Given the point with Cartesian coordinates, (3√3,−3), find the polar coordinates of the point.

The direction and angle of rotation include the following: C. 180° counterclockwise rotation.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point A (-6, 5)  →  Coordinates of point A' = (6, -5)

In conclusion, this transformation rule (x, y) → (-x, -y) is used for the 180° rotation of a geometric figure about the origin in a clockwise or counterclockwise (anticlockwise) direction.

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Brand B contains 3% saline solution by volume. Then, C is the right answer.

Percentage of saline solution in brand B, let x be.

We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.

Then the equation is given as,

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

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Answer: The width of the garden/fence will be 15 m.

Step-by-step explanation: First, we have to understand that there will be two wide sides and two long sides, and in a rectangle, the long sides always equal each other and the wide sides equal each other as well. This means that one width and one length will equal 120/2=60.

In other words:

one length of the garden + one width of the garden = 60

Now that we know this, we move on to the "3 times" part of the question. For this step, it is easiest to imagine quarters of something, because 3/4 of something will always be 3 x 1/4 of something; The proportion for 3/4:1/4 will always be 3:1.

60 x 3/4 is equal to 45 and 60 x 1/4 is equal to 15.

To check our answer, L+W+L+W = 45+15+45+15 = 120.

This means each wide side is equal to 15.

Answer: (a. x^4/2yz)^2       b. -3ab             c. 2(3a^2-2ab+1)/3ab                   d. -(xy^2+2y^2-4)/4xy             QUESTION 5: a. (7y^3+6v^3+3v^2)/v       b. 9x^2-7x-8

Step-by-step explanation:

For many of these, you must be able to see that anything to the first is just that number, so it will be useless to write z^1 in question one. You can then factor out, and cancel out the numbers that are the same. Then, you can simplify. This is how you can do all of these. This is a very complicated process nd will take a while to do, but once you are able to do it, it becomes easy. If you still are having trouble understanding, you can put it into a long division calculator for polynomials, and they will show you the steps. For the fifth questions, we can cancel out the common factors, and we can also apply rules such as the fraction rule or the exponent rule to do this. The key thing here is to simplify to make it easier when you divide and multiply.

Hope this helps

Mark brainlist please!

Answer:

Therefore, the percentage change from 20 to 50 is an increase of 150%.

Step-by-step explanation:

To work out the percentage change from 20 to 50, we can use the following formula:

((New Value - Old Value) / Old Value) x 100%

Plugging in the numbers, we get:

((50 - 20) / 20) x 100%

= (30 / 20) x 100%

= 1.5 x 100%

= 150%

28% of the mixture is fruit juice.

Given that, Adriana mixed 6 L of Brand A juice with 9 L of Brand B juice. Brand A contains 52% fruit juice and Brand B contains 12% fruit juice.

We need to find that what percent of the mixture is fruit juice,

So,

Fruit juice in Brand A = 6 × 0.52 = 3.12 L

Fruit juice in Brand B = 9 × 0.12 = 1.08 L

So, (3.12 + 1.08 / 6 + 9) × 100%

= 28%

Hence 28% of the mixture is fruit juice.

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1. The volume of the pyramid = 12 mm³.

2. Slant height (x) x ≈ 4.3 mm

3. Surface area of square pyramid = 86.4 mm²

1. The volume of the pyramid (V) = 1/3*a²h, where:

a is the base edge = 3 mm

h is the height = 4 mm

Plug in the values:

The volume of the pyramid (V) = 1/3*3²*4 = 12 mm³.

2. Slant height (x) = √(1.5² + 4²)

x ≈ 4.3 mm

3. Surface area of square pyramid = 6bs + b² = 6(3)(4.3) + 3²

= 86.4 mm²

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Part(a),

The exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^x[/tex]

Part(b),

The predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

Part(c),

The predicted total sales of food and drink in 2018 is 1756 billion dollars

Part(d),

If the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

(a) To model the total spent on food and drinks as an exponential function of the number of years since 1990, we can use the general form of an exponential function:

[tex]T = a \times b^t[/tex]

where T is the total spent in billions of dollars, t is the number of years since 1990, a is the initial amount spent in 1990, and b is the growth factor or base of the exponential function.

Using the given information, we can set up two equations:

T(0) = 641 (total spent in 1990)

T(13) = 1016 (total spent in 2003, which is 13 years after 1990)

Substituting these values into the exponential function, we get:

[tex]641 = a \timrd b^0[/tex] => a = 641

[tex]1016 = a b^{13[/tex] => [tex]b = (\dfrac{1016}{641})^{\frac{1}{13}[/tex]

Therefore, the exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13})^x[/tex]

(b) To predict the amount spent in 2000, we need to substitute t = 10 (since 2000 is 10 years after 1990) into the exponential function:

[tex]T(10) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{10[/tex] ≈ 964

Therefore, the predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

(c) To predict the total sales of food and drink in 2018, we need to substitute t = 28 (since 2018 is 28 years after 1990) into the exponential function:

[tex]T(28) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{28[/tex] ≈ 1756

Therefore, the predicted total sales of food and drink in 2018 is 1756 billion dollars (rounded to the nearest integer).

(d) To estimate when the total sales will reach 2 trillion dollars, we need to solve for t in the exponential function when T(t) = 2000 (since 2 trillion dollars is equivalent to 2000 billion dollars):

[tex]2000 = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^t[/tex]

[tex]ln(\dfrac{2000}{641}) = t \times ln((\dfrac{1016}{641})^{(\frac{1}{13})[/tex]

[tex]t = \dfrac{ln(\dfrac{2000}{641})} { ln((\dfrac{1016}{641})^{(\frac{1}{13})) }}[/tex]

t = 32.72

Therefore, if the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

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Jocelyn would need to save $1333.33 each year with 7% interest.

To calculate how much Jocelyn needs to save for the down payment over the next three years, we first need to determine the total down payment required. If the down payment is stated as $4000, then that is the total amount needed.

Assuming that Jocelyn wants to make the down payment in three years, we can calculate how much she needs to save each year by dividing the total down payment by three:

$4000 / 3 years = $1333.33 per year

So Jocelyn would need to save approximately $1333.33 each year for the next three years in order to have enough for the $4000 down payment.

Correct Question :

JUST $4000 DOWN PAYMENT!

LOW 7% INTEREST RATE!

5 YEARS TO REPAY YOUR LOAN!

In order to afford the down payment, how much will Jocelyn need to save for each of the next three years

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Suppose a trapezoid is defined as a quadrilateral with at least 1 pair of parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.

In geometry, a quadrilateral with at least one set of parallel sides is referred to as a trapezium in American or Canadian English, or a trapezium in British as well as other forms of English. In Euclidean geometry, a trapezium is a convex quadrilateral by definition. The bases of a trapezium are the parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.

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Answer:

Solution: It is given that Miguel needs to cut a board that is Two-thirds of a yard long into 3 equal pieces. It means is divided in 3 equal parts.

Step-by-step explanation:

The third term in the expansion of the expression (5x - 7y)³ is 735xy².

Given expression is,

(5x - 7y)³

We have to expand this.

We know that,

(a + b)³ = a³ - 3a²b + 3ab² - b³

Using this,

(5x - 7y)³ = (5x)³ - (3 × (5x)² × 7y) + (3 ×(5x) × (7y)²) - (7y)³

               = 125x³ - (3 × 25x² × 7y) + (3 × 5x × 49y²) - 343y³

               = 125x³ - 525x²y + 735xy² - 343y³

Here the third term is 735xy².

Hence the third term is 735xy².

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Answer:

The area of this polygon is 14 square units.

Answer:

Step-by-step explanation:

The option that is greater than 4 is option (a) 5. This is because 5 is a positive value that is larger than 4. Option (b) -5 is a negative value that is less than 4. Option (c) -1/2 is also negative and less than 4. Option (d) -25 is the most negative option and therefore less than 4. So, the only option that is greater than 4 in this case is 5.

Answer:

a

Step-by-step explanation:

got it right on edge

Answer:

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

Direct variation equation:

Use the first pair of coordinates, x = 3 and y = 8 to find the value of k:

The equation becomes:

Now use the value of x = 18 to find the missing coordinate:

The three sides of the triangle are a, b, P - (a + b)

The length of the missing side, and the lengths of all three sides of a triangular corner shelf.

Given that one side of the triangular shelf measures "a" units and another side measures "b" units, we can find the total of two sides by adding them together:

a + b = total of two sides

If the perimeter of the triangle measures "P" units, we know that the perimeter is the sum of all three sides, so:

a + b + c = P

where "c" is the length of the missing side. We can rearrange this equation to solve for "c":

c = P - a - b

To find the lengths of all three sides of the triangle, we can substitute the value of "c" that we just found into the Triangle Inequality:

a + b > P - a - b

Simplifying this inequality, we get:

2a + 2b > P

Dividing both sides by 2, we get:

a + b > P/2

So, if "a + b > P/2", then the triangle can exist, and we can use the value of "c" that we found earlier to get the lengths of all three sides:

a + b + c = P

a + b + (P - a - b) = P

c = P - (a + b)

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Answer:

Almost equals 28°

Step-by-step explanation:

cos(x)= 12/18

x= cos^-1 (12/18)

So it equals 48.1896°

Answer:

00:00 in 12-hour clock time is equivalent to 12:00 midnight. It is the start of a new day and is the first minute of the 12-hour time cycle.

We can answer the questions in the following way:

Barriers to economic development are all those things that hinder the growth and development of an economy of a nation.

Many factors act as barriers to economic development, like lack of education, healthcare, inadequate infrastructure, lack of access to capital, etc.

These barriers can hinder people's ability to achieve their full potential, and lead to lower levels of economic growth and development.

Taking care of these issues by the government is important to promoting sustainable economic development.

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The fish tank that has a capacity of 60 gallons is given as follows:

A. Pacific.

The fish tank that has a capacity of 60 gallons obtained applying the proportions in the context of the problem.

The rate between quarts and gallons is given as follows:

1 gallon = 4 quarts.

Hence the capacity in quarts equivalent to 60 gallons is given as follows:

60 x 4 = 240 quarts.

Meaning that the Pacific fish tank has a capacity of 60 gallons.

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Answer:

C. 3 pounds

Step-by-step explanation:

to use % as factors we need to represent them as what they are : parts of 100.

so, e.g. 20% = 0.2 and so on.

x = pounds of the metal with 20% nickel.

0.2x + 0.8×6 = 0.6×(x + 6) = 0.6x + 3.6

0.2x + 4.8 = 0.6x + 3.6

1.2 = 0.4x

x = 1.2/0.4 = 3

she needs to combine 3 pounds of metal with 20% nickel with 6 pounds with 80% nickel to get 9 pounds (3+6) of an alloy with 60% nickel.

If male and female students of section B in DPS and DAV are in ratio 3 : 2 and 4:3 respectively then male students of section B are 40% more than female students of section B considering both the schools (approx).

(A) 50% (C) 36% (B) 25% (D) 40%.

Hence, the correct option is D.

Let us assume that there are 3x male students and 2x female students in section B of DPS, and there are 4y male students and 3y female students in section B of DAV. We can set up the following equations to represent the given ratios

3x : 2x = male : female in DPS section B

4y : 3y = male : female in DAV section B

By simplifying these ratios, we get

3 : 2 = x/y for DPS section B

4 : 3 = x/y for DAV section B

Solving for x and y, we get

x = 6y for DPS section B

x = 4.5y for DAV section B

Now, let us add the male and female students in section B from both schools.

Male students = 3x + 4y = 3(6y) + 4(4.5y) = 30y

Female students = 2x + 3y = 2(6y) + 3(4.5y) = 21y

So, the ratio of male to female students in section B from both schools combined is

30y : 21y = 10 : 7

Therefore, male students are (10 - 7)/7 = 3/7 = 0.4286 (approx. 43%) more than female students in section B from both schools combined.

However, the question asks for the percentage more, so we need to multiply this answer by 100 to get a percentage.

0.4286 x 100 ≈ 42.86%

Therefore, male students in section B are approximately 42.86% more than female students in section B from both schools combined. Rounding to the nearest percent that is 40%.

Hence, the correct option is D.

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Answer: $105

Step-by-step explanation:

I would take 5+2=7 then take 7×15=105

Answer is $105 to ship.

Answer: 16

Step-by-step explanation:

I am not sure if this answer is 100% correct, but I believe this is a question involving proportions.

If you create a proportional equality equation that looks like this:

[tex]\frac{40}{30}=\frac{x}{12}[/tex]

It will give the x value as the answer to the problem. This is because the two triangles are proportional to one another.

The wheel will make one complete revolution around the circle after travelling a distance of 62.8 inches.

The distance that the wheel travels around the circle once is equal to the circumference of the circle.

The formula for circumference of a circle is given as;

D = 2πr

where;

The radius of the circle = 10 inches

The circumference of the circle is calculated as follows;

D = 2 x 3.14 x 10

D = 62.8 inches

Thus, the circumference of the circle is determined as 62.8 inches.

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Answer:

  9

Step-by-step explanation:

You want the least common denominator for the fraction in the sum ...

 (2/3)² -1/3

When the sum is simplified, it is ...

  4/9 -1/3

The denominator 9 is a multiple of the denominator 3, so the least common denominator of these two fractions is 9.

__

Additional comment

Using that denominator, the sum is ...

  4/9 -3/9 = 1/9

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Answer: x = -5, 5 y= 0

Step-by-step explanation:

vertical asymptotes = x= -5, 5

horizontal asymptotes = y= 0