![kobz](/avatars/6373.jpg)
kobz
27.02.2020 •
Mathematics
Solve (x-4)^2=5 get it correct and get brainliest
Solved
Show answers
More tips
- L Leisure and Entertainment 10 Ways to Celebrate Your Favorite Holidays: A Guide to Festivities and Traditions...
- S Sport When will the Biathlon World Championships 2011 take place in Khanty-Mansiysk? Answers to frequently asked questions...
- O Other What is a Disk Emulsifier and How Does it Work?...
- F Family and Home What does a newborn need?...
- F Family and Home Choosing the Right Car Seat for Your Child: Tips and Recommendations...
- F Food and Cooking How to Get Reconfirmation of Registration?...
- C Computers and Internet How to Get Rid of Spam in ICQ?...
- A Art and Culture Who Said The Less We Love a Woman, the More She Likes Us ?...
- F Family and Home How to Get Rid of Your Neighbors?...
- S Society and Politics How Could Nobody Know About the Dead Mountaineers?...
Answers on questions: Mathematics
- M Mathematics For this question, use the spinner shown in the picture. P(D) = _____________ Write your answer as a fraction in simplest form....
- M Mathematics Please Answer This N o w...
- M Mathematics I need this answer today i will give you a crown and good raitings if you get it write and you give it to me today...
- M Mathematics If the triangles are similar, what is the value of x?...
- M Mathematics Need to find the sum of the series but I’m not sure how to solve will give brainliest...
- M Mathematics Considere os conjuntos A = {2, 4, 5, 12, 40, 53} e B = { 9, 12, 30, 90} determine A-B...
- M Mathematics All Classes/Quarantine & DAEP (November 19 & 20 ) Upcoming Woohoo, no work due soon! View all Assignment: Chapter 25 & 26 Vocabulary Aftin Lovely posted...
- M Mathematics Opposite = 13 adjacent = 4 what is size of angle xyz...
- M Mathematics What rating would you give me 1-10? If u can guess my age right u get brainliest...
- M Mathematics Help pls need this for my grade (answers were wrong)...
Ответ:
Two solutions were found :
x =(8-√20)/2=4-√ 5 = 1.764
x =(8+√20)/2=4+√ 5 = 6.236
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x-4)^2-(5)=0
Step by step solution :
Step 1 :
1.1 Evaluate : (x-4)2 = x2-8x+16
Trying to factor by splitting the middle term
1.2 Factoring x2-8x+11
The first term is, x2 its coefficient is 1 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is +11
Step-1 : Multiply the coefficient of the first term by the constant 1 • 11 = 11
Step-2 : Find two factors of 11 whose sum equals the coefficient of the middle term, which is -8 .
-11 + -1 = -12
-1 + -11 = -12
1 + 11 = 12
11 + 1 = 12
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 8x + 11 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-8x+11
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 4.0000
Plugging into the parabola formula 4.0000 for x we can calculate the y -coordinate :
y = 1.0 * 4.00 * 4.00 - 8.0 * 4.00 + 11.0
or y = -5.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-8x+11
Axis of Symmetry (dashed) {x}={ 4.00}
Vertex at {x,y} = { 4.00,-5.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.76, 0.00}
Root 2 at {x,y} = { 6.24, 0.00}
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-8x+11 = 0 by Completing The Square .
Subtract 11 from both side of the equation :
x2-8x = -11
Now the clever bit: Take the coefficient of x , which is 8 , divide by two, giving 4 , and finally square it giving 16
Add 16 to both sides of the equation :
On the right hand side we have :
-11 + 16 or, (-11/1)+(16/1)
The common denominator of the two fractions is 1 Adding (-11/1)+(16/1) gives 5/1
So adding to both sides we finally get :
x2-8x+16 = 5
Adding 16 has completed the left hand side into a perfect square :
x2-8x+16 =
(x-4) • (x-4) =
(x-4)2
Things which are equal to the same thing are also equal to one another. Since
x2-8x+16 = 5 and
x2-8x+16 = (x-4)2
then, according to the law of transitivity,
(x-4)2 = 5
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-4)2 is
(x-4)2/2 =
(x-4)1 =
x-4
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-4 = √ 5
Add 4 to both sides to obtain:
x = 4 + √ 5
Since a square root has two values, one positive and the other negative
x2 - 8x + 11 = 0
has two solutions:
x = 4 + √ 5
or
x = 4 - √ 5
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-8x+11 = 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 = -8
C = 11
Accordingly, B2 - 4AC =
64 - 44 =
20
Applying the quadratic formula :
8 ± √ 20
x = —————
2
Can √ 20 be simplified ?
Yes! The prime factorization of 20 is
2•2•5
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).
√ 20 = √ 2•2•5 =
± 2 • √ 5
√ 5 , rounded to 4 decimal digits, is 2.2361
So now we are looking at:
x = ( 8 ± 2 • 2.236 ) / 2
Two real solutions:
x =(8+√20)/2=4+√ 5 = 6.236
or:
x =(8-√20)/2=4-√ 5 = 1.764
Two solutions were found :
x =(8-√20)/2=4-√ 5 = 1.764
x =(8+√20)/2=4+√ 5 = 6.236
Processing ends successfully
Ответ:
64/125 cubic meter
Step-by-step explanation:
volume = l × b × h
volume of a cube = s × s × s
∴ 4/5 × 4/5 × 4/5 = 64/125