x^2+4x+y^2-10y+20=30 find the center of the circle by completing the square

Answer:

27

Step-by-step explanation:

4.5*3*2 = 27

hi,

You just have to multiply the three measures.  

So :  

2*3*4.5 =  27 cm³

Easy, is it not ?  

Leah may utilize gg, or the amount of gigabytes of data she can consume while keeping under her spending limit, by solving the equation 4g + 42= 48.80, where g has a value of 1.7.

She is known to pay a fixed fee of 42, therefore that number will serve as our constant. We may use 4g to symbolize the $4 per gigabyte utilized that she pays. 4g + 42 = 48.80 will be our equation.

To isolate g is what we want. We can do that by taking 42 off of both sides. The result is 4g = 6.8. Next, multiply each side by four. Thus, we have g = 1.7.

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Answer:he's right

Step-by-step explanation:

The distance between the opposite sides of the trampoline can be found to be 14. 42 yards

To find the distance between the opposite sides of the trampoline, we are essentially finding the diagonal length. We can use the Pythagorean theorem to do this by dividing the trampoline into two right triangles.

The distance between the opposite sides would then be:

c ² = a ² + b ²

c ² = 8 ² + 12 ²

c ² = 64 + 144

c ² = 208

c = √ 208

c = 14. 42 yards

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Answer:

Step-by-step explanation:

Work out 2/13 of £208

208 * 2/13 =

16 * 2 =

32

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

A marketing survey of 1000 car commuters found that 600 answered yes to listening to the news, n(NM) = 300, n(NOM) = 800 and n((NM)') = 200.

500 answered yes to listening to music, and 300 answered yes to listening to both.

Notations:

N = set of commuters in the sample who listen to news.

M = set of commuters in the sample who listen to music.

Now, we have to find the following:n(NM) means the number of people who listen to news and music both.

Number of people who listen to both news and music is 300.

n(NM) = 300n(NOM) means the number of people who listen to news or music or both.

Number of people who listen to either news or music or both is given by the sum of people who listen to news and people who listen to music and then subtract the people who listen to both.

n(NOM) = n(N∪M) = n(N) + n(M) - n(NM)n(NOM) = 600 + 500 - 300n(NOM) = 800n((NM)') means the number of people who don't listen to both news and music.

The number of people who don't listen to both news and music is given by the number of people who listen to news or music or both subtracted from the total number of people surveyed.

n((NM)') = 1000 - n(NOM)n((NM)') = 1000 - 800n((NM)') = 200

Therefore, n(NM) = 300, n(NOM) = 800 and n((NM)') = 200.

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Yes, there are experts here in data forecasting methods who can help you with the topics you've mentioned including time series (holts, holts winter), naive method, regression, acf, pacf, arima, stl method and multivariate time series.

Below are brief explanations of each of these terms:

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To find the equation of a line, you need to use the formula \(m=\frac{y-y_0}{x-x_0}=\frac{rise}{run}\) to find the slope first.

To find the respective points that we need to plug into this formula, we need to use the axes and their values.

We can see that the first point (point on the left) has a position of (-1, -1). For the second point, we see that it has a position of (5, 1).

** remember, whenever you find the position of a point, it's always (x, y). Now that we have our values, we can plug and chug!

\(m=\frac{y-y_0}{x-x_0}\\m= \frac{1-(-1)}{5-(-1)} \\m=\frac{1+1}{5+1} \\m=\frac{2}{6} \\m=\frac{1}{3}\)

So your answer should be 1/3 for your slope.

Now you need to find your y intercept, or what y will equal if x = 0. We can find this by using the information we now have. Remember, the equation for a linear line is \(y=mx+b\). So now, we plug in any of the two points (it doesn't matter which pair!) and solve for b!

\(y=mx+b\\-1=\frac{1}{3}(-1)+b\\ -1=-\frac{1}{3}+b\\-1+\frac{1}{3}=b\\b=-\frac{2}{3}\)

Now we have b!

So now, we can fully finish the equation of this line. Your final answer should be: y = (1/3)x - 2/3 or \(y=\frac{1}{3}x-\frac{2}{3}\).

Hope this helps!

The answer is: it depends. If {c} is equal to {a} or {b}, then it is necessarily in the sigma-algebra, since {a} and {b} are already in the sigma-algebra and sigma algebras are closed under subsets.

In order to answer this question, we need to understand what a sigma-algebra is and what properties it has.

A sigma algebra is a collection of subsets of a set that has three properties:
1. It contains the empty set.
2. It is closed under complementation (i.e., if A is in the sigma-algebra, then A^c is also in the sigma-algebra).
3. It is closed under countable unions (i.e., if A1, A2, A3, ... are in the sigma-algebra, then their union is also in the sigma-algebra).

The answer is: it depends. If {c} is equal to {a} or {b}, then it is necessarily in the sigma-algebra, since {a} and {b} are already in the sigma-algebra and sigma algebras are closed under subsets.

However, if {c} is not equal to {a} or {b}, then we cannot say for sure whether it is in the sigma-algebra or not.

To see why, consider the following example. Let X = {a, b, c, d} and let the sigma-algebra be the power set of X (i.e., the collection of all subsets of X).

Then {a} and {b} are in the sigma-algebra, but {c} is not. Therefore, we cannot say that {c} is necessarily in the sigma-algebra.

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Answer:

I can't see the graph anywhere.

Step-by-step explanation:

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

Answer:

3

Step-by-step explanation:

71.38 in word form is Seventy-one and thirty-eight hundredths.

What is the decimal number?

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.

To write decimals in word form, you can read the whole number part, write "and," and then read the decimal part according to place value.

For example: 0.25 can be written as "zero and twenty-five hundredths"

Hence, the correct answer is 'D. Seventy-one and thirty-eight hundredths'.

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Answer: 42 gallons

Step-by-step explanation:

given data:

average gas mileage/day = 29miles/gallon

distance travelled each day by James = 87miles

How much gas does he use in 14days drive.

solution:

james drives 87miles daily, so in 14 days he would have travelled

= 87miles * 14

= 1218miles travelled.

gas used in 14days

1218miles distance traveled in 14 days

29miles/gallon

= 1218miles / 29miles

= 42gallons of gas have been used by janew to fuel his truck in 14days.

One way that adding and subtracting polynomials is similar to adding and subtracting whole numbers and integers is that both operations follow the same basic rules for combining like terms.

In both cases, you add or subtract the coefficients (numbers) of the same type of term or same variable with the same exponent.

Just like adding and subtracting integers, you also need to consider the signs (+ or -) when combining the terms.

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Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Answer:

0.1219512195122

Step-by-step explanation:

To write 10/82 as a decimal you have to divide numerator by the denominator of the fraction.

We divide now 10 by 82 what we write down as 10/82 and we get 0.1219512195122

The radius of this disk r is ± 9 √(1 - 2x^2).

The radius of the disk created by rotating the strip of width δx around the x-axis can be found using the Pythagorean theorem. Consider a right triangle with the horizontal leg equal to δx, the vertical leg equal to the height of the strip (which is equal to 9 - 9x^2), and the hypotenuse equal to r. We have:

δx^2 + (9 - 9x^2)^2 = r^2

Expanding and simplifying the square on the right-hand side, we get:

δx^2 + 81 - 162x^2 + 81x^4 = r^2

Since δx is infinitesimal, we can neglect it compared to 81 and 162x^2. Thus,

r^2 ≈ 81 - 162x^2

Taking the square root of both sides, we get:

r ≈ ± 9 √(1 - 2x^2)

where the positive sign corresponds to the upper half of the disk and the negative sign corresponds to the lower half.

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The ATM machine uses a predefined set of denominations. It then updates the remaining amount and moves to the next lower denomination until the remaining amount becomes zero. Finally, it dispenses the required number of notes for each denomination.

1. Compute the following sums:

a) To find the sum of the odd numbers from 1 to 999, we can observe that these numbers form an arithmetic sequence with a common difference of 2. The formula for the sum of an arithmetic sequence can be used to calculate the sum:

  \[S = \frac{n}{2}(a + l)\]

  where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term.

  In this case, \(n = \frac{999-1}{2} + 1 = 500\), \(a = 1\), and \(l = 999\).

  Plugging these values into the formula:

  \[S = \frac{500}{2}(1 + 999) = 250(1000) = 250,000\]

b) The sum \(\sum_{i=4}^n 1\) represents adding 1, \(n-3\) times. Therefore, the sum is equal to \(n-3\).

c) The sum \(\sum_{i=4}^{n+1} i\) represents adding the numbers from 4 to \(n+1\). This can be computed using the sum formula for an arithmetic sequence:

  \[S = \frac{n}{2}(a + l)\]

  where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term.

  In this case, \(n = (n+1) - 4 + 1 = n - 2\), \(a = 4\), and \(l = n+1\).

  Plugging these values into the formula:

  \[S = \frac{n-2}{2}(4 + n+1) = \frac{n-2}{2}(n+5)\]

2. Euclid's algorithm to find the greatest common divisor (gcd) between 46415 and 13142:

  The algorithm repeatedly divides the larger number by the smaller number and replaces the larger number with the remainder until the remainder is 0. The last non-zero remainder is the gcd.

  Pseudocode:

  ```

  function gcd(a, b):

      while b ≠ 0:

          temp = b

          b = a mod b

          a = temp

      return a

  ```

  Applying Euclid's algorithm to the given numbers:

  \[

  \begin{align*}

  a & = 46415, \\

  b & = 13142.

  \end{align*}

  \]

  Iteration 1:

  \[

  \begin{align*}

  a & = 13142, \\

  b & = 46415 \mod 13142 = 6341.

  \end{align*}

  \]

  Iteration 2:

  \[

  \begin{align*}

  a & = 6341, \\

  b & = 13142 \mod 6341 = 474.

  \end{align*}

  \]

  Iteration 3:

  \[

  \begin{align*}

  a & = 474, \\

  b & = 6341 \mod 474 = 37.

  \end{align*}

  \]

  Iteration 4:

  \[

  \begin{align*}

  a & = 37, \\

  b & = 474 \mod 37 = 29.

  \end{align*}

  \]

  Iteration 5:

  \[

  \begin{align*

}

  a & = 29, \\

  b & = 37 \mod 29 = 8.

  \end{align*}

  \]

  Iteration 6:

  \[

  \begin{align*}

  a & = 8, \\

  b & = 29 \mod 8 = 5.

  \end{align*}

  \]

  Iteration 7:

  \[

  \begin{align*}

  a & = 5, \\

  b & = 8 \mod 5 = 3.

  \end{align*}

  \]

  Iteration 8:

  \[

  \begin{align*}

  a & = 3, \\

  b & = 5 \mod 3 = 2.

  \end{align*}

  \]

  Iteration 9:

  \[

  \begin{align*}

  a & = 2, \\

  b & = 3 \mod 2 = 1.

  \end{align*}

  \]

  Iteration 10:

  \[

  \begin{align*}

  a & = 1, \\

  b & = 2 \mod 1 = 0.

  \end{align*}

  \]

  The gcd is the last non-zero remainder: gcd(46415, 13142) = 1.

3. Pseudocode for finding real roots of a quadratic equation \(a x^2 + b x + c = 0\):

  ```

  function findRealRoots(a, b, c):

      discriminant = b^2 - 4*a*c

      if discriminant < 0:

          print "No real roots"

      else if discriminant == 0:

          root = -b / (2*a)

          print "One real root:", root

      else:

          root1 = (-b + sqrt(discriminant)) / (2*a)

          root2 = (-b - sqrt(discriminant)) / (2*a)

          print "Two real roots:", root1, root2

  ```

4. Description of the algorithm used by an ATM machine for dispensing cash:

  Pseudocode:

  ```

  function dispenseCash(amount):

      denominations = [100, 50, 20, 10, 5, 1]  // available denominations

      remainingAmount = amount

      for denomination in denominations:

          count = remainingAmount / denomination  // number of notes of the current denomination

          remainingAmount = remainingAmount % denomination  // remaining amount to be dispensed

          print "Dispense", count, "notes of", denomination

  ```

  The ATM machine uses a predefined set of denominations. It starts with the highest denomination and calculates the number of notes of that denomination required to dispense the amount. It then updates the remaining amount and moves to the next lower denomination until the remaining amount becomes zero. Finally, it dispenses the required number of notes for each denomination.

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The value of x is 7/3, which can be rounded to two decimal places as approximately 2.33.

To solve the equation 2x + 8 + 4x = 22, we need to combine like terms and isolate the variable x.

Combining like terms, we have:

6x + 8 = 22

Next, we want to isolate the term with x by subtracting 8 from both sides of the equation:

6x + 8 - 8 = 22 - 8

6x = 14

To solve for x, we divide both sides of the equation by 6:

(6x) / 6 = 14 / 6

x = 14/6

Simplifying the fraction 14/6, we get:

x = 7/3

Therefore, the value of x is 7/3, which can be rounded to two decimal places as approximately 2.33.

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The statement is sometimes true. It depends on the relationship between the radius of the cone, the height of the cone, and the height of the prism.

The volume of a cone is given by the formula\(V_{cone} = (1/3)\pi r^2h\), where r is the radius of the cone and h is the height of the cone.

The volume of a prism is given by the formula\(V_{prism} = Bh\), where B is the base area of the prism and h is the height of the prism.

To determine if the statement is true, we need to compare the volumes of the cone and the prism.

If the base area of the cone is 3 times as great as the base area of the prism, it means that \(B_{cone} = 3B_{prism\).

Substituting these values into the volume formulas, we have \(V_{cone} = (1/3)\pi r^2h\) and \(V_{prism} = 3B_{prism} h\).

By comparing these formulas, we can see that the volume of the cone is indeed three times the volume of the prism, given the condition that \(B_{cone} = 3B_{prism\).

However, it is important to note that this relationship depends on the specific values of the radius and height of the cone and the height of the prism. If these values do not satisfy the condition \(B_{cone} = 3B_{prism\), then the statement would not hold true. Therefore, the statement is sometimes true, but it is not always true.

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The percentage increase in average commute times between these years = 2.25%

In 2010, the average commute time for wake county workers = 23.9 mins

In 2016, the average commute time for wake county workers = 25 mins.

The increase is = 25- 23.9 = 1.1

The average commute time between the two years,

23.9+25 = 48.9 mins

Therefore, the percentage,

= 1.1/48.9×100

= 110/48.9

= 2.249%

= 2.25% to the nearest two decimal places.

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Answer:

The angle that us congruent to angle 6 is angle 2 and angle 3.

The Laplace transform of the periodic function: ft, = t, 0 is F(s) = 1/s².

The Laplace transform of the periodic function f(t) = t, 0 is not well-defined because the function is not of exponential order. The Laplace transform requires functions to be of exponential order for convergence.

The Laplace transform is defined as:

F(s) = ∫[0, ∞) f(t) × \(e^{(-st)}\)  dt

In this case, the function f(t) = t is a linear function of t. To find its Laplace transform, we substitute f(t) = t into the Laplace transform integral:

F(s) = ∫[0, ∞) t × \(e^{(-st)}\)  dt

To evaluate this integral, we can use integration by parts or other methods. Applying integration by parts, we set u = t and dv =  \(e^{(-st)}\)  dt. Differentiating u gives du = dt, and integrating dv yields v = (-1/s) × \(e^{(-st)}\) .

Using the integration by parts formula

∫ u × dv = uv - ∫ v × du,

We can rewrite the integral as:

F(s) = [t × (-1/s) ×  \(e^{(-st)}\)] [0, ∞) - ∫[0, ∞) (-1/s) ×  \(e^{(-st)}\) dt

The first term on the right side evaluates to zero at both limits. Simplifying the remaining integral, we get:

F(s) = [-1/s ∫[0, ∞)  \(e^{(-st)}\) dt]

The integral of  \(e^{(-st)}\) dt can be evaluated as [-1/(s + t)] *  \(e^{(-st)}\). Substituting this result back into the equation, we obtain the Laplace transform of the periodic function f(t) = t:

F(s) = -[-1/s ∫[0, ∞)  \(e^{(-st)}\) dt]

      = -[-1/s × (-1/(s + t)) ×  \(e^{(-st)}\)]

      = 1/s²

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the value inside the square root must be positive or zero, then:

x - 7 ≥ 0

x - 7 +7 ≥ 0 + 7 adding 7 at both sides

x ≥ 7

The only option greater than or equal to 7 is 8

Answer:

x= 16.6ft

Step-by-step explanation:

The name of H2SO4 is sulfuric acid, which is also known as hydrogen sulfate. It is also known as oil of vitrol.

The chemical formula of sulfuric acid is H2SO4. Its paticipating elements are hydrogen, sulfer, and oxygen. Its common name is sulfuric acid or can also be called as hydrogen sulfate. It is dense, colourless, oily and highly corrosive liquid. It is one of the most important comercial chemicals. It has a very low pH value.

It is a very dense and strong mineral acid, typically used in the production of fertilizers, dtergents, pigments and other chemicals. Sulfuric acid is very reactive and in used is several industrial processes.

So, The name of H2SO4 is sulfuric acid and is also called hydrogen sulfate as it is basically a sulfate of hydrogen.

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