What are the corresponding rectangular coordinates for point Q equals the ordered pair 6 comma 5 times pi over 6 given in polar coordinates

Answer:

The first one is g(x)=1/4x-7

Step-by-step explanation:

Step-by-step explanation:

therefore, the correct option is option number 1.

Answer:

Step-by-step explanation: [tex](\sqrt[4]{x})^{2} - 3\sqrt[4]{x} -4=0[/tex]

[tex]\sqrt[4]{x} = u[/tex] ⇒ u² - 3u -4 =0 ⇒ [tex]\left \{ {{u=4} \atop {u=-1}} \right.[/tex] choose u=4 ( [tex]\sqrt{x} > 0[/tex] )

⇒ x=256

Answer:

To solve the system of equations:

2/3x + 3/5 y = 12 --- equation (1)

5/2y - 3x = 6 --- equation (2)

We can use the method of substitution or elimination. Here, we will use the elimination method to eliminate one variable and solve for the other.

Multiplying equation (1) by 5 and equation (2) by 3, we get:

10/3x + 9/5y = 60 --- equation (3) obtained from (1) by multiplying both sides by 5

15/2y - 9x = 18 --- equation (4) obtained from (2) by multiplying both sides by 3

Now, we can eliminate y by multiplying equation (3) by 10/9 and adding it to equation (4):

(10/3x + 9/5y) x 10/9 + (15/2y - 9x) = 0

Simplifying this equation, we get:

20x/9 - 27x/5 = -100/3

Multiplying both sides by 45, we get:

20x(5) - 27x(9) = -1500

Simplifying and solving for x, we get:

-65x = -1500

x = 23.08 (rounded to two decimal places)

Substituting x = 23.08 into equation (1), we can solve for y:

2/3(23.08) + 3/5 y = 12

15.39 + 0.6y = 12

0.6y = -3.39

y = -5.65 (rounded to two decimal places)

Therefore, the solution to the system of equations is x = 23.08 and y = -5.65.

So, the solution to the system of equations is (23.08, -5.65).

Hope this helps.

Answer:

[tex]\huge\boxed{\sf x = 130\°}[/tex]

Step-by-step explanation:

So,

90 + 90 + 50 + x = 360

230 + x = 360

x = 360 - 230

[tex]\rule[225]{225}{2}[/tex]

Answer:

156.76 days (approx.)

Step-by-step explanation:

To calculate the Cash Cycle, we need to consider the time it takes for a company to convert its investment in inventory and receivables back into cash. The formula for Cash Cycle is as follows:

Cash Cycle = Inventory Conversion Period + Receivables Collection Period - Payables Deferral Period

Now, let's calculate each component of the Cash Cycle using the given information.

1. Inventory Conversion Period:

Inventory Conversion Period measures the average number of days it takes to convert raw materials into finished goods.

Average Inventory = (Opening Raw Material + Closing Raw Material) / 2

= (4,00,000 + 5,00,000) / 2

= 4,50,000

Manufacturing Costs per day = Manufacturing Costs / 360 days

= 10,45,000 / 360

= 2,902.77 (approx.)

Inventory Conversion Period = Average Inventory / Manufacturing Costs per day

= 4,50,000 / 2,902.77

≈ 155 days

2. Receivables Collection Period:

Receivables Collection Period measures the average number of days it takes to collect payments from customers.

Average Receivables = (Opening Debtors + Closing Debtors) / 2

= (2,50,000 + 3,15,000) / 2

= 2,82,500

Sales per day = Total Sales / 360 days

= 4,20,00,500 / 360

= 1,16,666.67 (approx.)

Receivables Collection Period = Average Receivables / Sales per day

= 2,82,500 / 1,16,666.67

≈ 2.42 days

3. Payables Deferral Period:

Payables Deferral Period measures the average number of days the company takes to pay its suppliers.

Average Payables = (Opening Creditors + Closing Creditors) / 2

= (5,60,000 + 6,25,000) / 2

= 5,92,500

Purchases per day = Total Purchases / 360 days

= 3,23,00,000 / 360

= 8,97,222.22 (approx.)

Payables Deferral Period = Average Payables / Purchases per day

= 5,92,500 / 8,97,222.22

≈ 0.66 days

Now, we can calculate the Cash Cycle using the formula mentioned earlier:

Cash Cycle = Inventory Conversion Period + Receivables Collection Period - Payables Deferral Period

= 155 days + 2.42 days - 0.66 days

≈ 156.76 days (approx.)

Therefore, the Cash Cycle is approximately 156.76 days based on the given information.

The values of x and y are

1. x= 35 and y= 25

2. x = 4  and y = 1

3. x = 2 and y= 5

1. We know that opposite angle of parallelogram are equivalent

So, 2x = 70

x= 35

and, 3x +5 = x + 3y

105 + 5= 35 + 3y

110 - 35 = 3y

3y = 75

y = 25

2. Now, the diagonals bisect each other

3x = 12

x= 4

and, x + y = 5y

4 + y = 5y

4y = 4

y= 1

3. Now, opposite sides are congruent then

3x = 6

x= 2

and, x + 2= y-1

4 = y  -1

y = 5

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1) The values of x and y are,

x = 35, y = 25

2) The values of x and y are,

x = 4, y = 1

3)  The values of x and y are,

x = 2, y = 5

We know that;

Sum of opposite angles in a rectangle is 180 degree and diagonal are bisects each other.

And, Opposite sides of a parallelogram has equal length.

Hence, WE can formulate;

1) WE get;

2x = 70

x = 35

And, 3x + 5 = x + 3y

3 x 35 + 5 = 35 + 3y

105 + 5 = 35 + 3y

110 - 35 = 3y

3y = 75

y = 25

2) Since, diagonal are bisects each other.

Hence, we get;

3x = 12

x = 4

And, x + y = 5y

4 + y = 5y

4y = 4

y = 1

3) Opposite sides of a parallelogram has equal length.

Hence, WE get;

3x = 6

x = 2

And, x+ 2 = y - 1

2 + 2 = y - 1

y = 5

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The correct statement that F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

To determine whether the function shown in the table is exponential, we need to analyze the relationship between the x-values and y-values.

The table shows x-values that are increasing by a power of 2 (1, 2, 4, 8, 16, 32, 64) and y-values that are increasing by a constant rate of 1 (0, 1, 2, 3, 4, 5, 6).

The constant ratio between consecutive x-values indicates exponential growth or decay.

In this case, the function is growing exponentially because the y-values are increasing at a constant rate.

Based on this information, we can conclude that the function is exponential.

Therefore, we agree with statement F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

The other statements are incorrect because they do not accurately describe the relationship between the x-values and y-values in an exponential function.

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Answer:

x^3 + 2x - 1.

Step-by-step explanation:

To simplify the expression 2x + x^3 - 1, we can first rearrange the terms in decreasing order of the exponents:

x^3 + 2x - 1

So the simplified expression, rearranged in descending order, is x^3 + 2x - 1.

The scale factor used is:

1 centimeter equals half millimiter.

The scale factor tells us how many units in the sculpture represent a real unit.

We know that:

Real length = 9mm

Length in the sculpture = 18cm

Then we have the relation between the lengths:

18cm = 9mm

Dividing both sides by 18 we will get:

1cm = 9mm/18

1cm = 0.5mm

So the scale is 1 centimeter equals half millimiter.

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The correct way to calculate the percent change between the original value of $750 and the new value of $1,000 is option C.

C. (1,000 - 750)/750 = 250/750 = 1/3 ≈ 0.3333 = 33.33%

Therefore, the correct answer is option C, which represents a percent change of approximately 33.33%.

The 19  tykes  given away by the Shelter, that have room for only 4  tykes  per family.        

The number of different canine families that could be created from the 19  tykes  given away by the  sanctum, we need to calculate the number of combinations. room for only 4  tykes , we need to choose 4  tykes  from the aggregate of 19  tykes . The order of the  tykes  in the family doesn't count, as long as we choose different  tykes  for each family.  The number of combinations can be calculated using the formula for combinations  C( n, r) =  n!/( r!( n- r)!)  Where C( n, r) represents the number of combinations of choosing r  particulars from a set of n  particulars.  In this case, we've n =  19( total number of  tykes ) and r =  4( number of  tykes  per family).  Plugging these values into the formula, we get  C( 19, 4) =  19!/( 4!( 19- 4)!)  Calculating the factorial values  19! =  19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =  ! =  4 × 3 × 2 × 1 =  24  15! =  15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =   Substituting these values into the formula  C( 19, 4) = /( 24 ×)  ≈ 91,390  The 19  tykes  given away by the  sanctum, considering that you have room for only 4  tykes  per family.

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Hello!

√4 = ±2

√4x = ±2x

Y = -5x + 3 is the equation represents a line which is parallel to the line Y = -5x - 7 with y intercept 3

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the equation which  represents a line which is parallel to the line Y = -5x - 7 with y intercept 3

We know that the parallel lines will have same slope

In the above equal -5 is the slope and y intercept -7

The equation of parallel line y =-5x+3

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Which equation represents a line which is parallel to the line

Y = -5x - 7 and of intercept 3

Answer:

The answer is 3.1 to 1d.p

Step-by-step explanation:

1)4p+2q=2

2)5p+7q=8

3)7(4p+2q=2)

4)2(5p+7q=8)

3)28p+14q=14

4)10p+14q=16

18p=2

divide both sides by 18

18p/18=2/18

p=1/9

substitute into equation 1

4(1/9)+2q=2

4/9+2q=2

2q=2-4/9

2q=14/9

divide both sides by 2

2q/2=14/9/2

q=28/9

q=3.1 to 1d.p

The percentage strength of the compound is approximately 1.96%.

We have,

To determine the percentage strength of the compound, we need to calculate the ratio of the mass of the active ingredient (hydrocortisone powder) to the total mass of the compound and express it as a percentage.

Given:

Mass of hydrocortisone powder = 3 g

Mass of petrolatum = 150 g

Total mass of the compound

= Mass of hydrocortisone powder + Mass of petrolatum

= 3 g + 150 g = 153 g

To calculate the percentage strength, we divide the mass of the hydrocortisone powder by the total mass of the compound and multiply by 100:

Percentage strength = (Mass of hydrocortisone powder / Total mass of the compound) x 100

Percentage strength = (3 g / 153 g) x 100

Percentage strength ≈ 1.96%

Therefore,

The percentage strength of the compound is approximately 1.96%.

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Step-by-step explanation:

Let the boys be x

Girls = x - 14 (number of females is 14 less than the number of males)

x + x - 14 = 32

2x - 14 = 32

2x = 32 + 14 (add 14 to both sides or if 14 crosses over the bracket. The sign changes to plus or positive)

2x = 46

Divide both sides by 2

x = 23

Girls = x - 14 = 23 - 14

=9

Therefore, The boys are 23, while the girls are 9

The scale factor of the perimeters from figure A to figure B is 1.5. Scale factor is the ratio of any two corresponding lengths in two similar figures.

Here, the two figures are similar, that is why we can find the scale factor by dividing corresponding sides of one figure by the corresponding sides of another figure. We will find the scale factor for the perimeter of figures A and B below:Perimeter of figure A = 12 + 10 + 18 = 40 unitsPerimeter of figure B = 15 + 15 + 15 = 45 unitsTo find the scale factor of the perimeters, we divide the perimeter of figure B by the perimeter of figure

A:Scale factor of the perimeters = (Perimeter of figure B)/(Perimeter of figure A) = 45/40 = 1.125To simplify any fractional answer, we have to convert it to the lowest terms, which is 9/8. The decimal answer 1.125, when rounded to the nearest tenth is 1.1. Therefore, the scale factor of the perimeters from figure A to figure B is 1.5.

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The volume of the given triangular pyramid is 59.2 feet³.

Given figure is that of a triangular pyramid.

We have to find the volume of the pyramid.

Volume of a pyramid = 1/3 × base area × height

Here base is triangular.

Base area = 1/2 × 12 × 3.7

                  = 22.2 feet²

Height of the pyramid = 8 feet

Volume = 1/3 × 22.2 × 8

             = 59.2 feet³

Hence the volume is 59.2 feet³.

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Answer:

55

Step-by-step explanation:

You just need to divide 220 ÷ 4 = 55

Hope this helps :)

Pls brainliest...

Answer:

  (x, y) = (3, 4)

Step-by-step explanation:

You want to solve the system of equations by combining the equations:

The coefficients of x have the same value (1), so we can eliminate x by multiplying one of the equations by -1 and adding the result. Since we want the resulting coefficient of y to be positive, we choose to multiply the first equation by -1.

  [tex]\begin{array}{c,l,l,l}-1&(x&-y&=-1)\\+1&(x&+8y&=35\,)\end{array}[/tex]

Then the sum is ...

  [tex]\begin{array}{rcl}-x&+y&=1\\x&+8y&=35\\\cline{1-3}0x&+9y&=36\end{array}[/tex]

The solution to this is ...

  y = 36/9 = 4

  x = y -1 = 4 -1 = 3 . . . . . . from the first equation

The solution is (x, y) = (3, 4).

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Step-by-step explanation:

If the sin 0° = 0, then which statement is true?

1) cos 90° = 0, because the cosine and sine are complements

2) cos 180° = 1, because the cosine and sine are supplements

3) cos 90° = 1, because the cosine and sine are complements

4) cos 180° = 0, because the cosine and sine are supplementscc

Answer:

Rate of slower train: 110 km/h

Rate of faster train: 122 km/h

Step-by-step explanation:

The explanation is attached below.

The mean of this sample data consisting of 10 randomly selected values from the table is 21.

The mean describes the average value in the data set.

The average is one of the measures of central tendency, including the median and the mode.

We can compute the mean or the average by dividing the total value in the data set by the number of items.

7+ 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38

Total = 210

Mean = 21 (210 ÷ 10)

Thus, the mean is the quotient of the total value and the number of items in the data set or sample.

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What is the mean of this sample, which consists of 10 values randomly selected from the table?

7+ 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38

The probability of not selecting a blue marble is 3/5

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. It is the rate of the number of favorable outcomes to the total number of outcomes of an event.

How to determine this

A bag contains 6 blue marbles, 5 yellow marbles, 3 white marbles and 1 red marble

i.e 6 + 5 + 3 + 1 = 15 marbles

To calculate the probability of not selecting a blue marble

When blue marbles = 6

= [tex]\frac{15-6}{15}[/tex]

= [tex]\frac{9}{15}[/tex]

= 3/5

= 0.65

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Answer:

≈0.71441

Step-by-step explanation:

1. to calculate the area of the given circle;

2. to calculate the area of the rectangle ABCD;

3. to divide the area of the circle by the area of the rectangle ABCD

and to calculate the rest part.

All the details are in the attachment.

Ryan's Social Security retirement benefit, computed using the given formula, is $2,188.89 per month.

To calculate Ryan's Social Security retirement benefit, we'll break it down into three parts based on the given formula:

First, we shall estimate 90% of the first $926 of Ryan's average monthly earnings:

Benefit from level 1= 0.9 * $926

Next, we find out 32% of  the amount between $926 and $5,583:

Benefit from level 2= 0.32 * ($5,583 - $926)

Lastly, we compute 15% of the amount over $5,583:

Benefit from level 3= 0.15 * (Ryan's average monthly earnings - $5,583)

Ryan's retirement benefit is the sum of the benefits from all three level:

Retirement benefit = Benefit from level 1 + Benefit from level 2 + Benefit from level 3

Benefit from level 1:

= 0.9 * $926 = $833.40

Benefit from level 2:

= 0.32 * ($5,583 - $926) = 0.32 * $4,657 = $1,489.44

Benefit from level 3:

= 0.15 * (Ryan's average monthly earnings - $5,583)

= 0.15 * ($4,690 - $5,583)

= 0.15 * (-$893)

= -$133.95 (Ryan's average monthly earnings are less than $5,583, this amount is negative)

We now calculate the retirement benefit:

Retirement benefit = Benefit from level 1 + Benefit from level 2 + Benefit from level 3

= $833.40 + $1,489.44 - $133.95

= $2,188.89

Therefore, Ryan's Social Security retirement benefit is $2,188.89 per month.

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Al the nth term are,

1) a (n) = 6 + 4n

2) a (n) = 26 + 8n

3) a (n) = 23 - n

4) a (n) = 7n - 3

5) a (n) = 8n - 43

We have to given that;

All the sequence are,

1.10,14,18,22..

2.34,26,18,10,..

3.17;11;5;-1;-7;..

4.4;11;18;25;..

5.-35;-27;-19;-11;..​

Now, WE can find the nth term as;

1) 10,14,18,22..

Here, a = 10

Common difference = 14 - 10 = 4

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 10 + (n - 1)4

a (n) = 10 + 4n - 4

a (n) = 6 + 4n

2) 34,26,18,10,..

Here, a = 34

Common difference = 26 - 34 = 8

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 34 + (n - 1)8

a (n) = 34 + 8n - 8

a (n) = 26 + 8n

3) 17;11;5;-1;-7;..

Here, a = 17

Common difference = 11 - 17 = - 6

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 17 + (n - 1) (- 6)

a (n) = 17 - 6n + 6

a (n) = 23 - n

4) 4;11;18;25;..

Here, a = 4

Common difference = 11 - 4 = 7

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = 4 + (n - 1) (7)

a (n) = 4 + 7n - 7

a (n) = 7n - 3

5) -35;-27;-19;-11;..​

Here, a = - 35

Common difference = - 27 + 35 = 8

Hence, The nth term is,

a (n) = a + (n - 1) d

a (n) = - 35 + (n - 1) (8)

a (n) = - 35 + 8n - 8

a (n) = 8n - 43

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