Solve for x. Round to the nearest tenth, if necessary.

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:

A

Step-by-step explanation:

Answer: 50

Step-by-step explanation:

Step-by-step explanation:

the equation is y=mx + b. the m (or the thing that comes before the x in the equation) is your slope, the y intercept is the last number. if the last number is preceded by a minus sign, the intercept number is negative

Answer:

For example, number 1's slope is 5/3.  On a graph, you would go up 5 (not in block, but in numerical value) and right 3.   The y-intercept is -2.  This is where your line starts on the graph.

Step-by-step explanation:

y=mx+b       b= y-intercept   y-intercept=where the line crosses the y-axis    m=slope         slope== rise/run or slope formula, m=y2-y1/x2-x1

Answer:

The answer is 3.44

Step-by-step explanation:

4.3 × 0.8 = 3.44

The answer is 3.44

-TheUnknownScientist 72

Answer:

3.44

Step-by-step explanation:

Answer:x = 164686.592598

Step-by-step explanation:

219379.01−x/x = 0.3321

−x+219379.01/x = 0.3321

Step 1: Multiply both sides by x.

−x+219379.01≈0.3321x

−x+219379.01 − 0.3321x = 0.3321x−0.3321x (Subtract 0.3321x from both sides)

−1.3321x + 219379.01 = 0

−1.3321x + 219379.01 − 219379.01 = 0 − 219379.01 (Subtract 219379.01 from both sides)

−1.3321x = −219379.01

−1.3321x/−1.3321 = −219379.01/−1.3321

(Divide both sides by -1.3321)

x = 164686.592598

Answer:

  164,686.59

Step-by-step explanation:

Carry out the division, then solve for x.

  (219,379.01 - x) / x = .3321 . . . . . given

  219,379.01/x -1 = 0.3321

  219,379.01/x = 1.3321 . . . . add 1

  219,379.01/1.3321 = x ≈ 164,686.59 . . . . multiply by x/1.3321

Rounded to 8 significant digits, the value of x is 164,686.59.

_____

The fractional portion is 7894/13321, which has a very long repeating decimal equivalent.

Answer: he will have only one cookie left

Step-by-step explanation:

Answer:90

Step-by-step explanation:

let the number of cookies be x

let the number of friends by y

x - 5y = 0

x - 3y = 36

subtract them:

-2y = -36

y = 18

x - 5(18) = 0

x = 90

John has 90 cookies.

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 There!

According to the question,

It is said that we have to find calories in 4 cups.

First we have to find in each cup.

So

[tex] \frac{3}{4} \times x = 99 \\ \\ so \: x = 99 \times \frac{4}{3} \\ \\ [/tex]

simplify 99 and 3 then it will look like

[tex]33 \times \frac{4}{1} [/tex]

1 has no value so 33×4=132 calories

Now it is in each cup or 1 cup.

To find in 4 cups, multiply 132×4

[tex]132 \times 4 = 528[/tex]

So 528 calories is the answer.

[tex]\Large\textsf{Hope \: It \: Helped}[/tex]

[tex]\dfrac{x}{4} < -1.5\\\\\implies \dfrac x4 < -\dfrac 32\\\\\implies x < -\dfrac{3}2 \times 4\\\\\implies x< -\dfrac{12}2}\\\\\implies x<-6[/tex]

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:

Stem and Leaf Plot ⇒ Makes it easy to see the largest, smallest and most common data values.

Double Bar Graph ⇒ Compares two sets of data.

Bar Graph ⇒ Shows whether one type of data increases, decreases or neither when another type of data increases.

Scatter Plot ⇒ Shows the frequency of results and trends clearly.

Step-by-step explanation:

Stem and Leaf Plot makes a set of data easy to see and shows common data values together.

Double bar graph is the only graph that focuses solely on 2 sets of data.

Bar Graph description is a bit weird for this one to me but it's the last one (I did others first) and it is close enough.

Scatter plot is best at showing frequency and trends and to see the approximate increase/decrease of many data points.

Answer:

The two roots are -12/5 and 18/5

Step-by-step explanation:

One way of simplifying the work involved here is to isolate y:  start this by dividing all 3 terms by 5, obtaining:

|y - 3/5| = 3

Then 3/5 is the 'center' and 3 is the distance from this center to each of the two roots.

First root is 3/5 + 3, or 3 3/5, or 18/5.

Second root is 3/5 - 3, or -2 2/5, or -12/5

Answer:

the third one, y = 1/2x + 3

Answer:

y = 1/2x + 3

Step-by-step explanation:

The y intercept is 3 and the slope is 1/2.

Your answers are all on the attachments and the explanations as well

Step-by-step explanation:

Click the attachments pleaseee!

hope this helped :3!

32 x 28

you just have to flip them, and it'll be commutative! :D

Answer:

its about drive

its about power

Step-by-step explanation:

Answer:

58 /33

Step-by-step explanation:

Use math-way for math questions:)

Answer:

58/33

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

clearly C can be interpreted as the said word problem

Answer:

C.

Step-by-step explanation:

and the number is 9

Because 9 + 5 = 14.

Answer:

y=60

Step-by-step explanation:

196 - 16 = 180

7 + 5 = 12

12 + 3y = 15y

2 * 15y = 30y

180 ÷ 30 = 60

y = 60

Answer:

y=26

Step-by-step explanation:

Let's solve your equation step-by-step.

2(3y+7+5)=196-16

Step 1: Simplify both sides of the equation.

2(3y+7+5)=196-16

(2)(3y)+(2)(7)+(2)(5)=196+-16 (Distribute)

6y+14+10=196+-16

(6y)+(14+10)=(196=-16) (Combine Like Terms)

6y+24=180

Step 2: Subtract 24 from both sides.

6y+24-24=180-24

6y=156

Step 3: Divide both sides by 6.

6y/6 = 156/6

y=26

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:

10 meters

Step-by-step explanation:

C = D/N

Circumference = Distance / Number of Rotations

Answer:

10 meters

Step-by-step explanation:

500 meter divided by 50 is 10 metters making the circumfrerence of his wheel 10 meters

Answer:

Step-by-step explanation:

B is correct. Your starting amount is 210$ And you're taking away 15$ each time she uses the club,x.

Answer: 7776 :^

Step-by-step explanation:

Answer:

X20=35/100 do  35 times 20 which is 700do 700 divided by 100 so the answer is 7

Step-by-step explanation:

Answer:

±16

Step-by-step explanation:

the square root of 256 is positive or negative 16! (if it only lets you put one answer, put positive 16).

Answer:

16

Step-by-step explanation:

16*16=256

Answer:

they r all multiple by 3

Step-by-step explanation:

2×3=6

4×3=12

6×3=18

8×3=24

10×3=30

Answer:

Step-by-step explanation:

as hotdogs (x) increase by 2 the cost (y) increases by 6

6/2 = 3/1 = 3

y = 3x