angle of 2π/3 (or 120 degrees) is located in the second quadrant. In the second quadrant, the x-coordinate is negative.

Since the cosine function gives the x-coordinate of a point on the unit circle, we can conclude that cos(2π/3) is negative.

Therefore, the exact value of cos(-10π/3) or cos(2π/3) is -1/2.

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The probability that either event will occur is 0.62

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

Event A = 6 + 6 = 12

Event B = 20 + 6 = 26

Both A and B = 6

Other Events = 20

Using the above as a guide, we have the following:

Total = A + B + C + Others - Both

So, we have

Total = 12 + 26 - 6 + 20

Evaluate

Total = 52

So, we have

P(A) = 12/52

P(B) = 26/52

Both A and B = 6/52

For either events, we have

P(A or B) = (12 + 26 - 6)/52

Evaluate

P(A or B) = 0.62

Hence, the probability that either event will occur is 0.62

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Answer:

The equation that models the relationship between the time x (in minutes) and the distance y (in feet) from the ground is:

y = 2000x

This is because for every 2 minutes that go by (i.e. for every increase of x by 1), the balloon rises by 2000ft (i.e. a constant rate of change). So, the equation y = 2000x represents a straight line with a slope (rate of change) of 2000, passing through the origin.

150 degrees is the measure of the angle x from the figure

The given diagram is a circle and the angle x and 30 degrees can be seen to be on a straight line.

The sum of the measure of angle on a straight line is 180 degrees, hence:

x + 130 = 180

Subtract 130 degrees from both sides to have:

x + 30 - 30 = 180 - 30
x = 180 - 30
x = 150 degrees

Hence the measure of the angle x from the given equation is 150 degrees

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The surface area of the square pyramid is 224 square centimeters.

Since the base of the square pyramid is a square, all sides are equal in length.

Let's call the length of one side of the square base "s".

Then the surface area of the pyramid can be found using the formula:

Surface area = Area of base + Area of four triangles

The area of the base is just s², and the height of each triangle can be found using the Pythagorean theorem.

Let's call the height "h". Then:

h² = 14² - (s/2)² (using the longer side of the triangle as the hypotenuse)

h² = 196 - (s²/4)

Now, we need to find the surface area in terms of "s" and simplify:

Surface area = s² + 4(1/2)(s)(h)

Surface area = s² + 2sh

Surface area = s² + 2s√196 - s²/4))

Surface area = s²+ 2s√(784 - s²))/2

Surface area = s² + s√(784 - s²))

We are given that one side of the square base is 8cm, so:

Surface area = 8² + 8√784 - 8²

Surface area = 64 + 8√400

Surface area = 64 + 8(20)

Surface area = 224

Therefore, the surface area of the square pyramid is 224 square centimeters.

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The height of domino #7 is approximately 6.89 cm tall.

The formula for the nth term of a geometric progression is:

[tex]a_n = a * r^(^n^-^1^)[/tex]

where:

a is the first term (the height of the smallest domino, 4.00 cm),

r is the common ratio (the growth rate, 1.12), and

n is the term number (for domino #7, n = 7 + 1 = 8, because the sequence starts with domino #0).

Let's plug these values into the formula:

[tex]a_8 = 4.00 cm * (1.12)^7[/tex]

(Note that we're using 7, not 8, because the first domino is #0, not #1.)

Now, compute the value:

[tex]a_8 = 4.00 cm * (1.12)^7[/tex]

=  6.89 cm

So, domino #7 is approximately 6.89 cm tall.

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Answer:

(c):53

Step-by-step explanation:

Let's start with the equation:

3x+5y

Since we already have the values of x and y, we can just solve the equation.

3(11)+5(4)

33+20=53

The answer is (c)53

Answer:

The slope is 5.

Hope this helps!

Step-by-step explanation:

( x, y )

( 6, 50 ) and ( 12, 80 )

[tex]\frac{80-50}{12 - 6} < = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

[tex]\frac{30}{6} = \frac{5}{1} = 5[/tex]

The slope is 5.

The minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.

On the basis of the quantity of checks written, we can compare the overall costs of the two accounts.

Let's calculate the total cost for each account based on the given information:

First Account:

Monthly fee: $12

Per-check fee: $0.10

Total cost = Monthly fee + (Per-check fee * Number of checks)

Second Account:

Monthly fee: $9

Per-check fee: $0.25

Total cost = Monthly fee + (Per-check fee * Number of checks)

We must determine the point at which the first account's total cost is less than the second account's total cost. Let's construct the formula:

$12 + ($0.10 * Number of checks) < $9 + ($0.25 * Number of checks)

Simplifying the equation

$12 - $9 < ($0.25 - $0.10) * Number of checks

$3 < $0.15 * Number of checks

Dividing both sides by $0.15:

$3 / $0.15 < Number of checks

20 < Number of checks

Therefore, the minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.

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The sine function with a midline of y=4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2sin(2(x - π/4)) + 4.

To write a sine function with the given properties, we can use the general form of a sine function: y = A * sin(B(x - C)) + D, where A represents the amplitude, B represents the frequency (or inverse of the period), C represents the horizontal shift, and D represents the vertical shift (or midline).

In this case:

The midline is y = 4, so D = 4.

The amplitude is 2, so A = 2.

The period is π, so the frequency is B = 2π/π = 2.

The horizontal shift is π/4 to the right, so C = -π/4.

Plugging these values into the general form, we get the sine function:

y = 2 * sin(2(x - (-π/4))) + 4

Simplifying further:

y = 2 * sin(2(x + π/4)) + 4

Therefore, the sine function with a midline of y = 4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2 * sin(2(x + π/4)) + 4.

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The length of the midsegment of the trapezoid with bases 18 and 28 is gvien as follows:

23.

The trapezoid midsegment theorem, states that the length of the midsegment of the trapezoid is equals to the mean of the length of the bases of the trapezoid.

The bases of the trapezoid are given as follows:

18 and 28.

Hence the length of the midsegment of the trapezoid is given as follows:

(18 + 28)/2 = 23.

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Answer:

x = 3

y = -1

Step-by-step explanation:

             Method:  substitution

x - 3y = 6 --------------(I)

      x  = 6 + 3y -------------(II)

2x + 2y = 4 ----------(III)

Substitute x = 6 +3y in equation (II),

        2*(6+3y) + 2y = 4

Use distributive property to open the parenthesis,

     2*6 + 2*3y + 2y = 4

         12 + 6y + 2y = 4

Combine like terms.

            12 + 8y      = 4

Subtract 12 from both sides,

                        8y  = 4 - 12

                        8y = -8

Divide both sides by 8,

                          y = -8÷ 8

                            [tex]\boxed{\bf y = (-1)}\\[/tex]

Substitute y = -1 in equation (II) and find the value of x.

               x = 6 + 3*(-1)

                  = 6 - 3

               [tex]\sf \boxed{\bf x = 3}[/tex]

Answer:

(3, - 1 )

Step-by-step explanation:

x - 3y = 6 ( add 3y to both sides )

x = 3y + 6 → (1)

2x + 2y = 4 → (2)

substitute x = 3y + 6 into (2)

2(3y + 6) + 2y = 4

6y + 12 + 2y = 4

8y + 12 = 4 ( subtract 12 from both sides )

8y = - 8 ( divide both sides by 8 )

y = - 1

substitute y = - 1 into (1)

x = 3(- 1) + 6 = - 3 + 6 = 3

solution is (3, - 1 )

The multiplication of the expression (s - 3)³ is determined as s³ - 9s³ + 27s - 27.

The product of the expression given as (s - 3)³ is calculated  as follows;

The given expression;

(s - 3)³, this can also be written as;

(s - 3)³ =  (s - 3) (s - 3) x (s - 3)

We will simplify the expression as follows;

(s - 3)(s - 3) x (s - 3)

= (s - 3)(s - 3) x (s - 3)

= (s² - 3s -3s + 9 )(s - 3)

= ( s² - 6s + 9 ) (s - 3)

= s³ - 3s² - 6s² + 18s + 9s - 27

= s³ - 9s³ + 27s - 27

Thus, the given expression can be simplified using binomial theorem or using simple multiplication method as shown above.

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There are three area options for the number of bricks:

The number of bricks that can be painted out is equal to the paint area (A), in square centimeters, divided to the area of a brick (A'), in square centimeters. That is:

n = A / A'

A' = w · h

Where:

There are three possible answers:

Case 1: A = 93750 cm², w = 22.5 cm, h = 10 cm

A' = 22.5 · 10

A' = 225

n = 93750 / 225

n = 416.667

n = 416

Case 2: A = 93750 cm², w = 22.5 cm, h = 7.5 cm

A' = 22.5 · 7.5

A' = 168.75

n = 93750 / 168.75

n = 555.556

n = 555

Case 3: A = 93750 cm², w = 10 cm, h = 7.5 cm

A' = 10 · 7.5

A = 75

n = 93750 / 75

n = 1250

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Answer:

A. 4ab² + 2x

Step-by-step explanation:

If you want to get rid of those pesky parentheses, you have to use the superpower of distributive property. It lets you multiply everything inside the parentheses by the number outside. For example:

4(ab²+1/₂c + x) = 4ab² + 2c + 4x

Boom! No more parentheses!

To combine like terms, you have to add or subtract the numbers in front of the terms that have the same variable and exponent. For example:

2x - 4x = -2x

Bam! Only one x left!

Here are the steps to simplify the expression:

4(ab²+1/₂c + x) - 2(c+x)

= 4ab² + 2c + 4x - 2c - 2x (use superpower)

= 4ab² + 4x - 2x (combine like terms)

= 4ab² + 2x (simplify)

So, the answer is A. 4ab² + 2x.

Answer:

Set your calculator to Degree mode.

(1/2)(11.3)(5.2)(sin A) = 17.8

29.38sinA = 17.8

sin A = 890/1,469

A = sin^-1 (890/1,469) = 37.3°

The surface areas of the solids are listed below:

Case I: A = 216 ft²

Case O: A = 204 mm²

Case H: A = 216 ft²

Case L: A = 284.6 cm²

Case E: A = 25.657 yd

Case N: A = 356 yd²

Case S: A = 361.88 ft²

Case T: A = 150 cm²

In this problem we find eight solids, whose surface areas, that is, the sum of the areas of all faces of the solid, must be found. Each face can be represented by the following area formula:

Rectangle

A = w · h

Triangle

A = 0.5 · w · h

Where:

Now we proceed to determine the surface areas:

Case I:

A = 6 · (6 ft)²

A = 216 ft²

Case O:

A = 4 · 0.5 · (6 mm) · (14 mm) + (6 mm)²

A = 204 mm²

Case H:

A = 2 · (8 ft) · (6 ft) + (8 ft) · (5 ft) + (6 ft) · (5 ft) + (10 ft) · (5 ft)

A = 216 ft²

Case L:

A = 2 · 0.5 · (7 cm) · (5 cm) + 2 · (6.1 cm) · (13 cm) + (7 cm) · (13 cm)

A = 284.6 cm²

Case E:

A = 2 · 0.5 · (2 yd)² + 2 · (2 yd) · (4 yd) + (√2 yd) · (4 yd)

A = 25.657 yd

Case N:

A = 2 · (3 yd) · (8 yd) + 2 · (8 yd) · (14 yd) + 2 · (14 yd) · (3 yd)

A = 356 yd²

Case S:

A = 2 · 0.5 · (8 ft) · (6 ft) + 2 · (14 ft) · (7.21 ft) + (14 ft) · (8 ft)

A = 361.88 ft²

Case T:

A = 6 · (5 cm)²

A = 150 cm²

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The first term of a geometric sequence is 2 and the common ratio is 3.  The general term formula for the nth term of a geometric sequence is given by: an = a₁ × rⁿ⁻¹ Where, an is the nth term of the sequence, a₁ is the first term of the sequence, and r is the common ratio of the sequence. The 15th term of the sequence is 86,093,442.

To find the 15th term of the sequence, we need to use the above formula to find a₁ and r.The sequence is: 2, 6, 18, 54, ...Since the first term is 2, then a₁ = 2.The common ratio can be found by dividing any term by its preceding term. We will use the second and first term:6 / 2 = 318 / 6 = 3Again, the common ratio is 3. Now, we can use the formula to find the 15th term of the sequence: an = a₁ × rⁿ⁻¹a15 = 2 × 3¹⁵⁻¹a15 = 2 × 3¹⁴a15 = 2 × 43,046,721a15 = 86,093,442 The 15th term of the sequence is 86,093,442.

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Measure of angle 1 is,

Angler ACB = 36 degree

We have to given that;

In a parallelogram we get;

Angler CAD = 36 degree

Now, We know that;

Opposite sides are parallel to each other in a parallelogram.

Hence, We get;

Angler CAD = Angle ACB

Since, Angler CAD = 36 degree

Hence, We get;

Measure of angle 1 is,

Angler ACB = 36 degree

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Rounding to the nearest tenth, the mean lifespan for Kamila's sample is 11.9 years.

To find the mean (average) for Kamila's sample, you need to sum up all the lifespans and then divide by the total number of breeds in the sample.

Sum of lifespans = 13 + 11 + 12 + 14 + 12 + 10 + 11 + 12 = 95

Total number of breeds = 8

Mean = Sum of lifespans / Total number of breeds

= 95 / 8 = 11.875

Rounding to the nearest tenth, the mean lifespan for Kamila's sample is 11.9 years.

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It is possible for a sample to follow a normal distribution, depending on the nature of the data being accumulated.

The regular distribution is a bell-shaped curve that is symmetric across the mean, and it's far typically used to model various natural phenomena and measurements in fields such as information, engineering, and social sciences.

If the data being gathered is continuous and the sample length is large sufficient, it is regularly assumed that the pattern follows a normal distribution.

This assumption is based at the critical limit Theorem, which states that the sampling distribution of the suggest of any independent, random variable will tend toward a ordinary distribution because the sample size increases.

But, it's far critical to notice that not all samples will observe a ordinary distribution, and in a few cases, different distributions may be greater suitable for the records being amassed.

It's far consequently essential to analyze the information and evaluate the assumptions being made before using the regular distribution as a model.

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The products of the matrices A and B are [tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex] and [tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]

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

Matrix A = [tex]\left[\begin{array}{cc}-3&-8\\2&8\end{array}\right][/tex]

Matrix B = [tex]\left[\begin{array}{cc}6&3\\4&-2\end{array}\right][/tex]

Using the above as a guide, we have the following:

[tex]AB = \left[\begin{array}{cc}-3 * 6 + -8 * 4 &-3 * 3 -8 * -2\\2 * 6 + 8 * 4 &2 * 3 + 8 * -2\end{array}\right][/tex]

Evaluate

[tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex]

Next, we have

[tex]BA = \left[\begin{array}{cc}6 * -3 + 3 * 2&6 * -8 + 3 * 8 \\4 * -3 + -2 * 2&4 * -8 + -2 * 8\end{array}\right][/tex]

Evaluate

[tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]

Hence, the values are [tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex] and [tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]

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Answer:

The answer is 33°

Yes you are correct

Step-by-step explanation:

angles on a straight line equal 180°

57+90+x=180

x+147=180

x=180-147

x=33°

Hi, I can't tell if there's a little square drawn in red to indicate that there's a right angle in the middle. There's some squiggly lines and so it's kind of hard to tell.

I am going to assume that there is. Let me know if there isn't.

The sum of these 3 angles would be 180 degrees.

As an equation, 57 + 90 + x = 180

Solve for x.

147 + x = 180

x = 33 degrees.

So this would be correct ASSUMING that there's a little red square drawn indicating that there's a right angle.