Write in scientific notation. 0.000000459

The equation \(x^2 + y^2 + 10y + 20 = 0\) represents a circle with center (0, -5) and radius 5.

To determine if the equation represents a circle, we need to rewrite it in standard form. The standard form of a circle equation is \((x - h)^2 + (y - k)^2 = r^2\), where (h, k) represents the center of the circle and r represents the radius.

Completing the square for the y terms:

\(x^2 + y^2 + 10y + 20 = 0\\ x^2 + y^2 + 10y = -20\\ x^2 + y^2 + 10y + 25 = -20 + 25\\ x^2 + (y + 5)^2 = 5\)

Now the equation is in standard form, \((x - 0)^2 + (y + 5)^2 = 5^2\), which represents a circle.

By comparing the equation to the standard form, we can determine the center and radius of the circle. The center is given by the values (h, k), which in this case is (0, -5). Therefore, the center of the circle is (0, -5).

The radius is determined by the term \(r^2\), which in this case is \(5^2 = 25\). Therefore, the radius of the circle is 5.

In summary, the equation x^2 + y^2 + 10y + 20 = 0 represents a circle with center (0, -5) and radius 5. The completion of the square allowed us to rewrite the equation in standard form, making it evident that it represents a circle. The center of the circle is determined by the values of x and y, and the radius is determined by the value of r.

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Answer:

La cantidad de dinero en:

Primer bolsillo = x = 200 euros

Segundo bolsillo = 2x = 400 euros

Step-by-step explanation:

Nos dijeron:

En un bolsillo tengo una cantidad de dinero y en el otro tengo el doble.

Representemos, la cantidad de dinero en el:

Primer bolsillo = x

Segundo bolsillo = 2x

En total tengo 600.

Por eso:

x + 2x = 600

3 veces = 600

x = 600/3

x = 200

2x = 200 × 2

x = 400

Por lo tanto, la cantidad de dinero en:

Primer bolsillo = x = 200 euros

Segundo bolsillo = 2x = 400 euros

Answer:

y= 1200(0.92)^x

Step-by-step explanation:

Given data

Cost price= $1200

Rate of decrease= 8%

Let the time be x

The expression that describes an exponential function is

y= ab^x

for decrease b= 1-r

y= 1200(1-0.08)^x

y= 1200(0.92)^x

Hence the expression is

y= 1200(0.92)^x

Answer:

a)45min

b)900min

Step-by-step explanation:

We were told that it takes Matt 3 minutes to read one page in a book.

It implies that 3minutes = 1page of the book

Then he continues to read at the same pace, he can read 15 similar pages in minutes.

a)Then, he can read 15 similar pages in

15x3 minutes.which is 45minutes.

b)Then if the book has 300 pages, it will take him. 300×3 minutes to read it.which is 900mins

Answer: has anyone seen my dad?

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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Answer:

6

Step-by-step explanation:

change up the formula so:

sqrt (10^2-8^2)= 6

The statements about the given bar graph that are false are Statments A and B while Statement C is is True.

From the bar graph attached, we can see the different amount of times that different lengths of ribbons occur. Thus, we can answer the questions;

A) From the given graphs, we see that the ribbon that occurs the most is ribbon with length 10⁴/₈ as it occurs 7 times. Thus, statement A is False.

B) From the graph, the shortest length is 9⁷/₈ while the longest length is 11²/₈. Thus;

Sum of the longest and shortest lengths = 9⁷/₈ + 11²/₈ = 22¹/₈

Thus, statement B is false.

C) Difference between the longest and shortest lengths = 11²/₈ - 9⁷/₈ = 11/8 = 2¹/₈

Thus, statement C is True

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The addition of the polynomial is \(\rm 4x^2-13x+9\) will be a polynomial.

The correct option is c.

Given

Two polynomials 4x2 − 8x − 7 and −5x + 16 are added.

A polynomial is an expression consisting of coefficients and variables which are also known as indeterminates.

To add both the polynomial following all the steps given below.

Combine terms adding and simplifying the polynomials.

Therefore,

\(\rm =4x^2 -8x - 7 +(-5x+16)\\\\=4x^2 -8x - 7 -5x+16\\\\= 4x^2-8x-5x+16-7\\\\= 4x^2-13x+9\)

Hence, the addition of the polynomial is \(\rm 4x^2-13x+9\).

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Universe is 2.25 × \(10^4\) times much wider than our local galactic group

The Milky Way galaxy, that includes our solar system, gets its name from how it looks in the night sky from Earth: a hazy band of light composed of stars that are too near together to be seen individually.

Given data:

Width fo galactic group = 4 * \(10^2^2\) meters .

Width of universe = 9 * \(10^2^6\) meter

let the width our galactic group be x times than that of universe

so  x * Width fo galactic group = Width of universe

=> x * 4 * \(10^2^2\) meters  = 9 * \(10^2^6\) meters

=> x = 9/4 * \(10^2^6^-^2^2\)

=> x = 2.25 * \(10^4\)

so universe is 2.25 * \(10^4\) times greater than our local galactic group.

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The height of the pickle ball when it was hit is = h = AB = 8.5 feet

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant , cosine , cotangent , secant , sine , and tangent.

Applications of Trigonometry:

Measuring grounds lots, and fields,

Measuring ground surfaces,

Making building perpendicular and parallel,

Roof inclination and roof slopes,

Installing ceramic tiles and stones,

The height and width of the building.

Given in figure

(in feet)

ED = 3

BC = 34

BD = 22

AB = h = height of the pickle ball

Therefore DC = 34 - 22 = 12

In ΔEDC

Let ∠ECD = a

tan a = ED/DC

⇒ tan a = 3/12

⇒ tan a = 1/4         (1)

In ΔABC

∠ACB = a

tan a = h/34

⇒ 1/4  = h/34      (from 1)

⇒ h = 34/4

⇒ h = 8.5

Hence height of the pickle ball is 8.5 feet.

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Tasha can make 1 1/6 an improper number making 1 1/6=7/6. Then she can subtract 7/6-5/6, which is 2/6. Simplified 1/3.

Now it's not impossible! ;D

The length of MP is approximately 12.11.

To solve this problem, we can start by using the fact that N is the midpoint of MO. This means that MN = NO = 7, since we know that NO = 7.

Next, we can use the fact that O is between M and P to find the length of OP. We know that NP = 15, so we can add this to NO to get:

OP = NP + NO = 15 + 7 = 22

Now, let's call MP = x. We can use the Pythagorean theorem to relate the lengths of OM, MP, and OP:

x^2 = OM^2 + MP^2

We can also express OM in terms of x, since O is between M and P:

OM = OP - MP = 22 - x

Substituting this into the Pythagorean equation, we get:

x^2 = (22 - x)^2 + 7^2

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

x^2 = 484 - 44x + x^2 + 49

This simplifies to:

44x = 533

Dividing both sides by 44, we get:

x = 533/44

This is equivalent to x ≈ 12.11 when rounded to two decimal places.

Therefore, the length of MP is approximately 12.11.

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\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=196\pi \end{cases}\implies \begin{array}{llll} 196\pi =4\pi r^2\implies \cfrac{196\pi }{4\pi }=r^2 \implies 49=r^2 \\\\\\ \sqrt{49}=r\implies 7=r~\hfill \underset{diameter}{\stackrel{2(7)}{14}} \end{array}\)

Answer:

-1.5

Step-by-step explanation:

m=-6/4

m=-3/2

-1.5

Answer:

-3/2

Step-by-step explanation:

[4-(-2)] / [1-5] = 6 / -4 = -3/2

Answer:

J (-5,2)

Hope this helps!

The correct explicit formula is f(1) = 6; f(n) = 6 + d(n − 1), n > 0

The arithmetic sequence explicit formula can be easily computed from the term of the sequence.

For the arithmetic sequence a, a + d, a + 2d, a + 3d, ........a + (n - 1)d, and the nth term of the sequence forms the explicit formula. Hence the explicit formula for the arithmetic sequence is an = a + (n - 1)d.

Given:

The first layer has 6 squares.

The second layer has 12 squares.

The sequence can be

6, 12, ...

then f(1)= 6

So, for n square we can write

f(n) =  6 + d(n − 1)

Hence, the explicit formula is  f(n) = 6 + d(n − 1),

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Answer:

bh/2

Step-by-step explanation:

So first, you have to multiply the base times height and you get a value. Then, you divide the value by 2. For example, a triangle that has a base of 3 and height of 4, you would multiply 4x3 which is 12 and then divide by 2 which is 6. Hope this helps :)

The Delhi metro track increased by 20% in the last two years.

The Delhi metro track increased from 200 km to 240 km in the last two years. To calculate the percentage increase, we need to find the difference between the new and old lengths, divide it by the old length, and then multiply by 100.
The difference in length is 240 km - 200 km = 40 km.
The percentage increase, we divide the difference by the old length: 40 km ÷ 200 km = 0.2.
Finally, we multiply by 100 to get the percentage: 0.2 × 100 = 20%.
Therefore, the Delhi metro track increased by 20% in the last two years.
Another way to calculate the percentage increase is by using the formula:
Percentage increase = (new value - old value) ÷ old value × 100.
In this case, the new value is 240 km and the old value is 200 km.
So, the percentage increase = (240 km - 200 km) ÷ 200 km × 100 = 40 km ÷ 200 km × 100 = 0.2 × 100 = 20%.
Therefore, the Delhi metro track increased by 20% in the last two years.

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The mean number of external parasites is 153.8, the median is 36, the standard deviation is 247.8, and the IQR is 41.5.

To find the mean, we sum up all the values and divide by the total number of observations:

mean = (5 + 0 + 0 + 54 + 512 + 26 + 24 + 36 + 556 + 43 + 15 + 42 + 1262 + 36 + 35 + 59 + 23) / 20 = 153.8

To find the median, we arrange the values in order from smallest to largest and find the middle value:

0, 0, 5, 15, 23, 24, 26, 35, 36, 36, 42, 43, 54, 59, 512, 556, 1262

The middle value is 36.

To find the standard deviation, we first find the variance:

variance = [(5-153.8)^2 + (0-153.8)^2 + ... + (23-153.8)^2] / 19 ≈ 61345.9

Then, we take the square root of the variance to get the standard deviation:

standard deviation = sqrt(variance) ≈ 247.8

To find the IQR, we first find the median of the lower half and the median of the upper half:

Lower half: 0, 0, 5, 15, 23, 24, 26, 35, 36, 36

Upper half: 42, 43, 54, 59, 512, 556, 1262

Lower median = 23, Upper median = 54

IQR = Upper median - Lower median ≈ 31.5.

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The peak, the largest deposit, made in July

It's the tallest one in the plot.

Let's arrange the number from smallest to greatest:

50<80=80<95<100<110<250<300<320

Jan<Feb=Sep<May<Apr<Mar<June<Aug<July

So, the greatest amount of deposit was in July.

These trades took place between June and August 2020. June 1 After giving it some deliberation, Natalie decides to offer Curtis a mixer for $1,150 (mixer cost: $620) on credit with terms of n/30. 30 Curtis gives Natalie a call. He signs a one-month, 8.35% note payable since he won't be able to pay the sum due for another month. Curtis calls on July 31.

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Answer: it’s 40

hope this helps :)

Step-by-step explanation:

Just substitute the variable with the number and use pemdas.

First you have to multiply 5/13 by -26, then add 50 to what you get.

To find the upper and lower bounds of a 95% confidence interval, we need to use the sample mean (X), sample standard deviation (s), and the sample size (n).

Given that the sample mean (X) is not provided in the question, we cannot calculate the confidence interval. Please provide the value of the sample mean.

Regarding the second part of the question, to limit the error to 1000 miles, we need to calculate the required sample size (n) using the formula:

n = (Z * s / E)^2

Where Z is the z-score corresponding to the desired confidence level (in this case, 95%), s is the sample standard deviation, and E is the desired maximum error (1000 miles).

Since the sample standard deviation (s) is not provided, we cannot calculate the required sample size. Please provide the value of the sample standard deviation or any additional relevant information to proceed with the calculations.

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Answer:

1: 3

Step-by-step explanation:

3:9

divide both sides by 3

1: 3

Answer:

1 :3

Step-by-step explanation:

3 apples : 9 plum

3 ÷ 3 = 1 : 9÷3 = 3

1 : 3

The sum of the series \(\sum_{k=0}^\infty \frac{3}{7^{k} }\)  is 7/2. Therefore, the correct answer is option C. The sum of a geometric series can be found only if the ratio is between -1 and 1.

To find the sum of the series \(\sum_{k=0}^\infty \frac{3}{7^{k} }\), we can use the formula for the sum of an infinite geometric series, which is \(\frac{a}{1-r}\), where a is the first term and r is the common ratio.

In this case, the first term is \(\frac{3}{7^0}=3\) and the common ratio is \(\frac{1}{7}\). Substituting these values into the formula, we get:

\(\frac{3}{1-\frac{1}{7}}=\frac{3}{\frac{6}{7}}=\frac{7}{2}\)

Therefore, the sum of the series is c. 7/2. Alternatively, we can also find the sum of the series by adding up the terms:

\(\frac{3}{1}+\frac{3}{7}+\frac{3}{49}+\frac{3}{343}+...\approx 4.5\)

This method involves adding up an infinite number of terms, so it may not always be practical or accurate. Using the formula for the sum of an infinite geometric series is a more efficient and reliable method. Therefore, the correct answer is option C.

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Complete Question:

Find the sum of the series:

\(\sum_{k=0}^\infty \frac{3}{7^{k} }\)

a. 7/3

b. 21/2

c. 7/2

d. 21/4

e. 7

Given:

The figure of a triangle.

\(IW= x-2\)

\(IU=2x-6\)

To find:

The value of x

Solution:

From the given figure it is clear that \(VI\) is a median of the given triangle. It means \(I\) divides \(UW\) is two equal parts.

\(IU=IW\)

\(2x-6=x-2\)

\(2x-x=6-2\)

\(x=4/tex]

The value of x is 4. Therefore, the correct option is D.

Answer:

5(9)+20

Step-by-step explanation:

5(9+4) can be expanded to get 5(9)+5(4). And 5(4)=20.

Answer:

Option D

Step-by-step explanation:

This will seem weird but all you are is doing distrubitive property.

Replace w with nine and you have this.

Step 1 (Replace/Substitute)

5(9 + 4)

5(9) + 20

We distribute the five to the numbers in the parentheses. Or we multiply 5 to the other numbers within the parentheses.

Thus, D is your answer.

Answer:

4*5 1/2,. 2/10.

Step-by-step explanation:

l think it's the answer

Answer:

I think

4*5 1/2

is correct

For the first differential equation:

y' + 5y' + 2y = 0, y(0) = 1, y'(0) = 2

We can apply the Laplace transform to both sides of the equation:

L{y'} + 5L{y'} + 2L{y} = 0

Using the linearity property of the Laplace transform, we can write:

L{y'} = sY(s) - y(0)

L{y''} = s^2 Y(s) - sy(0) - y'(0)

L{y} = Y(s)

Substituting these expressions into the differential equation, we get:

sY(s) - y(0) + 5(sY(s) - y(0)) + 2Y(s) = 0

Simplifying and solving for Y(s), we get:

Y(s) = (y(0) s + y'(0)) / (s^2 + 5s + 2)

    = (1s + 2) / (s^2 + 5s + 2)

To solve for y(t), we can apply partial fraction decomposition to express Y(s) in terms of simpler fractions:

Y(s) = (1s + 2) / (s^2 + 5s + 2)

    = A / (s + α) + B / (s + β)

where α and β are the roots of the quadratic denominator, and A and B are constants to be determined.

The roots of s^2 + 5s + 2 = 0 can be found using the quadratic formula:

s = (-5 ± √(5^2 - 4(1)(2))) / (2(1))

 = (-5 ± √17) / 2

Therefore, we have:

α = (-5 + √17) / 2

β = (-5 - √17) / 2

Using partial fraction decomposition, we can write:

Y(s) = A / (s + α) + B / (s + β)

    = [A(s + β) + B(s + α)] / [(s + α)(s + β)]

Equating the numerators, we get:

1s + 2 = A(s + β) + B(s + α)

Substituting s = -α, we get:

-αA + βB = 1α + 2

Substituting s = -β, we get:

-βA + αB = 1β + 2

Solving for A and B by solving the system of linear equations:

A = (2 + α) / (√17)

B = (2 + β) / (-√17)

Substituting the values of A and B, we get:

Y(s) = [(2 + α) / (√17)] / (s + α) - [(2 + β) / (√17)] / (s + β)

Using the inverse Laplace transform, we can find y(t):

y(t) = [(2 + α) / (√17)] e^(-αt) - [(2 + β) / (√17)] e^(-βt)

For the second differential equation:

y''' + y = A8(t - 3.), y(0) = 1, y'(0) = 0

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