Find the polar coordinates of a point with Cartesian coordinates (x,y)=(2√3,2).Select the correct answer below:


(4,π/6)
(2,2π/3)
(4,2π/3)
(2,7π/6)
(4,7π/6)
(2,π/6)

The rank of the matrix is 3, since there are three linearly independent rows.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.

To find the rank of the matrix:

[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]

We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.

[tex]R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2[/tex]

This gives us the following matrix:

[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]

We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.

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The length of the hypotenuse is 7m.

Let the side opposite to 30° be the shortest leg.

The side opposite to 60° is the longest leg.

So, the side opposite to 90° is hypotenuse.

Length of the shortest side is x.

Length of longest side is [tex]\sqrt{3}x[/tex]

Length of the hypotenuse is 2x.

We know x = 7

So, [tex]\sqrt{3}(x)=\sqrt{3}(7)[/tex]

Thus, the length of the longer leg is [tex]\sqrt{3}(7)[/tex] m

Length of hypotenuse = 2x = 2(7) = 14m

[tex]x^{2} +(\sqrt{3} x)^2 =(2x)^2\\\\(7)^2+(\sqrt{3} (7))^2=(2x)^2\\\\49 + (3(49)) = (2x)^2\\\\49 + 147= (2x)^2\\\\(2x)^2=196[/tex]

Taking square root on both sides:

[tex]2x = \sqrt{196}[/tex]

2x = 14

x = 7

Therefore, the length of the hypotenuse is 7m.

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Answer:

h(t) = 11 * sin(π/6 * t) + 15

Step-by-step explanation:

To find the height function h(t) for the piece of gum, we'll use a sinusoidal function since the height of the gum changes in a periodic manner as the tire rotates. The general formula for a sinusoidal function is:

h(t) = A * sin(B * (t - C)) + D

where A is the amplitude, B is the angular frequency, C is the horizontal shift, and D is the vertical shift.

1. Amplitude (A): The amplitude is half the distance between the highest and lowest points of the gum. Since the diameter of the tire is 22 inches, the radius is 11 inches. Thus, the amplitude is 11 inches.

2. Angular frequency (B): Since the gum completes 1 full revolution in 12 seconds, the period of the function is 12 seconds. The angular frequency, B, is found by dividing 2π by the period: B = 2π / 12 = π/6.

3. Horizontal shift (C): Since the gum starts at the three o'clock position, and we want the height to be at its maximum at t = 0, there is no horizontal shift. So, C = 0.

4. Vertical shift (D): The platform is 4 inches above the ground, and the radius of the tire is 11 inches. Therefore, the midpoint of the gum's motion is 4 + 11 = 15 inches above the ground. So, D = 15.

Now we can write the height function h(t):

h(t) = 11 * sin(π/6 * t) + 15

Answer:

D. It is a two-dimensional object.

The statement D is true about the figure above. The figure is a circle, which is a two-dimensional object.

Statement A is not true. A point is a location in space, but a circle is a shape that takes up space and has a defined area.

Statement B is not true either. A circle has only one measurement, which is its radius or diameter. The radius is the distance from the center of the circle to any point on its circumference, while the diameter is the distance across the circle through its center.

Statement C is also not true. A circle cannot "grow" into a three-dimensional object because it is a two-dimensional object that exists in a flat plane. However, multiple circles can be stacked on top of each other to form a cylinder, which is a three-dimensional object.

The solution is, simplification of  the expression 4√ 2 + 2√ 32 is 12√2 .

We know that,

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Here, given expression is,  

4√ 2 + 2√ 32

=4√ 2 + 2√ 16 × 2

we know that,

√16 = 4

so, we get,

=4√ 2 + 2√2 × 4

=4√ 2 + 8√2

=12√2

Hence, The solution is, simplification of  the expression 4√ 2 + 2√ 32 is 12√2 .

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An expression that represents the amount of Huang's change include the following: A. 100 – (12(3x)).

In this scenario and exercise, you are required to write and determine an expression that represents the amount of change which Huang should receive from the seller.

This ultimately implies that, an expression that models or represents the amount of Huang's change would have the form;

Huang's change = Money presented - Total cost of 3 shirts

Huang's change = 100 - (12(3x))

By simplifying further, we have the following expressions;

Huang's change = 100 - 36x

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Answer:

C

Step-by-step explanation:

cos x and sin(90 - x) are cofunctions and are equal , then

cos x = [tex]\frac{1}{3}[/tex] , then sin(90 - x) = [tex]\frac{1}{3}[/tex]

Answer:

41 grams

Step-by-step explanation:

trust i jus took it

The mass of an American Eagle Silver Bullion Coin is about 41 grams.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Each coin has a diameter of 40.6 millimeters and is 2.98 millimeters thick. The density of silver is 10.5 grams per cubic centimeter.

Hence, Volume is,

V = 3.14 x (40.6/2)² x 2.98

V = 3857.96 mm³

Since, 1000 mm³ = 1 cm³

Hence, The mass of an American Eagle Silver Bullion Coin is,

⇒ 33857.9 / 1000 x 10.5

⇒ 41 grams

Thus, The mass of an American Eagle Silver Bullion Coin is, 41 grams

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The sum of 150, 20 , and 20 is more than 180 degrees, therefore, it is not possible to draw a triangle.

A triangle is simply a three sided polygon that has three sides and three interior angles. When all three interior angles are added together, the sum is equal to 180 degrees according to the triangle sum theorem.

If we have a set of angles with the measure of 150, 20, and 20 degrees, respectively, the sum of these is more than 180 degrees.

150 + 20 + 20 = 190 degrees.

Therefore, it is not possible to draw a triangle with those set of angles.

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Answer: The volume of the cylinder is 924 cubic centimeters.

Step-by-step explanation:

The formula to calculate the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.

Given, radius (r) = 6 cm and height (h) = 7 cm.

Using the formula, we have V = (22/7) x 6^2 x 7 = 924 cubic centimeters.

Therefore, the volume of the cylinder is 924 cubic centimeters.

If Olivia followed either of those two methods, then she is correct. Both Angelica and Michael have incorrect methods.

Problem 1

One method Olivia could have used is to reflect over the x axis and then translate 10 units to the right.

Let's apply this set of steps to point C.

C = (-2,-4)

C' = (-2,4) after reflecting over the x axis; y coordinate flips in sign

C'' = (8,4) after shifting to the right 10 units; add 10 to the x coordinate

Point C(-2,-4) moves to C''(8,4) which is shown in the diagram. I'll let you check the other four points.

-----------

Another method Olivia could have used is to shift to the right 10 units first, then reflect over the x axis. In this case, the order doesn't matter. Though for some other combinations of transformations, order does matter.

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

Problem 2

Reflecting over the y axis will have the point (x,y) turn into (-x,y). Only the x coordinate changes, and we flip the sign here. The y coordinate stays the same.

A point like C(-2,-4) becomes C'(2,-4) after the y axis reflection. Shifting up 8 units means we add 8 to the y coordinate to arrive at C''(2,4) but this does not match what the diagram shows. Therefore, Angelica's method is incorrect.

You should find other inconsistencies for the other four points as well.

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

Problem 3

Michael's method isn't correct either. He does not apply an x axis reflection and instead relies entirely on translations to move ABCDE to A''B''C''D''E''

At a quick glance, it looks like Michael may be correct. But upon a much closer look, you'll see that things don't line up perfectly.

Instead of point C, we'll pick on point D this time.

D is located at (-6,-2). If we shift up 8 units, then we add 8 to the y coordinate to get to D'(-6,6). Then add 10 to the x coordinate to shift 10 units to the right. This leads us to D''(4,6).

However, the diagram shows D'' is actually at (4,2)

Feel free to examine the remaining points. It will become apparent that merely C and E are accurately plotted; however, the others are not. This is, once again, due to Michael's failure in implementing an x-axis reflection.

The A''B''C''D''E'' diagram he produced is essentially inverted compared to its intended form.

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

To summarize, the methods described in problem 1 are the correct way to get ABCDE to move to A''B''C''D''E''.

If Olivia followed either of those two methods, then she is correct. Both Angelica and Michael have incorrect methods.

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Answer:

We can see that the sequence is formed by multiplying each term by 2 to obtain the next term. Therefore, the fourth term is 12 x 2 = 24, the fifth term is 24 x 2 = 48, and so on.

To find the ninth term, we can multiply the third term by 2 six times:

3 x 2^6 = 3 x 64 = 192

Therefore, the ninth term of the sequence is 192.

a. 3 students read comics and novel only.

b. 1 student read textbook and novel only.

c. 31 students read none of the three categories.

Here's a Venn diagram that shows the information given:

  _________

     /         \

    /           \

   /             \

  /               \

 /        A       \

/                   \

/__________\

|          |          |

|          |          |

|     C  |     B    |

|          |           |

|__________|__________|

  \         |         /

    \       |       /

      \     |     /

        \   |   /

          \ |  /

           \ | /

            \|/

             |

             |

             |

            D

The three circles represent the three categories: novel, comics, and textbook.

The overlap between the circles represents the number of students who read more than one category.

The letters A, B, C, and D represent the following regions:

A: Only comics and novel (not textbook)

B: Only textbook and novel (not comics)

C: Only textbook and comics (not novel)

D: All three categories

To answer the questions:

a. To find the number of students who read comics and novel only (region A), we need to add up the number of students who read both comics and novel (5) and subtract from it the number of students who also read textbook (2).

So, the number of students who read comics and novel only is 5 - 2 = 3.

b. To find the number of students who read textbook and novel only (region B), we follow the same process.

We add up the number of students who read both textbook and novel (3) and subtract from it the number of students who also read comics (2).

So, the number of students who read textbook and novel only is 3 - 2 = 1.

c. To find the number of students who read none of the three categories, we start with the total number of students (50) and subtract from it the number of students who read at least one category.

To find the latter number, we add up the number of students who read only novel (3), only comics (9), only textbook (2), and all three (5), which gives us 19. So, the number of students who read none of the three categories is 50 - 19 = 31.

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It is assumed that the purchase of equipment and loan receipt occur in July. Although cash sales are evaluated with a 5% reduction, they make up 40% of totality.

Monthly Cash Flow Statement for Gable Supplies Ltd for the three months ending on 30th September 2018:

Month: July August September

Opening Cash: £0 £3,550 £16,700

Cash Inflows:

Share Capital: £55,000

Loan: £110,000

Cash Sales: £45,600 £49,400 £57,000

Credit Sales: £0 £72,000 £78,000

Total Inflows: £160,600 £125,950 £135,000

Cash Outflows:

Loan Repayment: -£2,450 -£2,450 -£2,450

Equipment: -£80,000

Inventory: -£50,000 -£54,000 -£67,500

Wages: -£12,000 -£12,000 -£12,000

Overheads: -£15,000 -£15,000 -£15,000

Rent: -£36,000

Total Outflows: -£157,050 -£109,250 -£118,450

Closing Cash: £3,550 £16,700 £33,250

It is assumed that the purchase of equipment and loan receipt occur in July. Although cash sales are evaluated with a 5% reduction, they make up 40% of totality.

Additionally, credit sales to be accrued in the subsequent month from when the product was sold.

Inventory acquisition constitutes approximately 45% of revenue each month, whereas payments to suppliers get delayed by one month.

Rent, on the other hand, needs to be paid annually but paid beforehand instead of scheduled billing periods.

To note, the non-cash category of expenditures does not encompass depreciation according to the cash flow statement rules.

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The verification of given segments in a triangle are parallel is as follow,

In triangle ABE, AC/ CE = BD/DE  are in proportion ⇒ CD || AB.

In triangle RVS, VT/TR = VU/US  are in proportion ⇒ UT || SR.

In the triangle ABE,

CD is the line segment divides AE and BE into equal parts.

AC = 1.5

CE = 1.5

BD = 1.5

DE = 1.5

AC/ CE = BD/DE

Line divides the two adjacent sides of a triangle are in proportion.

This implies ,

CD is parallel to AB.

In triangle RVS,

VT /TR = 90 /72

⇒VT /TR = 1.25

VU/US = 67.5/54

⇒VU/US = 1.25

This implies ,

VT/TR = VU/US are in proportion.

Hence , triangle proportionality theorem UT is parallel to RS.

Therefore, using triangle proportionality theorem in both the triangle that is,,

In triangle ABE , CD is parallel to  AB and in triangle RVS , UT || RS.

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[tex]\frac{5}{25} = \frac{9}{x +4}[/tex] when simplified, the value of x = 41

Equation is  a mathematical statement that is made up of two expressions connected by an equal value.It says that two things are equal and it expresses equality of two mathematical expressions.

How to determine this

[tex]\frac{5}{25} = \frac{9}{x +4}[/tex]

To find the value of x,

By cross multiplying

5(x+4) = 9(25)

Open bracket

5x + 20 = 225

Collect like terms

5x = 225 - 20

5x = 205

Divides through by 5

5x/5 = 205/5

x = 205/5

x = 41

Therefore, the value of x = 41

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The valid inference based on the information provided is:

Inferences cannot be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.

The study involved only 200 volunteers who were already taking blood pressure medication. This is a relatively small sample size and may not be representative of all blood pressure patients. Inferences about all blood pressure patients cannot be made from this limited sample.

While the group taking the new medication showed a significantly lower overall blood pressure than the group taking the original medication, it was also mentioned that the new medication did not significantly lower cholesterol levels.

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From the pharmaceutical company's test, we can conclude that the new medication is more effective than the original in lowering blood pressure for patients already taking blood pressure medication. However, this conclusion doesn't apply to all blood pressure patients.

A valid conclusion from the scenario about the pharmaceutical company's testing of its new medication would be the following: Inferences cannot be made about all blood pressure patients, though the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients who are already taking blood pressure medication. The study has a specific sample population: people who are already taking blood pressure medication. We can't extrapolate this to all blood pressure patients, because the study didn't include those who don't take any medication. However, it was observed that the new medication was more effective in lowering blood pressure than the original one within this specific group.

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Answer:

Step-by-step explanation:

b. the length of the adjacent side :11

c. you want to know the x which is hypotenuse

d. SOH CAH TOA, you know a and wants to know h, so should use cos function

[tex]g(x)=\sin^2(x)+3\cos(x) \\\\[-0.35em] ~\dotfill\\\\ g(\pi )=\sin^2(\pi )+3\cos(\pi )\implies g(\pi )=[\sin(\pi )]^2+3\cos(\pi ) \\\\\\ g(\pi )=(0)^2+3(-1)\implies g(\pi )=-3[/tex]

For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

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Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

The solution of the each given equations:

(1) x = 9

(2) x = -2

(3) x = -2

(4) x = 26

(5) x = 3/5

(6) x = 13/12

(7) x = 15

(8) x = 26

(9) x = 7/3

(10) x = 5/8

We have to solve this given equation in on variable.

(1) Given equation is,

x - 7 = 2

x = 2 + 7 = 9

Hence, the solution is, x = 9

(2) Given equation is,

3x + 4 = -2

3x = -2 -4

3x = -6

x = -6/3 = -2

Hence, the solution is, x = -2

(3) Given equation is,

2x + 7 = x + 5

2x - x = 5 - 7

x = -2

Hence, the solution is, x = -2

(4) Given equation is,

x/2 = 13

x = 2*13 = 26

Hence, the solution is, x = 26

(5) Given equation is,

5(2 + x) = 13

10 + 5x = 13

5x = 13 - 10

5x = 3

x = 3/5

Hence, the solution is, x = 3/5

(6) Given equation is,

6(2x - 1) = 7

12x - 6 = 7

12x = 7 + 6 = 13

x = 13/12

Hence, the solution is, x = 13/12

(7) Given equation is,

2x/5 = 6

2x = 6*5 = 30

x = 30/2 = 15

Hence, the solution is, x = 15

(8) Given equation is,

x/2 = 13

x = 2*13 = 26

Hence, the solution is, x = 26

(9) Given equation is,

(x - 1)3 = 4

3x - 3 = 4

3x = 4 + 3 = 7

x = 7/3

Hence, the solution is, x = 7/3

(10) Given equation is,

(2x - 1)4 = 1

8x - 4 = 1

8x = 1 + 4

8x = 5

x = 5/8

Hence, the solution is, x = 5/8

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Answer: 30 Feet

Step-by-step explanation: Martin threw the ball 9 feet so we have Martins distance, next we know that Wyatt throws the ball 3 times as far which is 9x3 which is 27, Adeyla threw it 3 feet farther then Wyatt who threw it 27. 27+3=30

So the answer is 30 feet

Using Laws of Exponents, the solution to the given algebraic expression is: m⁹n¹⁵

Some of the Laws of Exponents are:

1) When multiplying the like bases, ensure you keep the base the same and then add the exponents.

2) When raising a base that has a power to another power, ensure you keep the base the same and then multiply the exponents.

3) When dividing like bases, ensure you keep the base the same and then subtract the denominator exponent from the given numerator exponent.

We are given the expression:

(m⁻³n⁻⁵)⁻³

Using the second law of exponents above, we have:

m⁻³*⁻³ x n⁻⁵*⁻³

= m⁹n¹⁵

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Answer:

If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.

To find the value of k, we can use the given values of y and x:

y = kx

24 = k(12)

k = 2

Now that we know k, we can use the equation to find the value of y when x=16:

y = kx

y = 2(16)

y = 32

Therefore, when x=16, y=32.

If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.

Speed is simply referred to as distance traveled per unit time.

It is expressed as:

Speed = distance / time

Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.

The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:

Speed = distance / time

time = distance / speed

time = 50 km / 60 km/h

time = 5/6 hour

Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:

Speed = distance / time

time = distance / speed

time = 50 km / 50 km/h

time = 1 hour

Now, the difference in time between the two scenarios would be:

time difference = 1 hour - 5/6 hour

time = 1/6 hour

Convert to minutes

time = 1/6 × 60

time = 10 minutes

Therefore, the train would be late by 10 minutes.

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Answer:

2 Dozen Chocolate, 3 Dozen Vanilla, 5 Dozen Sugar.

Explanation:

0.5 x 10 = 5.

0.3 x 10 = 3.

0.2 x 10 = 2.

Answer: .025

Step-by-step explanation: we first have to find the distance between each term we divide 12/5 by 6 you have to change it into multiplication so you invert is to 12/5 times 1/6 you then get 12/30 you reduce that to become 2/5 if you want to test this to make sure it is right then you can. you then use a formula but I can't remember it so then you can just multiply it several times to find the answer. you get the answer by round from the thousandths

The equation of the line in the slope-intercept form will be y = (-2/3)x - 2.

Given that:

Points, (-3, -4) and (6, -10)

The equation of the line in slope-intercept form is written as,
y = mx + b

The slope of the line is calculated as,

m = (y2 - y1) / (x2 - x1)

m = (-10 - (-4)) / (6 - (-3))

m = -6 / 9

m = -2/3

Now, to find the y-intercept, we can use the point-slope form of a line:

y - y1 = m(x - x1)

y - (-4) = (-2/3)(x - (-3))

y = (-2/3)x - 2

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The comparison of the function A(t) to the function H(t) is given as follows:

The function A(t) in the context of this problem is given as follows:

A(t) = 1.2H(3t).

The transformations, compared to the function H(t), are then listed and explained as follows:

(multiplication by a value greater than 1 on the range stretches, on the domain it compresses).

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