What property is (4 + b) + 8= 4 + (b + 8)

Answer:

STEP

1

:

Equation at the end of step 1

 (32x2 -  8x) -  2  = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  9x2-8x-2

The first term is,  9x2  its coefficient is  9 .

The middle term is,  -8x  its coefficient is  -8 .

The last term, "the constant", is  -2

Step-1 : Multiply the coefficient of the first term by the constant   9 • -2 = -18

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -8 .

     -18    +    1    =    -17

     -9    +    2    =    -7

     -6    +    3    =    -3

     -3    +    6    =    3

     -2    +    9    =    7

     -1    +    18    =    17

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

 9x2 - 8x - 2  = 0

STEP

3

:

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = 9x2-8x-2

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 9 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   0.4444  

Plugging into the parabola formula   0.4444  for  x  we can calculate the  y -coordinate :

 y = 9.0 * 0.44 * 0.44 - 8.0 * 0.44 - 2.0

or   y = -3.778

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 9x2-8x-2

Axis of Symmetry (dashed)  {x}={ 0.44}

Vertex at  {x,y} = { 0.44,-3.78}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-0.20, 0.00}

Root 2 at  {x,y} = { 1.09, 0.00}

Solve Quadratic Equation by Completing The Square

3.2     Solving   9x2-8x-2 = 0 by Completing The Square .

Divide both sides of the equation by  9  to have 1 as the coefficient of the first term :

  x2-(8/9)x-(2/9) = 0

Add  2/9  to both side of the equation :

  x2-(8/9)x = 2/9

Now the clever bit: Take the coefficient of  x , which is  8/9 , divide by two, giving  4/9 , and finally square it giving  16/81

Add  16/81  to both sides of the equation :

 On the right hand side we have :

  2/9  +  16/81   The common denominator of the two fractions is  81   Adding  (18/81)+(16/81)  gives  34/81

 So adding to both sides we finally get :

  x2-(8/9)x+(16/81) = 34/81

Adding  16/81  has completed the left hand side into a perfect square :

  x2-(8/9)x+(16/81)  =

  (x-(4/9)) • (x-(4/9))  =

 (x-(4/9))2

Things which are equal to the same thing are also equal to one another. Since

  x2-(8/9)x+(16/81) = 34/81 and

  x2-(8/9)x+(16/81) = (x-(4/9))2

then, according to the law of transitivity,

  (x-(4/9))2 = 34/81

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(4/9))2   is

  (x-(4/9))2/2 =

 (x-(4/9))1 =

  x-(4/9)

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-(4/9) = √ 34/81

Add  4/9  to both sides to obtain:

  x = 4/9 + √ 34/81

Since a square root has two values, one positive and the other negative

  x2 - (8/9)x - (2/9) = 0

  has two solutions:

 x = 4/9 + √ 34/81

  or

 x = 4/9 - √ 34/81

Note that  √ 34/81 can be written as

 √ 34  / √ 81   which is √ 34  / 9

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    9x2-8x-2 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     9

                     B   =    -8

                     C   =   -2

Accordingly,  B2  -  4AC   =

                    64 - (-72) =

                    136

Applying the quadratic formula :

              8 ± √ 136

  x  =    —————

                   18

Can  √ 136 be simplified ?

Yes!   The prime factorization of  136   is

  2•2•2•17

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 136   =  √ 2•2•2•17   =

               ±  2 • √ 34

 √ 34   , rounded to 4 decimal digits, is   5.8310

So now we are looking at:

          x  =  ( 8 ± 2 •  5.831 ) / 18

Two real solutions:

x =(8+√136)/18=(4+√ 34 )/9= 1.092

or:

x =(8-√136)/18=(4-√ 34 )/9= -0.203

Two solutions were found :

x =(8-√136)/18=(4-√ 34 )/9= -0.203

x =(8+√136)/18=(4+√ 34 )/9= 1.092

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

ax² + bx + c = 0

In the quadratic formula the "b" coefficent gets sqaured

bx = 8x

b = 8

Answer:

The decision made by the researcher based on this information is to reject the null hypothesis.

Step-by-step explanation:

Two-tailed hypothesis test:

Critical value: [tex]z_c[/tex]

Test statistic: z

If [tex]|z| < |z_c|[/tex], we do not reject the null hypothesis.

If [tex]|z| > |z_c|[/tex], we reject the null hypothesis.

In this question:

[tex]z_c = 1.96, z = -2.05, |z| = 2.05[/tex]

Since [tex]|z| > |z_c|[/tex], we reject the null hypothesis.

The decision made by the researcher based on this information is to reject the null hypothesis.

Answer:

Step-by-step explanation:

scam . smď

Answer:

[tex]P(x<3.12)= 0.21186[/tex]

Step-by-step explanation:

Mean [tex]\=x=\$3.20[/tex]

Standard deviation [tex]\sigma =\$0.10[/tex]

Estimated price [tex]y=\$3.12[/tex]

Generally the equation for P(x<3.12) is mathematically given by

 [tex]P(x<3.12)=P(\frac{y-x}{\sigma}<-\frac{3.12-3.20}{0.10})[/tex]

 [tex]P(x<3.12)=(z<-0.8)[/tex]

Since from Z table

 [tex]P(x<3.12)= 0.21186[/tex]

Therefore the  proportion of the milk vendors that have prices that were less than $3.12 per gallon is

 [tex]P(x<3.12)= 0.21186[/tex]

multiplication

hope this helped <3

Answer:456.63

Step-by-step explanation:

The weight (in grams) of a liquid is 456.63 grams.

Weight is a quantity representing the force exerted on a particle or object by an acceleration field, particularly the gravitational field of the Earth at the surface.

V = Volume of liquid = 182.8 milliliter

[tex]\rho[/tex] = Density of liquid = 0.135 grams over milliliter

We know that,'

mass= volume x density

        = 465 x 0.982

      = 456.63 grams

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Answer:

Option C

Step-by-step explanation:

Given :

And we need to find out that which cube has the larger surface area. We know that ,

[tex]\dashrightarrow [/tex] 1 ft = 12 inch

So the conversion factor becomes ,

[tex]:\implies[/tex] 12 in : 1ft

[tex]:\implies[/tex] 12in : 12 in

[tex]:\implies[/tex] 1 : 1

Hence the both cubes have same surface area .

Answer: 224

Step-by-step explanation:

The total degrees of a 7-sided shape is 900. You can find that out using the equation (n-2) times 180. Where n is the number of sides. If you add up all the interior angles they equal 676. Then just subtract 676 from 900. 900-676= 224 degrees. That is the missing interior angle.

Answer:

I think it's B. but I'm not too sure. sorry if I'm wrong

Answer:

20 times 3, do the math and you get

Answer:

60

Step-by-step explanation:

20x3=60 ............

Answer:

20(x+15)(x+10)

Step-by-step explanation:

Hi there!

As your question states, we need to fully factor the polynomial: 20x²+500x+3000

These are pretty big numbers; let's pull out the GCF, as that will make it easier to factor

the GCF is 20

so factoring 20 out of the polynomial will get:

20(x²+25x+150)

As you can see, the polynomial inside the parenthesis is a lot easier to factor than the original with really big numbers.

Now use FOIL to factor x²+25x+150 into 2 binomials

25 is the sum of the last terms

150 is the product of the last terms

think: which two numbers add up to 25 but multiply to get 150?

those two numbers are 15 and 10

x²+25x+150 factored is (x+15)(x+10)

but remember we have the 20 in front of x²+25x+150  (or now, (x+15)(x+10))

therefore the fully factored binomial is 20(x+15)(x+10)

Hope this helps! :)

Answer:

1) 81.67 cm² (Option A)

2) 28.26 m² (Option B)

3) 153.86 mi.² (Option D)

4) 329.90 m² (Option A)

5) 63.585 ft.² (Option C)

Step-by-step explanation:

GENERAL FORMULAES TO BE USED IN THIS QUESTION :-

Diameter of a circle with radius 'r' = 2r

Area of a circle with radius 'r' = πr²

SOLUTION :-

1) Diameter of the dinner plate = 10.2 cm

Radius of the dinner plate = 10.2/2 = 5.1 cm

⇒ Area of the circle = π(5.1)² = 26.01π cm² ≈ 81.67 cm²

2) Length of his leash = 3m

⇒ Area the dog has to run around = π(3)² = 9π m² = 28.26 m²

3) Radius of the circular range of storm = 7 mi.

⇒ Area of the circular range of storm = π(7)² = 49π mi.² = 153.86 mi.²

4) Diameter of carousel = 20.5 m

Radius of carousel = 20.5/2 = 10.25 m

⇒ Area of the carousel = π(10.25)² = 105.0625π m² ≈ 329.90 m²

5) Radius of the range of sprinkler = 4.5 ft.

⇒ Area of the range of sprinkler = π(4.5)² = 20.25π ft.² = 63.585 ft.²

Answer:

It's D on EDGE

Step-by-step explanation:

The compliment of the set S is {x|x is a rational non-integer}

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the universal set be represented as U

where the value of U is

U = {x|x is a rational numbers}

And , let the second set be represented as S,

where S = {x|x is an integer}

Now , the compliment of set S is given by = S'

And , S' = 1 - S

On simplifying , we get

S' = 1 - {x|x is an integer} and it belongs to U

So , S' = {x|x is a rational non-integer}

Hence , the set is S' = {x|x is a rational non-integer}

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Answer:

y=5x

Step-by-step explanation:

If the input is x, then the out put is 5x. So y=5x

Answer:

its option C

Step-by-step explanation:

because ages 51-60 have around 30 more in years and since the 51-60 is half way in the collums it would be 5 so then its 35 more voters :)

Answer:

x = 12.5

Step-by-step explanation:

Answer:

Ratio is 12:27  ratio as a fraction is 12 over 27

Step-by-step explanation:

no need for explaination lolz

Answer:

5,800,000,000,000

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

x= -22

Step-by-step explanation:

3x=5x+44

subtract 2x from both sides and leave only x on one side 3x(-2x)=5x(-2x)+44

then you get

x=3x+44

then you subtract the 3x to both sides

x(-3x)=3x(-3x)+44

then you get

-2x=44

and divide 2 on each side so-

x= -22

Answer:

43

Step-by-step explanation:

interior angles add up to 180

Answer:

62 sq cm

Step-by-step explanation:

if you find the area of the entire shape (12x6) you can then subtract out the cut-out portion (5x2)

72 - 10 = 62

Answer:

8y^3+6y^2-29y+15

Step-by-step explanation:

the correct expression is

(4y − 3)(2y^2 + 3y − 5)

Given data

We have the expression

(4y − 3)(2y^2 + 3y − 5)

let us open bracket

8y^3+12y^2-20y-6y^2-9y+15

Collect like terms

8y^3+12y^2-6y^2-20y-9y+15

8y^3+6y^2-29y+15

Answer:

area of triangle =1/2 x b x h

Step-by-step explanation:

=1/2 x 7 x 12

= 1/2 x 84

= 42 units

Answer:

60$

Step-by-step explanation:

divide 32 by 8 which gives you 4. so each individual CD is 4 dollars. if you multiply 4$ per CD by the number of CDs (15) it's 60. so the answer is 60$ :)

Answer:

60$

Step-by-step explanation:

Answer:

Six multipled by four to get how many girls and boy he will sayhrllo to.

Answer:

3

Step-by-step explanation:

Answer:

3 + 6 = 6 + 3

Step-by-step explanation:

3 + 6 = 6 + y

9 = 6 + y

y + 6 = 9

y + 6 - 6 = 9 - 6

y = 3