a park is in the shape of a regular hexagon 22 km on a side. starting at a corner, alice walks along the perimeter of the park for a distance of 55 km. how many kilometers is she from her starting point?

Answer:

Area= l+b) ×2

6.5x+5ft +5ft

13x+20ft

The point of intersection of the given three planes is (3, -2, 5/3). Elimination is the method for solving a system of equations in which we cancel out a variable.

We may do this by adding or subtracting two or more equations.

Solving the given system of equations using elimination method;

2x + y - 4z - 6 = 0 --- equation 1

x + y + 8z + 13 = 0 --- equation 2.

4x - 5y - 10z - 29 = 0 --- equation 3

Since x and y are already having a coefficient of 1, they would be the easiest to eliminate.

Multiplying equation 1 by -1 and adding to equation 2 eliminates y and results in:

2x + y - 4z - 6 = 0  × -1        -

2x - y + 4z + 6 = 0                        

0 - 3z + 19 = 0                    

Let's denote it as equation 4.

Multiplying equation 1 by 5 and subtracting from equation 3 eliminates y and results in:

2x + y - 4z - 6 = 0     × 5        

10x + 5y - 20z - 30 = 0                        

4x - 10z - 29 = 0                  

Let's denote it as equation 5.

Now we have two equations and two variables:

0 - 3z + 19 = 04x - 10z - 29 = 0

Solving these two equations will give us the values of x, y, and z.

x = 3

y = - 2

z = 5/3

Substitute the value of x, y and z in the equation 1:

2x + y - 4z - 6 = 0

2(3) + (-2) - 4(5/3) - 6 = 0

6 - 2 - 20/3 - 6 = 0

Hence the point of intersection of the given three planes is (3, -2, 5/3).

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Answer:

30 ft squared of border

Step-by-step explanation:

You need to find the area in order to find out how many feet she used.  Length x Width = Area

5x6=30 ft squared

Answer:

30 ft

Step-by-step explanation:

su

Answer:

10a²+5ab+2b²

Step-by-step explanation:

Start by combining like terms aka the ones that match:

Step 1: (4a²-5ab-6b²) + (10ab+6a²+8b²)

Step 2: (10a²-5ab-6b²) + (10ab+8b²)

Step 3: (10a²+5ab-6b²+8b²)

Final answer: 10a²+5ab+2b²

In step 1, I added the 4 and 6. In step 2, I added -5 and 10. In step 3, I added -6 and 8. For each I attached the proper ending (a², ab, and b²).

I hope this clears some confusion!

Answer: d

Step-by-step explanation:

Answer:

V ≈471.24 mm^3

Step-by-step explanation:

The formula for cylinder volume is πr^2 x h, so ((π x 25) x h). That's just 25π x 6. That is about 471.238898, which rounded is almost 471.24. Or, in terms of π, you could leave your answer as 150π mm^3

Answer:

Step-by-step explanation:

The amplitude of a sine function is equal to one-half the distance between the maximum and minimum values of the function.

In this case, the maximum value is approximately 84 customers, and the minimum value is approximately 30 customers

Therefore, the value that is closest to the amplitude of the transformed function is 27 customers.

Answer:

Step-by-step explanation:

So the Yardley people got a raise! Hurray! They make ALL that they made before and a little bit more.

Let x = original pay

100% of x is what they made before.

25% of x is the amount of raise they got.

100% of x should be written 1x, or just x (convert the % to a decimal)

25% of x should be written .25x

So a math sentence that says their original pay plus their raise is now $35 would be written

1x + .25x = 35

Combine the x terms.

1.25x = 35 Now divide both sides by 1.25 to get the x all by itself.

1.25x/1.25 = 35/1.25

x = 28 Remember what x stood for? x is the original pay. The mechanics used to make $28 per hour.

Answer:

A

Step-by-step explanation:

I hope I got it right. If I didn't I'm sorry.

To solve the recurrence relation aₙ = (n+1)aₙ₋₁, we can use iteration to find some terms of the sequence and then look for a pattern.

a₁ = 2a₀ = 2(7) = 14

a₂ = 3a₁ = 3(14) = 42

a₃ = 4a₂ = 4(42) = 168

From these calculations, we might guess that aₙ = (n+1)! * 7 for n ≥ 0. We can prove this by induction.

Base case: a₀ = 7 = (0+1)! * 7 is true.

Inductive step:

Assume that aₙ = (n+1)! * 7 for some arbitrary n ≥ 0.

We want to show that aₙ₊₁ = ((n+1)+1)! * 7.

Using the recurrence relation, we have:

aₙ₊₁ = (n+2)aₙ = (n+2)(n+1)! * 7 = (n+2)! * 7

Therefore, aₙ₊₁ satisfies the formula ((n+1)+1)! * 7, completing the inductive step.

By induction, we have shown that aₙ = (n+1)! * 7 for n ≥ 0. This is the closed-form formula for the given recurrence relation.

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Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

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Answer:

14 5/8

Step-by-step explanation

1) Convert the mixed number to an improper fraction

3 3/8 = 3 x 8 + 3 / 8 = 24 + 3/ 8=  27/8

2) Convert the second mixed number to an improper fraction

4 1/3 = 4 x 3 + 1/ 3 = 12 + 1/3= 13/3

3) Multiply 27/8 x 13/3= 351/24 divided by 3 = 117/8 117/8 as a mixed number is 14 5/8

4) 14 5/8 is the final answer simplified

Answer:

\(\frac{117}{8}\) (or \(14\frac{5}{8}\) in mixed number form)

Step-by-step explanation:

1) First, convert \(3\frac{3}{8}\) and \(4\frac{1}{3}\) into improper fractions. (Multiply the denominator by the whole number at the front, then add the numerator. The number that you receive from this would be the new numerator, and the denominator would still be the same.) This would be \(\frac{27}{8}\) and \(\frac{13}{3}\) respectively.

2) Multiply the two improper fractions. Multiply the numbers of the numerators and denominators together:

\(\frac{27}{8}\)·\(\frac{13}{3}\)

\(\frac{351}{24}\)

3) Simplify the fraction. Find a number that both 351 and 24 can divide evenly into - in this case, it is 3. Divide both 351 and 24 by 3 and receive the final answer:

\(\frac{351}{24}\)÷\(\frac{3}{3}\)

\(\frac{117}{8}\)

If you need it in mixed number form, find what times 8 can get closest to the number 117 without going over it. In this case, it is 14, since 14 times 8 is 112, and 112 is the biggest number closest to 117 that is still under it. 14 would be the whole number at the front Include the remainder, or how far away 112 is from 117, which is 5, at the numerator. The denominator would stay the same. Therefore, the answer in mixed number form is \(14\frac{5}{8}\).

The GCF of 15 and 64 is 1.

The ratio of c and 10 is c:10.

According to the question,

We have the following information:

We have one variable and one number which are c and 10 respectively.

Now, we already know that ratio can be simply understood as division. So, to find the ratio of c and 10 we will divide c by 10. We also know that a variable can not be divided by a number.

(For example, x can not be divided by 20.)

So, we will replace the sign of division by that of the ratio.

c/10

c:10

Hence, the ratio of c and 10 is c:10.

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Answer:

Solve for x

Solve for x is all related to finding the value of x in an equation of one variable that is x or with different variables like finding x in terms of y. When we find the value of x and substitute it in the equation, we should get L.H.S = R.H.S.

x

3

+

11

=

32

3

(

x

+

11

)

=

32

3

(

x

+

11

)

=

32

3

x

+

11

=

32

3

x

+

11

=

32

Step-by-step explanation:

Solve for x

Solve for x is all related to finding the value of x in an equation of one variable that is x or with different variables like finding x in terms of y. When we find the value of x and substitute it in the equation, we should get L.H.S = R.H.S.

What Does Solve for x Mean?

Solve for x means finding the value of x for which the equation holds true. i.e when we find the value of x and substitute in the equation, we should get L.H.S = R.H.S

If I ask you to solve the equation 'x + 1 = 2' that would mean finding some value for x that satisfies the equation.

Do you think x = 1 is the solution to this equation? Substitute it in the equation and see.

1 + 1 = 2

2 = 2

L.H.S = R.H.S

That’s what solving for x is all about.

How Do You Solve for x?

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Let’s start with a simple equation as, x + 2 = 7

How do you get x by itself?

Subtract 2 from both sides

⇒ x + 2 - 2 = 7 - 2

⇒ x = 5

Now, check the answer, x = 5 by substituting it back into the equation. We get 5 + 2= 7.

L.H.S = R.H.S

Answer:

-16

Step-by-step explanation:

-10 + 7/4p = -38  [multiply the entire equation by 4 to get rid of fraction]

-40 + 7p = -152 [add 40 to each side of equation]

7p = -112

p = -112/7 = -16

the second one, as the fraction (4/5) is less than 1

There are a few different steps we need to take in order to answer this question. First, we need to calculate the number of possible rankings for the six corporations. Then, we need to determine the probability of a specific ordering being correct if it is the result of a guess.

a. To calculate the number of possible rankings, we can use the formula n! where n is the number of corporations. In this case, we have 6 corporations, so the number of possible rankings is 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720. So there are 720 different possible rankings for the six corporations.

b. If a specific ordering is the result of a guess, then the probability of it being correct is 1/720. This is because there is only one correct ordering out of the 720 possible rankings. So the probability of a guess being correct is 1/720.

Overall, we can see that there are a large number of possible rankings for the six corporations, and the probability of a guess being correct is very low. This highlights the importance of careful financial analysis in order to accurately evaluate and predict earnings growth rates for corporations.

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Answer:

x=-5

Step-by-step explanation:

First set the values equal to each other;

5x-10=3x-20

Add 10 to both sides;

5x-10+10=3x-20+10

Simplify;

5x=3x-10

Subtract 3x from both sides;

5x-3x=3x-10-3x

Simplify;

2x=-10

Divide both sides by 2;

2x/2=-10/2

Simplify 2x/2;

2/2=1

=x

Simplify -10/2;

Apply the fraction rule;

=-10/2

Divide the numbers ; 10/2

x=-5

Answer:

x = 15

Step-by-step explanation:

<CBD and <DBA equal 90 degrees

5x - 10 + 3x - 20 = 90

8x - 30 = 90

8x = 120

x = 15

Answer:

g(-9)+h(-9)=59

the answer is B

The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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Answer:

101

Step-by-step explanation:

The leftover weight that can be put onto the container (x)

x = 24500 - 12300

x = 12200

The amount of crates that can be hauled into the container

x = 12200 / 120

= 101.6667

We need a whole number so we round down.

= 101

:)

Answer:

\(x-1\)

Step-by-step explanation:

Hi there!

Let \(x\) represent "the number".

The difference of a number and 1

⇒ \(x-1\)

I hope this helps!

False. The intercepted arc is actually twice the measure of the inscribed angle only if the inscribed angle is an angle at the center. If the inscribed angle is not at the center, the intercepted arc will have a different measure.

So, in general, the relationship between the measure of the intercepted arc and the inscribed angle it was created from depends on the location of the inscribed angle in the circle. This is a long answer, but it provides a detailed explanation of the relationship between the intercepted arc and the inscribed angle in different scenarios.

AN intercepted arc is twice the measure of the inscribed angle it was created from.
In a circle, when an inscribed angle is formed by two chords, it intercepts an arc on the circle. According to the Inscribed Angle Theorem, the measure of the inscribed angle is half the measure of the intercepted arc. Therefore, the intercepted arc is indeed twice the measure of the inscribed angle.

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The sum of the values of x where the vertical asymptotes of f/g are located is -2+6+(-3)=1.

The vertical asymptotes of a rational function occur at the values of x that make the denominator equal to zero. Thus, we need to find the values of x that make either 2x^2-2x-24 or 3x+9 equal to zero, since these are the denominators of f(x) and g(x), respectively.

The quadratic equation 2x^2-2x-24=0 can be factored as 2(x+2)(x-6)=0, so the values of x that make f(x) undefined (i.e. the vertical asymptotes of f/g) are x=-2 and x=6.

The linear equation 3x+9=0 can be solved to give x=-3, which is the value of x that makes g(x) undefined.

Thus, the sum of the values of x where the vertical asymptotes of f/g are located is -2+6+(-3)=1.

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The sample space for rolling a fair eight-sided die is {1, 2, 3, 4, 5, 6, 7, 8}.

We have to find the sample space for rolling a fair eight-sided die.

The sample space for rolling a fair eight-sided die consists of all the possible outcomes of a single roll of the die.

As the die has eight sides numbered from 1 to 8, the sample space can be represented as:

S = {1, 2, 3, 4, 5, 6, 7, 8}

Therefore, the sample space for rolling a fair eight-sided die is {1, 2, 3, 4, 5, 6, 7, 8}.

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The future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

To find the future value of the fund on January 1, 2018, just after the third deposit, we can use the compound interest formula:

\(FV = P(1 + r/n)^{nt}\)

Where:

FV = Future Value

P = Principal amount (initial investment)

r = Annual interest rate (expressed as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

Let's calculate the future value step by step:

First deposit:

P = $16000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 4.333 years (from September 1, 2010, to March 1, 2015)

\(FV_1 = 16000(1 + 0.072/12)^{(12*4.333)}\\= 16000(1 + 0.006)^{52}\\= 16000(1.006)^{52}\\= 20,296.43\)

Second deposit:

P = $13000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 2.917 years (from March 1, 2015, to January 1, 2018)

\(FV_2 = 13000(1 + 0.072/12)^{(12*2.917)}\\= 13000(1 + 0.006)^{35}\\= 15,618.04\)

Third deposit:

P = $12000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 0.084 years (from January 1, 2018, to January 1, 2018)

\(FV3 = 12000(1 + 0.072/12)^{(12*0.084)}\\= 12000(1 + 0.006)\\= $12,072.00\\\)

Adding up the future values:

\(Total FV = FV_1 + FV_2 + FV_3\)

= $20,296.43 + $15,618.04 + $12,072.00

≈ $47,986.47

Therefore, the future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

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The number that is 9 times greater than a given number "d" can be found by multiplying "d" by 9, the number is 9d.

The greater than symbol indicates that one number is greater than the other. When a number is marked with a larger than or equal sign, it signifies the leftmost number is more than or on par with the rightmost number. The number on the left is less than the number on the right if the less than symbol is present.

The symbols for larger than and less than are additionally referred to as inequality symbols. Inequality means not equal. These symbols are great when comparing two values that may not be equal.

The number that is 9 times greater than a given number "d" can be found by multiplying "d" by 9. Therefore, the number is 9d.

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From the question;

we are to state the three reasons why a function might be discontinuous at the point x=c

A funtion f(x) is discontinuous at a point x = c if

1.

2.

3.

If all this condition are statisfied, then the function is discontinuous at x = c