Simplify the expression √9x^3/25y^2 and be sure to explain your steps!

The numerical values of a in the points Q(-1, a) and P(3, -2) with a distance of 4√5 are  6 and -10.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point Q( -1, a )

Point P( 3, -2 )

To find the numerical value of a, plug the given coordinates into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

Square both sides

( 4√5 )² = ( 3 - (-1) )² + ( -2 - a )²

( 4√5 )² = ( 3 + 1 )² + ( -2 - a )²

( 4√5 )² = ( 4 )² + ( -2 - a )²

80 = 16 + ( -2 - a )²

80 - 16 = ( -2 - a )²

64 = ( -2 - a )²

( -2 - a )² = 64

Expand the parenthesis

( -2 - a )( -2 - a ) = 64

a² + 4a + 4 = 64

a² + 4a + 4 - 64 = 0

a² + 4a - 60 = 0

solve for a

( a - 6 )( a + 10 ) = 0

a - 6 = 0, a + 10 = 0

a = 6, a = -10

Therefore, the values of a are 6 and -10.

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7/3 in notation one can be written as 7 : 3 and 7/3 in notation two can be written as 0.7 and 0.3.

The ratio is a comparison between two similar quantities in the simplest fraction form. We can write ratios in fractions and in decimals also.

We know we can write a : b as a/b in fraction form and a/(a+b) and b/(a+b) in decimal form.

∴ 7/3 in decimal form can be written as 7 : 3 and 7/3 can also be written as 7/(7+3) = 7/10 = 0.7 and 3/(7+3) = 3/10 = 0.3.

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Each person will get a 5/24 portion of the available cake with Paige

Cake available with Paige = 5/6

Number of people = 4 people

Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Fraction of cake each person gets:

Cake available with Paige/Number of people with whom the cake is to share equally

= (5/6)/(4)

= (5/6)*(1/4)

= 5/24

The fraction of cake each person will get is 5/24

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89 squares will be present.

Given that the rectangle has the following dimensions: length = 96 cm, breadth = 84 cm, and

its total area is 8064 square centimeters, we may deduce that the maximum square area

[tex]\sqrt[2]{8064}[/tex]

that can be removed from the rectangle with its total area of 8064 square centimeters is equal to 89.8 square centimeters.

In order to determine the total number of squares, divide 8064 by 89.8 to arrive at 89.

Taking an integer's square root is the opposite of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root value is obtained by finding a number that, when squared, produces the original value of the number.

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Answer:

13/20 is the greatest because it is equal to 65% of 100%.

Step-by-step explanation:

5/8 = to 12.5x5=62.5%. 3/5= 20x3=60%. 3/10 = 10x3=30%. So 13/20 is the greatest.

The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.

Given,

The equation; [tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]

We have to solve this equation to get the value of x.

That is,

[tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]

Square both sides to remove square root.

[tex]\sqrt{3x-4} ^{2} = (2\sqrt{x-5} )^{2}[/tex]

We get,

3x - 4 = 4 (x - 5)

That is,

3x - 4 = 4x - 20

Here,

20 - 4 = 4x - 3x

Then,

x = 16

That is,

The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.

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Answer:

B and c

Step-by-step explanation:

182/7=26

168/6=28

The length of the side is 11.79cm

The area is the entire amount of space occupied by a flat (2-D) surface or shape of an object.

On a sheet of paper, draw a square with a pencil.

It is a two-dimensional figure.

The area of a shape on paper is the area it occupies.

Area of a square i= 139cm^2

a^2 = 139

The length of the side (a) = [tex]\sqrt{139}[/tex] = 11.79cm

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Step-by-step explanation:

(f○g)(x) means f(g(x))

(g○f)(x) means g(f(x))

f(g(x)) means to use the expression of g(x) as input to f(x). so, we replace all simple x in f(x) by g(x) = x².

f(g(x)) = x²/(x² + 2)

using the same principle we get for

g(f(x)) = (x/(x + 2))² = x²/(x + 2)²

now we need to solve

x²/(x² + 2) = x²/(x + 2)²

let's multiply both sides with both denominators :

x²(x + 2)² = x²(x² + 2)

x²(x² + 4x + 4) = x²(x² + 2)

so, one solution is clear : x = 0.

because then we have 0 = 0.

for x <> 0 we can divide both sides by x² and get

x² + 4x + 4 = x² + 2

4x + 4 = 2

4x = -2

x = -2/4 = -1/2

both expressions are equal for x = 0 and x = -1/2

Answer:

Find the Inverse f(x)=3x-1/4. f(x)=3x−14 f ( x ) = 3 x - 1 4. Step 1. Write f(x)=3x−14 f ( x ) = 3 x - 1 4 as an equation. y=3x−14 y = 3 x - 1 4.

Step-by-step explanation:

Answer:

2000 pounds is 1 ton

6 tons is 12,000

7 tons is 14,000

16,000 pounds is 8 tons

Answer:

QPR SAS

Step-by-step explanation:

As you can see. Hope it can help

area of triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is

(x1 (y2 - y3 ) + x2 ( y3 - y1 )+ x3 ( y1 - y2))/2

hence, substituting the points (x1, y1)= (-2, 1);

( x2, y2)= (0,3) ; and (x3, y3)= (4,-4) in the area formula ,we get

area of triangle =

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

(-14+0-8)\2

22\2

11 sq unit

Answer: x^2-9x+20

Step-by-step explanation: you have to distribute (x-5) (x-4)

which would be x^2-4x -5x +20 when you simplify that you get x^2-9x+20

Answer:

-18

Step-by-step explanation:

first subtract ten from both sides now you're left with -2y=36 ,lastly divide both sides by -2 and you're left with y= -18

Answer:

y-21 = 4(x+9)

For the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.

As given in the question,

On a tour of a gold mine,

Ounce of gold contained by nuggets found in the mine = 0.82 ounce

Worth of gold per ounce = $1323.80 per ounce

Worth of nuggets containing 0.82 ounce of gold

Worth of 1 ounce of gold = $1323.80

⇒ Worth of nuggets containing 0.82 ounce of gold =$( 1323.80 ×0.82 )

                                                                                      = $1085.516

Therefore, for the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.

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The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7

Given,

The binomials; (2x² + 4x - 7) (3x - 1)

We can use FOIL method to solve this;

FOIL method;

Binomials are multiplied using the FOIL Method. An acronym is FOIL FOIL. First, Outside, Inside, and Last are the letters that stand for the order of multiplying terms. To get your answer, multiply the first term, then the outside term, then the inside term, then the last term, and then combine terms that are similar.

Here,

(2x² + 4x - 7) (3x - 1)

= (3x × 2x²) + (3x × 4x) - (3x × 7) - 2x² + 4x - 7

= 6x³ + 12x² - 21x - 2x² + 4x - 7

= 6x³ + 10x² - 17x - 7

That is,

The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7

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Answer:

x=65

Step-by-step explanation:

47+68+x=180

x=65

:]

Answer: 65 = x

Step-by-step explanation:

1) First find the mini triangles, left and right angles

We will be calling the left one A and the right one B.

2) Next use triangle sum to find B.

62 + 50 + b = 180

b=68

3) Use triangle sum again to find A.

53 + 80 + a = 180

a = 47

4) Use triangle sum to find the top mini angle.

47 + 68 + c = 180

c = 65

5) Since x is in the vertical angle of c, they are equal

c = x

65 = x

Answer: x = 22

Step-by-step explanation:

       We will use the exterior angle theorem to solve. First, we will write an equation, then we will solve by combing like terms are using inverse operations.

(6x - 7) = (2x) + (103 - x)

6x - 7 = 2x + 103 - x

6x - 7 = x + 103

5x = 110

x = 22

The union of two sets contains all the elements contained in either set (or both sets). The intersection of two sets contains only the elements that are in both sets

Therefore the answer is B.

The new length of the building will be 110 feet.

Volume of Cuboid:

                              Volume of cuboid is

                        V =  length x breadth x height cubic unit

Given,

The building was going to be 100 feet long, 75 feet deep, and 30 feet high.

Therefore, the volume will be:

               = 75 × 100 × 30 ft³

               = 225000 ft³

Now owner decided increase the volume of the building by 10% without changing the dimensions of the depth and the height.

There was an increase by 10%,

New volume will be,

V' = 225000 + (10% × 225000)

  = 247500 ft³

Therefore, the new length will be:

as,

        Volume =  length x breadth x height

        length  =  Volume/ (breadth x height)

New length will be

                      = 247500/(30 × 75)

= 110 feet

Thus the new length of the building will be 110 feet.

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Answer:

  (a)  y < 3(x +2)² +2

Step-by-step explanation:

You want to know the inequality representing the region less than the quadratic with vertex (-2, 2) and containing the point (-4, 14).

The vertex form equation for a quadratic with vertex (h, k) and some scale factor 'a' is ...

  y = a(x -h)² +k

For the given vertex (-2, 2), the boundary line equation is ...

  y = a(x -(-2))² +2 = a(x +2)² +2

The value of 'a' is positive when the curve opens upward.

Here, the point (-4, 14) has a y-value greater than that of the vertex, so we know the curve opens upward (a > 0).

The only reasonable answer choice is ...

  y < 3(x +2)² +2

Answer

The polynomial is

P(x) = 2x⁴ - 5x³ + 3x²

Explanation

We are told to write a polynomial of degree 4 with zeros (roots)

x = 1

x = (3/2) = 1.5

x = 0

x = 0 (multiplicity of 2 means it appears twice)

So, we can piece together the polynomial

P(x) = (x - 1) (x - 1.5) (x) (x)

We can write this as

P(x) = x² (x - 1) (x - 1.5)

= (x³ - x²) (x - 1.5)

We can multiply through by 2 to turn the 1.5 into a whole number

P(x) = (x³ - x²) (2x - 3)

= x³ (2x - 3) - x² (2x - 3)

= 2x⁴ - 3³ - 2³ + 3x²

= 2x⁴ - 5x³ + 3x²

Hope this Helps!!!

Answer:

Hope this helps!!

Answer:

See below

Step-by-step explanation:

y-0=2/3(x-6)         (expand L side)

What is the equation in slope-intercept form?

y = 2/3 x - 4

a)I WILL USE THE THEOREM OF PYTHAGORAS IN TRIANGLE BCD

[tex] {y}^{2} = {(5.3)}^{2} - {(4.4)}^{2} \\ {y}^{2} = 28.9 - 19.36 \\ {y}^{2} = 9.54 \\ y = \sqrt{9.54} \\ y = 3.09[/tex]

y=3.90cm

b)

[tex] \sin(x) = \frac{cb}{ac} \\ \sin(x) = \frac{5.3}{8.2} \\ x = sin^{ - 1} ( \frac{5.3}{8.2} ) \\ x =40.27[/tex]

x=40,27 cm

GOODLUCK.

Answer:

15

Step-by-step explanation:

16c+4(-5)=220

16c-20=220

16c=240

C=15