Two quantities are related, as shown in the table:

x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship?
1. y = 1/2x + 2

2. y = 1/2x + 1

3. y = x + 2

4. y = 2x + 1

Answer:

X=4 or X=-2

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant   1 • -8 = -8  

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

     -8    +    1    =    -7  

     -4    +    2    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  2  

                    x2 - 4x + 2x - 8

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-4)

             Add up the last 2 terms, pulling out common factors :

                   2 • (x-4)

Step-5 : Add up the four terms of step 4 :

                   (x+2)  •  (x-4)

            Which is the desired factorization

Equation at the end of step

1

:

 (x + 2) • (x - 4)  = 0  

STEP

2

:

Theory - Roots of a product

2.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2      Solve  :    x+2 = 0  

Subtract  2  from both sides of the equation :  

                     x = -2

Solving a Single Variable Equation:

2.3      Solve  :    x-4 = 0  

Add  4  to both sides of the equation :  

                     x = 4

Supplement : Solving Quadratic Equation Directly

Solving    x2-2x-8  = 0   directly  

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

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

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, 1 , 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   1.0000  

Plugging into the parabola formula   1.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 1.00 * 1.00 - 2.0 * 1.00 - 8.0

or   y = -9.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-2x-8

Axis of Symmetry (dashed)  {x}={ 1.00}  

Vertex at  {x,y} = { 1.00,-9.00}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-2.00, 0.00}  

Root 2 at  {x,y} = { 4.00, 0.00}  

Solve Quadratic Equation by Completing The Square

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

Add  8  to both side of the equation :

  x2-2x = 8

Now the clever bit: Take the coefficient of  x , which is  2 , divide by two, giving  1 , and finally square it giving  1  

Add  1  to both sides of the equation :

 On the right hand side we have :

  8  +  1    or,  (8/1)+(1/1)  

 The common denominator of the two fractions is  1   Adding  (8/1)+(1/1)  gives  9/1  

 So adding to both sides we finally get :

  x2-2x+1 = 9

Adding  1  has completed the left hand side into a perfect square :

  x2-2x+1  =

  (x-1) • (x-1)  =

 (x-1)2

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

  x2-2x+1 = 9 and

  x2-2x+1 = (x-1)2

then, according to the law of transitivity,

  (x-1)2 = 9

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-1)2   is

  (x-1)2/2 =

 (x-1)1 =

  x-1

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

  x-1 = √ 9

Add  1  to both sides to obtain:

  x = 1 + √ 9

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

  x2 - 2x - 8 = 0

  has two solutions:

 x = 1 + √ 9

  or

 x = 1 - √ 9

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    x2-2x-8 = 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   =     1

                     B   =    -2

                     C   =   -8

Accordingly,  B2  -  4AC   =

                    4 - (-32) =

                    36

Applying the quadratic formula :

              2 ± √ 36

  x  =    —————

                   2

Can  √ 36 be simplified ?

Yes!   The prime factorization of  36   is

  2•2•3•3  

√ 36   =  √ 2•2•3•3   =2•3•√ 1   =

               ±  6 • √ 1   =

               ±  6

So now we are looking at:

          x  =  ( 2 ± 6) / 2

Two real solutions:

x =(2+√36)/2=1+3= 4.000

or:

x =(2-√36)/2=1-3= -2.000

Answer:

It is similar to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).

Step-by-step explanation:

Answer:

510.7817 or 511

explanation:

First you’re going to have to substitute 10 in for x, so

Y= 52.7515(10) -16.7333

Y=527.515-16.7333

Then subtract

Y=510.7817

Answer:

32 * 28

Step-by-step explanation:

Just flip the positions of the two and you have your answer

Answer:

5 7/8

Step-by-step explanation:

Do the inverse operation.

5 + 7/8 = 5 7/8

Or, do this instead!

Add 7/8 to both sides of the equation. On the side before the equal sign, -78 and +78 cancel out, leaving m all by itself. Bring down the equals sign and we have m = 5 7/8!

Answer:

Step-by-step explanation:

364000

[tex]m = slope\\(x1, y1) = coordinates of first point in the line\\(x2, y2) = coordinates of second point in the line[/tex]

Answer:

I don’t know the answer but I can try to help.

Step-by-step explanation:

The slope is the measurement of the steepness of a line, so all you would have to do is find the steepness of the line on that graph.

I hoped this helped :)

THe answer to this problem is 78.57 percent.

Answer:

The answer is 192 ft. :D

Step-by-step explanation:

PLEASE mark me brainliest! :)

Step-by-step explanation:

a) 108 - double the equation

b) -3 - divide by 3

C) -54 - multiply by -3

d) 6 - divide by 9

Answer:

230,344,996 is my answer. Hope this could help you!

Answer:

i wish i could help  i would of

Step-by-step explanation:

Answer:

The answer is 1.54 × 10^1.

Hope this helps. :D

Step-by-step explanation:

Pls mark brainliest.

Answer:

True, true ,true, true?, false

Answer:

4 2/21

Step-by-step explanation:

2/3 and 3/7 have a common denominator, 21

so, 14/21 and 9/21

plug in the whole numbers: 1 14/21 and 2 9/21

which will give you: 3 23/21

so, simplify it which will give u the answer: 4 2/21

Answer:

x = 6.40312423743      y=12.8062484748

Step-by-step explanation:

To find the value of x, you must use the Pythagorean Therom.

a^2+b^2=c^2

5^2+4^2=c^2

25+16=c^2

41=c^2

Then find the square root of 41 so x = 6.40312423743.

Then to find y you must substitute the value of x in and use the triangle formula: 1/2(b)(h).

1/2(4)(6.40312423743)

y=12.8062484748

The answer is x = 6.40312423743      y=12.8062484748

Answer:

the awnser is 651 I hope this helps

Answer:

30 inches

Step-by-step explanation

because the other triangle is the same and its 30inches

Answer:

this doesn't even make any sense

Step-by-step explanation:

both -5.4 and 5.4 go off the m.f grid

Answer:

a and b would work in my opinion because it doesn't say in which specific order.

Answer:

the answer is b

Step-by-step explanation:

im sorry if it was wrong

Answer:

$1.10

Step-by-step explanation:

17.60 ÷ 16 and you have your answer 1.1 or $1.10

Answer:

q6 : b=-22

Q7.60×4=3h. 240=3h. 80=3h

Answer:

56m..................

Answer:

Well all you need is 2 points to calculate slope

You can follow the equation,

{y2-y1 / x2-x1} = slope

-2-1=-3

4-0=4

-3/4

-3/4 is the slope

Answer:

$45.13

Step-by-step explanation:

what is 12% of 51.28 change 12% to a decimal by moving two spaces to left =0.12. multiple by 51.28= 6.15 that is the amount of the tip then subtract it from 51.28-6.15= $45.13 original amount before the tip.

Answer:

43

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify.

(x + 3)² - 6

x = 4

Step 2: Evaluate

Follow Order of Operations.

Answer:

43

Step-by-step explanation:

Assuming you meant "evaluate x+3 squared          - 6    when x = 4, we get:

(x + 3)^2 - 6

Substituting 4 for x, we get 7^2 - 6, or 43.

Answer: Jacki did not subtract 12 from 8 correctly

Step-by-step explanation: it should be -4

Answer: C

Step-by-step explanation:

Jacki didn’t subtract 12 from 8 correctly he was suppose to get a negative and not 12

Answer:

6 minutes

Step-by-step explanation:

every minute is 120

720/120=6