The table shows values for a linear function, f (x ). What is an equation for f (x )?
Select the two values into the correct location.

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:

32 * 28

Step-by-step explanation:

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

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:

$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:Hello Uhhhhcora,

Scotts Miracle-Gro Mechanical Maintenance Technicians earn $61,000 annually, or $29 per hour, which is 32% higher than the national average for all Mechanical Maintenance Technicians at $44,000 annually and 8% lower than the national salary average for ​all working Americans.

Step-by-step explanation:

Hoped i helped. Ask me anything for questions. ♥Please subscribe to Addie Nahoe.♥

Answer:

$27.66

Step-by-step explanation:

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:

trucks: 8, cars: 18

Step-by-step explanation:

Answer:

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

Answer:

The answer if B. Hope this helps.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

To calculate the left side of the ratio, our calculator multiplies the right side by 14 and then divides the product by 4. To calculate the right side of the ratio, our calculator multiplies the left side by 4 and then divides the product by 14. Answers are rounded to two decimals if necessary.

Solved the given question by addition rules and the value of START is 10430.

Given-

The given problem is from the alphabetical puzzle. In the given problem the equation given is,

JOHN + CAN = START.

It can be written as,

   J  O  H  N

+      C  A  N

__________

S  T  A  R  T

__________

                N

            +  N

            ____

              1 0

            ____

J must be 9 with carried 1 to make the T 0.

A must be more than 10 to have a carry on J. A can not 1 as S has 1 digit. 2 and 3 disturbs the equation. Thus a must be 4. and for this o and c must be 6 and 7.

If a is 4 than the H and R must be 8 and 3.

The sum will look like,

  9  6  8  5

 +   7  4  5

________

1  0  4  3  0

_________

Hence, solved the given question by addition rules and the value of START is 10430.

For more about the addition follow the link below-

https://brainly.com/question/1709448

Answer:

11 with a remainder of 11

Step-by-step explanation:

the answer is 11 extra

Answer:

So the question is 341 divided by 30 = 11

I am thinking 11 is the remainder?

Step-by-step explanation:

Answer:

30 inches

Step-by-step explanation

because the other triangle is the same and its 30inches

Answer:

y=x-32

Step-by-step explanation:

y=mx+b where m is the slope and b is the y-intercept.

slope=change in y/change in x

=5/5

y=5x+b --> choose a random point

(7,3) ---> 3=5(7)+b=35+b

b= -32

y=x-32

Answer:

a.(x+5)(x-5) b.(y+6)(y-6) c.(x-1)(x+13) d. (s+2)(s+5)

Step-by-step explanation:

Sorry no step for c and d

for a 25 is a perfect square 5*5=25 -5*5=-25

for b it's same

sorry I'm rushing

Answer:

Its A i do believe

Step-by-step explanation:

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:

The answer is 192 ft. :D

Step-by-step explanation:

PLEASE mark me brainliest! :)

Answer:

Step-by-step explanation:

364000

Answer:

the awnser is 651 I hope this helps

Answer:

um

Step-by-step explanation:

Answer:

$1.10

Step-by-step explanation:

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

==================================================

Explanation:

The customer saves 15%, but still pays the remaining 85%. The two percentages add to 100%.

85% of $900 = 0.85*900 = 765

After the 15% discount is applied, the customer would pay $765

---------

Then after the sale, the price is marked up by 15%

This means we'll multiply by 1.15 to indicate a 15% increase

1.15*765 = 879.75

Notice that we don't get back to the original price (900) even though we increased by the same percentage as before. This is because 15% of a smaller number is a smaller amount; ie we have a smaller increase compared to the decrease earlier.

---------

Afterwards, divide the value 879.75 over the original price of $900

879.75/900 = 0.9775

Move the decimal point two spots to the right to end up with 97.75%

That percentage rounds to 98% when rounding to the nearest whole percent.

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:

True, true ,true, true?, false

Answer:

The answer would be 280

Step-by-step explanation:

If there are about 4 weeks in each month and she eats out every week for 45 dollars.

45x4=180

and if she goes to the movies each week at 25 dollars do the same thing.

25x4=100

when you add the two sums together

180+100=280

finally you subtract 280 from the original number,

500-280=220

so delores would have 220 dollar left over for other activities.

Answer:

She has 17 video games. (Possible answer.) Hope this helps!

Step-by-step explanation:

[tex]2x+5<40[/tex]

     -5.     -5

[tex]2x<35[/tex]

2.      2

[tex]X<17.2[/tex]

or 17 since it is less than 17.2