Rosie's garden is 14 feet long. If she divides the length of the garden into 1/6-foot sections, how many sections will there be in the garden?

The equation for hyperbola with given foci is \(\frac{(x+3)^{2}}{49}-\frac{(y-6)^{2}}{32}=1\)

What is hyperbola?

In analytical geometry, a hyperbola is a conic section that results from the intersection of a plane with a double right circular cone at an angle that touches both of the cone's halves. The two distinct unbounded curves that result from the intersection of the plane and cone are known as hyperbolas.

The standard equation of a horizontal hyperbola with center (h,k) is

\(\frac{(x-h)^{2}}{a^{2} } -\frac{(y-k)^{2}}{b^{2} }=1\)

The given hyperbola has vertices at (–10, 6) and (4, 6).

The length of its major axis is 2a= 4-(-10)

2a=14

a=7

The center is the midpoint of the vertices (–10, 6) and (4, 6).

The center is \((\frac{-10+4}{2} , \frac{6+6}{2} )= (-3,6)\)

Now, we need to use the relation a^2+b^2=c^2 in order to find b^2.

The c-value is the distance from the center (-3,6) to one of the foci (6,6)

c= 6-(-3)=9

So, 7^2+b^2=9^2

b^2= 9^2-7^2

b^2= 81-49

b^2= 32

Hence, on substituting the obtained values in the standard equation of hyperbola, we get

\(\frac{(x-(-3))^{2} }{7^{2}}-\frac{(y-6)^{2} }{32} =1\)

\(\frac{(x+3)^{2} }{49}-\frac{(y-6)^{2} }{32} =1\)

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There are two elements in A' ∩ B.

The given sets are: U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 4, 5}, B = {1, 3, 5, 7}To find the number of elements in A' ∩ B, we first need to find the complement of A,

which is the set of all elements that are not in A.Complement of A: A' = {3, 6, 7}

Now, we need to find the intersection of A' and B.Intersection of A' and B: A' ∩ B = {3, 7}

Therefore, there are two elements in A' ∩ B, which are 3 and 7.

To summarize, we have U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 4, 5}, and B = {1, 3, 5, 7}. The complement of A is A' = {3, 6, 7}.

The intersection of A' and B is A' ∩ B = {3, 7}.

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You would use the ratio to solve this problem.

12:15=4:5

Since the ratio of expected numbers of games they would win to the total number of games they will play is equal to the ratio of number of games they won to the total number of games they played, the answer would be YES.

The equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

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

5y+4= (x+3)²+12

Swap x and y in the equation

So, we have

5x + 4= (y + 3)² + 12

When we make the vairiable y the subject, we have

y = -3 ± √(5x - 8)

Hence, the equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

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The solution to the equations are b = 15, b = 22, c = 21 and n = 28

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

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Next, we collect the like terms in each of the equation

This gives

b = 31 - 16

b = 50 - 28

c = 54 - 33

n = 52 - 24

Lastly, we evaluate the like terms

b = 15

b = 22

c = 21

n = 28

The above are the solutions to the equations

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Question

Solve the following equations:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Answer:

10

Step-by-step explanation:

7*6=3+4+6+9+a+10

42=32+a

42-32=a

a=10

Step-by-step explanation:

Mean =7

⇒(3+4+6+9+a+10)/6=7

⇒32+x=42

⇒x=10

Answer:

x = 10

Step-by-step explanation:

Distribute 4(x - 2)

4x - 8 = 32

Add 8 to both sides

4x = 40

Divide 4

x = 10

Answer:

x = 10

Step-by-step explanation:

4(x-2) = 32

divide both sides of the equation by 4 which gives you

x - 2 = 8

Move the constant to the right and change it's sign which gives you

x = 8 + 2

Add those numbers and you get

x = 10

Answer:

6x  =  36

1 3

Cross multiply:

6x * 3 = 1 * 36

Simplifying

6x * 3 = 1 * 36

Reorder the terms for easier multiplication:

6 * 3x = 1 * 36

Multiply 6 * 3

18x = 1 * 36

Multiply 1 * 36

18x = 36

Solving

18x = 36

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '18'.

x = 2

Simplifying

x = 2

Answer:

1/3 times 1/3

Step-by-step explanation:

the answer is 1/3 * 1/3 because when you divide with fraction you make the 3 or 3/1 turned around which is 1/3, then you multiply 1/3 * 1/3

Therefore, the maximum revenue is $2,925 for a group of 65 people.

An equation is a mathematical statement that shows the equality of two expressions, usually consisting of variables and/or constants. It contains an equals sign (=) that separates the expressions on either side of the sign. Equations are used to solve problems, model real-world situations, and represent mathematical relationships. They can be solved by performing operations on both sides of the equals sign until a solution is obtained.

Here,

Let x be the number of people in the group above 35. If the fair is $60 for a group of exactly 35 people, the revenue for this group would be:

R(35) = $60 x 35 = $2,100

For a group of x people, the fair would be:

$60 - $1x

So, the revenue for this group would be:

R(x) = ($60 - $1x) x

Expanding the expression:

R(x) = $60x - $1x²

To find the number of people that maximize revenue, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:

x = -b/2a

where a = -1 and b = 60

x = -60/(2*(-1))

= 30

So, the size of the group for which the revenue is the greatest is 35 + 30 = 65 people.

To find the maximum revenue, we substitute x = 30 in the equation for R(x):

R(65) = ($60 - $1*30) * 65

= $2,925

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The sustainable growth rate is calculated by subtracting the payout ratio from the ROE.

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE. To calculate the sustainable growth rate for Gold Corp., we must first calculate the retention ratio. The retention ratio is calculated by subtracting the payout ratio from 100%. In this case, the retention ratio would be 100% - 20% = 80%. The sustainable growth rate is then calculated by multiplying the retention ratio by the ROE. In this case, the equation would be 80% * 12% = 9.6%. The sustainable growth rate for Gold Corp. is 9.6%, which can be rounded to 9.6%.

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Answer:

To find the probability of selecting a Coke person from this group, we need to divide the number of people who prefer Coke by the total number of people in the group.

The number of people who prefer Coke is 29. The total number of people in the group is 29 + 21 + 37 + 28 + 19 + 16 + 150 + 150 + 2 = 452.

Therefore, the probability of selecting a Coke person from this group is:

P(Coke) = Number of people who prefer Coke / Total number of people in the group = 29 / 452 ≈ 0.064

So the probability of selecting a Coke person from this group is approximately 0.064.

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

Answer:

y=-7

Step-by-step explanation:

y=3(-4)+5

y=-12+5

y=-7

The solution to the linear system is c = -6 and d = 3.

To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:

(1) 12c + 28d = 12

(2) -20c + 16d = 168

To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:

(1) 60c + 140d = 60

(2) -60c + 48d = 504

Now, we can add the equations:

(60c + 140d) + (-60c + 48d) = 60 + 504

188d = 564

d = 564/188

d = 3

Substituting the value of 'd' back into equation (1):

12c + 28(3) = 12

12c + 84 = 12

12c = 12 - 84

12c = -72

c = -72/12

c = -6

The solution to the linear system is c = -6 and d = 3.

Now let's analyze the second linear system:

(1) 7x - 3y = 43

(2) 7x - 3y = 13

By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.

The linear system has no solution.

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Answer:

65/100 that is the answer to this question

Answer:

6 is 100 times 0.06

Step-by-step explanation:

0.06 times 100 = 6

Answer:

1.5 × 10^14 m²

Step-by-step explanation:

71% of the surface is covered with water.

The total surface of the Earth is 100% of the surface.

100% - 71% = 29%

29% of the surface is not covered with water.

29% of 5.1 × 10^14 m² =

= 0.29 × 5.1 × 10^14 m²

= 1.479 × 10^14 m²

= 1.5 × 10^14 m²

The circumference of the circle is approximately 95.84 cm.

The formula to calculate the circumference of a circle is C = πd, where C represents the circumference and d represents the diameter of the circle.

However, in this case, only the radius (half the diameter) is given. To find the circumference, we need to double the radius and multiply it by the value of π.

Given that the radius is 30.5 cm, we can calculate the circumference as follows:

C = 2πr

C = 2 * 3.14 * 30.5

C ≈ 191.08 cm

Rounding to the nearest hundredth, the circumference of the circle is approximately 95.84 cm.

The circumference of a circle is the total distance around its outer edge. It is calculated by multiplying the diameter of the circle by the value of π (pi), which is approximately 3.14.

In this case, the diameter is not provided, but the radius (half the diameter) is given as 30.5 cm.

To find the circumference, we double the radius (2 * 30.5 = 61) and multiply it by π (61 * 3.14 = 191.54).

Rounding to the nearest hundredth, the circumference of the circle is approximately 95.84 cm.

It's important to note that π is an irrational number and cannot be expressed exactly as a decimal or fraction, which is why we use an approximation like 3.14 in calculations involving circles.

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Answer:

Step-by-step explanation:

The correct answer is true. If you know that the relationship between quantities is proportional, you can use proportions to find missing quantities.

Answer:

c

Step-by-step explanation:

Answer:

1/4 and 3/12

Step-by-step explanation:

1/4=0.25

3/12=0.25

Answer:

geometric

Step-by-step explanation:

Answer:

6.5%

Step-by-step explanation:

The formular used to calculate the cost of preferred stock is:

= Fixed dividend/Net proceeds

Fixed dividend= $50 × 8/100

= $50×0.08

=$4

Net proceeds= Market price-Flotation costs

= $65-(6/100×$65)

= $65-(0.06×$65)

= $65-3.9

= $61.1

Therefore cost of preferred stock is

= 4/61.1 ×100

= 0.065×100

= 6.5%

Hence the cost of preferred stock is 6.5%

Chris' gross pay for the week after selling computer equipment worth $17,000 is $2,600.

The gross pay is the addition of the base pay and the sales commission.

The sales commission is graduated and computed as follows:

Chris' base pay = $300

Sales Commissions:

First $5,000 = 10%

Above $5,000 = 15%

Last week's sales = $17,000

10% Commission = $500 ($5,000 x 10%)

15% Commission = $1,800 ($17,000 - $5,000 x 15%)

Total Commission = $2,300

Gross pay = Base Pay + Commission

= $2,600 ($300 + $2,300)

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The value of x is 30 degrees as it is a complimentary angle. When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.

Reflex angles are those that are larger than 180 degrees and less than 360 degrees. So 270 degrees is a reflex angle.

Since it is a right angle triangle,

hence

\((2x+1)+29=90\\2x+1=61\\2x=60\\x=30\)

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Answer:

For The First Line the answer is 0

For the second line the answer is  0,0

Step-by-step explanation:

I put the picture :)

Enter numbers in the blanks to complete the sentences.

For equations in the form y=kx, if x=0, then y= 0

So the point, 0 then the other box is 0 must be on the graph of every equation in the form y=kx.

I got this correct if this doesn't help I also put the picture that I got it correct :)

Answer:

Step-by-step explanation:

So we know he arrived at 8:11 am. He should've arrived at 8:05 am if he rode the bus. So, we know that it took 27 minutes for him to get to school by walking. If he arrived at 8:11, then he started walking at 7:44 am. Since the school bus arrived 2 minutes before he started walking, we can say that the school bus arrived at 7:42 am.

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Answer:

6 ft

Step-by-step explanation: