HCF of 405 and 1605 answer it fast

Answer: W= 8.34A

Step-by-step explanation:

Given: Weight of a gallon of water = 8.34 pounds

Then,  weight of the water in container = (Weight of a gallon of water ) x (amount of water)

If A  = amount of water (in gallons)

W =  weight of the water in container ( in pounds)

i.e. \(W= 8.34A\)

Hence, the required equation : W= 8.34A

Answer:

\(y = C_1J_2(3\sqrt{x})+C_2Y_2(3\sqrt{x})\)

Step-by-step explanation:

\(x^{2} \dfrac{d^2 y}{dx^2} + x\dfrac{dx}{dy} + (x-1)y =0\)

Considering \(x=0\) ordinary point we could use Frobenius method assuming

\($y = \sum_{n=0}^{\infty} c_nx^n$\)

and consider the series representation given by the method to solve the equation. I think this way is harder.

In your case, It seems to have something to do with Bessel differential equation

\(x^2 y'' + x y' + (x^2-n^2) y = 0\)

that will have the same representation as the Frobenius method. To get the form \((x^2-n^2)\) as we have \( (x-1)\) in the given equation we can substitute \(x\) and take \(x = \dfrac{t^2}{9}\)

Thus,

\(\dfrac{dy}{dx} = \dfrac{3}{t}\dfrac{dy}{dt} \implies \dfrac{d^2y}{dx^2} = \dfrac{9}{t^2}\dfrac{d^2y}{dt^2}-\dfrac{9}{t^3}\dfrac{dy}{dt} \)

\($\implies \frac{1}{3^2}\left(t^2\frac{{d}^2y}{{d}t^2}+t\frac{{d}y}{{d}t}+(t^2-3^2)y\right) = 0$\)

The solution will have the format

\(y( x) = {C_1}{J_n}( x) + {C_2}{Y_n}( x )\)

such that

\(${J_n}( x ) = \sum\limits_{p = 0}^\infty {\frac{{{{( { - 1} )}^p}}}{{\Gamma ( {p + 1} )\Gamma ( {p + n + 1} )}} {{\left( {\frac{x}{2}} \right)}^{2p + n}}}$ \)

\(${Y_n}\left( x \right) = \frac{{{J_n}\left( x \right)\cos \pi n - {J_{ - n}}\left( x \right)}}{{\sin \pi n}}$ \)

and \(C_1, C_2\) are constants

And the order of the Bessel equation is \(n=2\)

In our case, we can just write

\(y(t) = C_1J_2(t)+C_2Y_2(t)\)

\(y = C_1J_2(3\sqrt{x})+C_2Y_2(3\sqrt{x})\)

Answer:

-2<=y<=-7

Step-by-step explanation:

, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: The fraction 3/9

Now we can simplify the fraction further by dividing both the numerator and denominator by 3

let p=3/9

then p=3/3 / 9/3

       p= 1/3

Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

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Answer:

C

Step-by-step explanation:

180

The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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The perimeter of the trapezoid is given as follows:

44 cm.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The missing side is a side of a right triangle, in which the other side is of 18 - 10 = 8 cm, while the hypotenuse is of 10 cm, hence:

8² + h² = 10²

64 + h² = 100

h² = 36

h = 6.

Hence the perimeter is given as follows:

P = 18 + 10 + 10 + 6 = 44 cm.

The trapezoid is given by the image presented at the end of the answer.

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Step-by-step explanation:

1+9

2+8

3+7

4+6

5+5

6+4

7+3

8+2

9+1

10+0

If the dilation is centered at the origin, the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).

In Geometry, dilation refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:

Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).

Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).

Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).

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Answer:

Step-by-step explanation:

2/7 + 4/5 mixed forms

2/7 + 4/5 =

38/35 or 1 3/35

Answer:

38/35

Step-by-step explanation:

1. convert to like fractions

2/7-> 10/35

4/5-> 28/35

2. add fractions

10/35 + 28/35 = 38/35

Answer:

Step-by-step explanation:

12(17/3 - 3/4x = 1/2x + 5)

68 - 9x = 6x + 60

-15x = -8

x = 8/15

Answer of the given question are respectively,

\(-x^2y , 2w ,\\\\h^6 , -14a^5b^2\\x^6 , 4m^8\\9x^4/14 , y^2\\-5/x^2 , 1/2k\\7 , 1\)

Exponent:

                          A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.

        Example:

                             \(2^3\) = 2 × 2 × 2

Combine like term:

 1. \(9x^2y -10x^2y\) = \(-x^2y\)

 2. Subtract 6w from 8w

          8w -6w = 2w

Rule:

          \(x^{a} * x^{b} = x^{a+b} \\\\\)

1.

        \(h^2 * h^4 = h^{2+4} \\ \\\\= h^6\)              

2.  

        \((-2a^2b).(7a^3b)\\\\-14 a^{2+3} b^{1+1} \\\\= -14 a^5 b^2\)

Rule:

       \((x^a)^b = x^{ab}\)

  1.  \((x^2)^3 = x^6\)

  2.

         \((-2m^3)^2 * m^2 \\\\4m^6*m^2\\\\4m^8\)

Rule:

           \(x^a/x^b = x^{a-b}\)

1.

   \(27x^5/42x\\\\= 9x^4 /14\)

2.

          \((y^3)^2/y^4\\\\y^6/y^4\\\\y^2\\\)        

Rule:

            \(x^{-a}= 1/x^a\)

1.

    \(-5x^{-2} \\\\= -5/x^2\)

2.

    \(4k^2/8k^3\\\\= k^{-1} /2\\\\= 1/2k\)

Rule:

           \(x^0 =1\)

1.

         \(7x^0\\\\= 7\)

2.

         \((w^4)^2/w^8\\\\w^8/w^8\\\\w^0\\\\=1\)

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Answer:

B. 10x -40

Step-by-step explanation:

To rewrite the expression 5(2x-8) using the distributive property, we need to separate the expression inside the parentheses and then multiply the two expressions by 5. The answer is: 10x-40.

Answer:

38 plain chocolate bars and 17 king-size chocolate bars.

Step-by-step explanation:

Let's define the variables:

P = number of plain chocolate bars sold

K = number of king chocolate bars sold

We know that each plain one costs $1.50, and each king one costs $2.25, then the total revenue is:

P*$1.50 + K*$2.25

Now we know that Jim sells a total of 55 candy bars, then:

P + K = 55

And we know that the total revenue is $95.25, then:

P*$1.50 + K*$2.25 = $95.25

Then we have the system of equations:

P + K = 55

P*$1.50 + K*$2.25 = $95.25

To solve this we need to isolate one of the variables in one of the equations, I will isolate P in the first equation to get:

P = 55 - K

Now we can replace is on the second one to get:

(55 - K)*$1.50 + K*$2.25 = $95.25

Now we can solve this for K

$82.50 - K*$1.50 + K*$2.25 = $95.25

K*($2.25 - $1.50) = $95.25 - $82.50 = $12.75

K*$0.75 = $12.75

K = $12.75/$0.75 = 17

This means that Jim sold 17 king-size chocolate bars.

Now we can replace this in the equation:

P + K = 55

P + 17 = 55

P = 55 - 17  =38

P = 38

Jim sold 38 plain chocolate bars.

The solution is,

-2A = (-6, -8, 0, 8, 2, -8)

B - 2A = (2, -7, -4, 3, 4, -12)

AC is undefined.

CD = (3, 2, 12, 5)

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

here, we have,

Given the matrices:

A = (3 4 0 -4 -1 4)

B = (8 1 -4 -5 2 -4)

C = (1 -1 3 1)

D = (3 -2 4 5)

We are required to compute the following

-2A, B - 2A, AC, CD

For -2A:

-2(3 4 0 -4 -1 4)

= (-6, -8, 0, 8, 2, -8)

For B - 2A:

Because B - 2A = B + (-2A),

we have:

(8 1 -4 -5 2 -4) + (-6, -8, 0, 8, 2, -8)

(2, -7, -4, 3, 4, -12)

For AC:

(3 4 0 -4 -1 4)(1 -1 3 1)

This is undefined.

For CD:

(1 -1 3 1)(3 -2 4 5)

= (3, 2, 12, 5)

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The expanded and simplified form of the expression (x + 5)(x - 1) is  x² - x + 5x - 5.

Given the expression in the question;

(x + 5)(x - 1)

To expand and simplify the expression (x+5)(x-1),

we use the distributive property:

(x + 5)(x - 1)

x(x - 1) + 5(x - 1)

Now we can simplify each term by using the distributive property again:

x(x - 1) = x² - x

5(x - 1) = 5x - 5

Putting these terms back together, we have:

(x+5)(x-1) = x² - x + 5x - 5

Combining like terms, we get:

(x+5)(x-1) = x² + 4x - 5

Therefore, (x+5)(x-1) simplifies to the quadratic expression x² + 4x - 5.

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The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.

After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.

However, Caesar, true to his word, had the pirates crucified on his own authority.

This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

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Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

The quotient of 47.61 and 15.87 has the result given as follows:

47,61 : 15,87 = 3.

The operation for this problem is defined as follows:

47,61 : 15,87 =

The : symbol means that the operation is a division, that is, we must obtain the quotient of dividing 47.61 by 15.87.

Using a calculator, we have that 47.61 is three times 15.87, hence the result of the quotient is given as follows:

47,61 : 15,87 = 3.

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Answer

96

Step-by-step explanation:

1/2x+12=60

1/2x=48

x=96

Answer:

No, it is not a right triangle

Step-by-step explanation:

We use the pythagorean theorem to determine if a triangle is a right triangle, therefore this triangle is not right.

Hope this helps :-)

Answer:

No

Step-by-step explanation:

\(c^{2}= a^{2} + b^{2}\)

To find if this is true, you would do the suqare root of \(\sqrt{9^{2} +5^{2}\), and if it does not equal 13 it's not a right triangle

Answer:

y = - \(\frac{1}{3}\) x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 3 ← is in slope- intercept form

with slope m = 3

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{3}\) , then

y = - \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (- 6, 9 ) into the partial equation

9 = - \(\frac{1}{3}\) (-6) + c = 2 + c ( subtract 2 from both sides )

7 = c

y = - \(\frac{1}{3}\) x + 7 ← equation of perpendicular line

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

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The Number of Soccer Balls is 16 and the Number of T-Shirts is 68

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form         ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

Number of Soccer Balls = x

Number of T-Shirts = y

Equation 1:

x + y = 84 -----------(i)

Equation 2:

25x + 9.5y = 1046 ----------(ii)

Multiplying Equation 1 by 25

25x + 25y = 2100 ---------(iii)

Substracting Equation2 from Equation 1

15.5y = 1054

y = 68

So, x = 16

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Answer:

\(( \sqrt{h} + \sqrt{g} )( \sqrt{h} - \sqrt{g} )\)

Step-by-step explanation:

1) Convert h½ to square root.

\(( \sqrt{h} + g^{ \frac{1}{2} } )( \sqrt{h} - g^{ \frac{1}{2} } )\)

2) Convert g½ to square root.

\(( \sqrt{h} + \sqrt{g} )( \sqrt{h} - \sqrt{g} )\)

Therefor the answer is

\(( \sqrt{h} + \sqrt{g} )( \sqrt{h} - \sqrt{g} )\)

Answer:

\((\sqrt{h}+\sqrt{g} )(\sqrt{h} -\sqrt{g} )\)

Step-by-step explanation:

Have a great day

Answer:

3.5

Step-by-step explanation:

the one length 3.5 inche