solve for x enter the solution from least to greatest (x - 1)^2 - 9 = 0 Lesser x = ___ greater x = ____

Solve For X Enter The Solution From Least To Greatest (x - 1)^2 - 9 = 0 Lesser X = ___ Greater X = ____

Answers

Answer 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 2
Answer: X=4 or X= -2

Related Questions

The bottom of a ladder must be placed 5 feet from a wall. The ladder is 18 feet long. How far above the ground does the ladder touch the wall?

Answers

Answer:

The ladder meets the wall at 17.29 feet from the ground.

Step-by-step explanation:

Pythagorean Theorem ⇒ a^2 + b^2 = c^2

5^2 + b^2 = 18^2

25 + b^2 = 324

b^2 = 299

b = 17.291616

13 feet pal now go get ‘em

when keisha installed a fence along the 200 feet perimeter of her rectangular back yard she left and opening for GATE in diagram below she used X to represent the length of the gate

Answers

Perimeter of her rectangular back yard is: 200 ft

⇒ 2(30 + 60 + x) = 200

⇒ 30 + 60 + x = 200/2 = 100

⇒ 90 + x = 100

⇒ x = 100 - 90 = 10

ANSWER: A.10

Ok done. Thank to me :>

Please help with these three questions! Thank you! (No links! No trolls! Will mark brainliest!)

Answers

Answer:

1. 4*10^7

2. 5.1*10^-7

3.9,842,000,000(9.842*10^9)

Answer:

im answering so you can give them brainliest!

Step-by-step explanation:

Marielle is cutting equal-sized strips of ribbon for her scrapbook. She has 59 inches of ribbon. if she cuts 8 equal-sized pieces of ribbon, how long will each piece of ribbon be?

Answers

Answer:

7 .375

Step-by-step explanation:

First you need to divide 59 by 8.
59 divided by 8=7.375
7.375 is the answer

how do i find x and y

Answers

Answer:

The x is the x-axis, which is a horizontal line. The y is the y-axis, which is a vertical line. The y-axis goes up or down, while the x-axis goes left or right.

hope this helped.

have a great day!

the x-axis is the one on the bottom. the y-axis is the one on the right. when people say “rise over run” they mean y over x.

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help pls :) ... ....

Answers

Answer:

40°

Step-by-step explanation:

According to the Triangle Sum Theorem: The sum of the measures of the angles in a triangle will add up to 180°.

So with this, you need to add 70° and 70°.

You get 140°

Then to find the last angle, you will subtract the 140° by 180°.

180°-140° = 40°

Hope this helped! :)

Answer:

 40

Step-by-step explanation:

First you add 70 and 70 together to get 140 then minus it by 180.

Then you will get 40 degrees as your answer.

Hope This Helps :)

Could someone show me the streamline for this problem? The answer is 909, but I'd like to know how

1000-100+10-1

Answers

Answer:

1000-100=900,900+10=910,910-1=909

Step-by-step explanation:

Hey there!

1,000 - 100 + 10 - 1

1,000 - 100 = 900

= 900 + 10 - 1

900 + 10 = 910

= 910 - 1

= 909

Thus that’s why 1,000 - 100 + 10 - 1 is most likely equal to 909

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

pls help! i need this done in less than 20 minutes!

Answers

Answer:

46 units

Step-by-step explanation:

So first of all you do 8 × 2 which equals 16 units, then you do 15 × 2 which equals 30 units, then you 30 + 16 which equals 46 units. Hope this helps.

46 units
is the answer

Match the expression after you replace each variable.

a = 5 b = 6 c = 7

Answers

Step-by-step explanation:

ab                 =>    (5)(6) = 30

b + 3             =>    6 + 3 = 9

a + b + c       =>    5 + 6 + 7 = 18

3b + 4          =>    3(6) + 4 = 22

5a - c           =>    5(5) - 7 = 18

Help me please I dont get it

Answers

Answer:

x>10

Step-by-step explanation:

I hope it helps. Please let me know.

Answer:

2.5x > 25

Step-by-step explanation:

1. 10 + 2.5x > 35

2. 10 + 2.5x - 10 > 35 - 10 (Subtracting 10 from both sides)

3. 2.5x +10 - 10 > 35 - 10 (Group like terms)

4. 2.5x > 35 - 10 (Simplify the arithmetic)

5. 2.5x > 25

sterling plants a tree that is 4 3/4 feet tall. please do step by step!!!

Answers

Answer:

There's not really a question to answer there, you've only stated the information that we know. From what I can see the only conclusion I can make is that Sterling plants a tree that is 4 3/4 feet tall, but that's already written and with all the information provided that's really all I can say.

Sorry if that's not exactly what you were looking for, maybe if there's more to the question re-post it with the entire question?

The answer is 0.65
Hope this helps!

YOU BE THE TEACHER Your friend finds the slope of the line shown. Student work is shown. A line graphed on a coordinate plane. The line passes through the points at ordered pair 2 comma 3 and ordered pair 4 comma 1. A calculation is shown for the slope of the line. The first line reads, m equals start fraction 3 minus 1 over 4 minus 2 end fraction. The second line reads, equals start fraction 2 over 2 end fraction. The third line reads, equals 1.

Answers

Answer:

The slope of the line is -1

Find the selling price.

Markup ($) = percent markup (%) x original cost ($)

Selling price ($) = original cost ($) + markup ($)


A local gaming store bought a gaming console for $90. The gaming store sold the console, and the percent markup was 162%. What is the selling price?

The selling price is: $_________

Skip to navigation

Answers

Answer:

$145.80

Step-by-step explanation:

The original cost of the product was $90.  There was a 162% markup.  In order to get the selling price, I like to take away 100 percent and simply add original price+(original price*62%).  After taking away 100%, I am left with 62%.  I then multiply the original cost ($90) by the remaining percent (62%), getting 55.8.  Following the steps that I originally wrote, I now add 90 to 55.8, getting 145.8.

Answer:$145.80

Step-by-step explanation:

Look at this picture and answer plz

Answers

Answer: First top box is 2400, 2nd top box is 120

423x6 = 2400 + 120 +18 = 2538

Step-by-step explanation:

423 x 6=2400+120+18=2538

An object is traveling at a steady speed of 9 9/10 km/h. How long will it take for the object to travel 2 1/10 km? First round to the nearest integer to find the estimated answer. Then find the exact answer. (I don't know what I'm doing.)

Answers

Answer:

7/33

Step-by-step explanation:

9 9/10= 99/10

2 1/10= 21/10

21/10 / 99/10 = 21/10 x 10/99 = 210/990 = 21/99 = 7/33

Answer:

12

step by step

I got it wrong and it said the answer is 12

Mathematically, why am i so uneducated?

Answers

I getchu the education system is a mess!!

Answer:

I know this is most likely a joke but I'll answer anyways :)

"Mathematically" you might have poor education whether it's bad teachers, bad school, or maybe you're just not working hard enough. Maybe you are educated and you're just comparing yourself against smarter people which might make you seem not very educated. Or maybe you're secretly a super genius prodigy and you're just too lazy too show it. Who knows...

help with question number 40 please

Answers

y = 1.5x + 6.5
hope this is helpful!
y=1.5+6.5 good luck

5/7 of __ is 1/7 plz help asap

Answers

[tex]\dfrac 57 x = \dfrac 17 \\\\\implies 5x =1 \\\\\implies x = \dfrac 15 \\\\\\\text{Hence }~ \dfrac 57 ~ \text{of}~ \dfrac 15 ~ \text{is }~\dfrac 17[/tex]

Answer:

1/5

Step-by-step explanation:

'of' is the same as multilpy

5/7 × ? = 1/7

? = 1/7 ÷ 5/7

? = 1/7 × 7/5 = 7/35

?=7/35

? = 1/5

check answer:

5/7 of 1/5 = 5/7 ×1/5 = 5/35 = 1/7

Please give Examples for real life examples for expressing very small number sin standard form.

Answers

Scientific notation is a system for expressing very large or very small numbers in a compact manner. It uses the idea that such numbers can be rewritten as a simple number multiplied by 10 raised to a certain exponent, or power.

Since the sanctuary was established, the estimated population of American robins in the area has increased from 86 to 102.
Describe the percent change in the estimated population of American robins. Round to the nearest whole percent.
Enter your answer in the box to complete the sentence.

Answers

Answer:

15.7%

Step-by-step explanation:

102-86=16

(16*100)/102

The diameter of each wheel of the car is 80 cm. How many complete rounds does each wheel rotate in 10 minutes when the car is moving at 60 km / h?

Answers

Answer:

The answer is 140cm

please help this is my last question

Answers

The chief will need 3 cups of water.

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?
A. y = 1/2x + 2

B. y = 1/2x + 1

C. y = x + 2

D. y = 2x + 1

Answers

Answer:

B. y = 1/2x + 1

Step-by-step explanation:

y is added up by 1, while it is split 1/2 from x.

hope this helps.

a store sells laptops for 720 each. this price is 20 percent more than what it cost the store to buy each of them. before the next model's release, store employees can purchase any remaining laptops at 23% off the store's cost cost. how much would it cost an employee to purchase one of these laptops at the sale?

Answers

Answer:

462

Step-by-step explanation:

720 is 120% of the store price so to find the store price, we can muliply by the reciprical or 5/6.

720*5/6= 600

The employee can purchase the laptop at 23% off this price or at 77%. Multiply the price by 0.77 to get the employee price.

600*0.77 = 462

The total cost of the laptop at which an employee purchase is 482 and this can be determined by using the unitary method.

Given :

A store sells laptops for 720 each. This price is 20 percent more than what it cost the store to buy each of them. Before the next model's release, store employees can purchase any remaining laptops at 23% off the store's cost.

The following steps can be used in order to determine the total cost of the laptop at which an employee purchase:

Step 1 - The unitary method can be used in order to determine the total cost of the laptop at which an employee purchases.

Step 2 - According to the given data, 720 is the 120% cost at which the store sells. So, the value of the 100% cost is:

[tex]=\dfrac{720}{120}\times 100[/tex]

= 600

Step 3 - Now, the employee can purchase the laptop at a 23% discount that is 77% of the original cost.

Step 4 - So, the total cost of the laptop at which an employee purchase is:

[tex]=\dfrac{77}{100}\times 600[/tex]

= 462

For more information, refer to the link given below:

https://brainly.com/question/12116123

Write the equation of the line that passes through the points (8,−7) and (−9,7). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answers

Answer:

y + 7 = (-14/17)(x - 8)

Step-by-step explanation:

We want the equation of this line in the point-slope form y - k = m(x - h).

We are given two points (8, -7) and (-9, 7), and may arbitrarily choose one of them to serve as the point (h, k) in the point-slope form shown above.  Then the other point is represented by (x, y) in the point slope form shown above:

Let (h, k) be 8, -7) and let (x, y) be (-9, 7).  Then,  y - k = m(x - h) becomes:

7 - (-7) = m(-9 - 8), so that 14 = m(-17), and the slope is thus m = -14/17

The desired equation is then y + 7 = (-14/17)(x - 8) (which is in point-slope form).  

Another way to get this result would be to find m in the usual way:

          rise           14

m = ------------- = --------- = -14/17 (same as before).

           run           -17

(−4)(−5)−(−10÷−5) .....

Answers

With PEMDAS it would be 18 I believe

Answer:

18

Step-by-step explanation:

PLS HELP!! ME I NEED HELP!!!!

Answers

Answer:

i think its c

Step-by-step explanation:

The product is a positive exponent

The table shows the number of blue marbles and red marbles that four friends have collected.


Which person has the HIGHEST!!!! ratio of blue to red marbles?

Jasmine

Aaron

Lucian

Gretchen

Answers

Answer:

Gretchen

Step-by-step explanation

Jasmine: 12/10 : 1

Aaron: 3/2 : 1

Lucian: 1 : 1

Gretchen: 7 : 1

Gretchen has the most blue marbles :/

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

Answers

Answer:

[tex]\sqrt19[/tex]

Step-by-step explanation:

First we solve for the biggest triangle: using the Pythagorean theorem, (a^2 + b^2 = c^2) we put in the sides,

9^2 + b^2 = 10^2.

solve, 81 + b^2 = 100

then we subtract 81 from both sides. b^2 = 19, and the answer is [tex]\sqrt 19[/tex].

Now we know what the third side is, which is the hypotenuse for the smaller triangle, so we use the Pythagorean theorem again.

4^2 + x^2 = 19.

Solve

16 + x^2 = 19

Subtract 16 from both sides

x^2 = 19

and finally, we take the square root of both sides

x = [tex]\sqrt19[/tex]

Square root of 19 would be your answer

HELP PLS


Decode the

×&[ >s ;[;


Who is Gary
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Please more info,
This is very confusing
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