1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
iragen [17]
3 years ago
12

How do you solve (x+11)^2=2

Mathematics
1 answer:
True [87]3 years ago
5 0

Answer:

(x-11)2=2  Two solution  

Step-by-step explanation:

Step by step solution :

Step  1  :

1.1     Evaluate :  (x-11)2   =    x2-22x+121

Trying to factor by splitting the middle term

1.2     Factoring  x2-22x+119

The first term is,  x2  its coefficient is  1 .

The middle term is,  -22x  its coefficient is  -22 .

The last term, "the constant", is  +119

Step-1 : Multiply the coefficient of the first term by the constant   1 • 119 = 119

Step-2 : Find two factors of  119  whose sum equals the coefficient of the middle term, which is   -22 .

     -119    +    -1    =    -120

     -17    +    -7    =    -24

     -7    +    -17    =    -24

     -1    +    -119    =    -120

     1    +    119    =    120

     7    +    17    =    24

     17    +    7    =    24

     119    +    1    =    120

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  1  :

 x2 - 22x + 119  = 0

Step  2  :

Parabola, Finding the Vertex :

2.1      Find the Vertex of   y = x2-22x+119

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  11.0000  

Plugging into the parabola formula  11.0000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 11.00 * 11.00 - 22.0 * 11.00 + 119.0

or   y = -2.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-22x+119

Axis of Symmetry (dashed)  {x}={11.00}

Vertex at  {x,y} = {11.00,-2.00}

x -Intercepts (Roots) :

Root 1 at  {x,y} = { 9.59, 0.00}

Root 2 at  {x,y} = {12.41, 0.00}

You might be interested in
Help me please
Goshia [24]
Midpoint is (-2 , -0.5)
6 0
3 years ago
Terry rides her bike for 40 minutes and plays basketball for an hour. How many calories does she burn..? (Per Minute).
Ivan

Answer:

12

Step-by-step explanation:

6 0
3 years ago
What is 27 divide by 6588
Ipatiy [6.2K]
27 / 6588 = 0.00409836065
5 0
3 years ago
Read 2 more answers
Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. Th
denpristay [2]

Answer:

(1) Correct option is B.

(2) Correct option is C.

Step-by-step explanation:

The information provided is:

n_{1}=200,\ \bar x_{1}=22.7,\ s_{1} = 4.5\\n_{2}=200,\ \bar x_{2}=19.7,\ s_{2} = 4.3

The (1 - <em>α</em>)% confidence interval for the difference between two mean is:

CI=\bar x_{1}-\bar x_{2}\pm t_{\alpha/2, (n_{1}+n_[2}-2}\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}} }

The critical value of <em>t</em> is:

\alpha /2=0.05/2=0.025

degrees of freedom =n_{1}+n_{2}-2=200+200-2=398

t_{\alpha/2, n_{1}+n_{2}-2}=t_{0.025, 398}=1.96

Compute the 95% confidence interval for the difference between two mean as follows:

CI=22.7-19.7\pm 1.96\sqrt{\frac{4.5^{2}}{200}+\frac{4.3^{2}}{200} }\\=3\pm0.8624\\=(2.1376, 3.8624)\\\approx(2.14, 3.86)

Thus, the 95% confidence interval, (2.14, 3.86) implies that the true mean difference value is contained in this interval with probability 0.95.

Correct option is B.

The null value of the difference between means is 0.

As the value 0 is not in the interval this implies that there is a difference between the two means, concluding that priming does have an effect on scores.

Correct option is C.

4 0
3 years ago
4x + y = 3 -2x + 3y = -19 what's the solution plz help
Rainbow [258]

The solution to given system of equations is x = 2 and y = -5

<em><u>Solution:</u></em>

<em><u>Given the system of equations are:</u></em>

4x + y = 3 ---------- eqn 1

-2x + 3y = -19 ---------- eqn 2

We have to find the solution to above system of equations

<em><u>We can solve the system by substitution method</u></em>

From eqn 1,

4x + y = 3

Isolate y to one side

y = 3 - 4x ----------- eqn 3

<em><u>Substitute eqn 3 in eqn 2</u></em>

-2x + 3(3 - 4x) = -19

-2x + 9 - 12x = -19

Combine the like terms

-14x = -19 - 9

-14x = -28

Divide both sides of equation by -14

<h3>x = 2</h3>

<em><u>Substitute x = 2 in eqn 3</u></em>

y = 3 - 4(2)

y = 3 - 8

<h3>y = -5</h3>

Thus the solution is x = 2 and y = -5

5 0
3 years ago
Other questions:
  • Which is heavier 9 5/8 pounds or 9 3/4 pounds
    9·1 answer
  • Cooper is at the grocery store buying lunch meat for a party. Ham costs $4.50 per pound and turkey costs $2.75 per pound. If Coo
    7·2 answers
  • Identify the property or rule shown by each equation
    7·1 answer
  • Smallest to largest 7/12 1/2 2/3 4/10 1/6
    10·1 answer
  • Ali bounces a ball while Tim counts. Tim counts 11 tens and 2 ones. How many bounces did Tim count?
    14·1 answer
  • A geyser Erupts every fourth day . Another geyser erupts every sixth day. Today both geysers erupted. In how many days will both
    15·1 answer
  • Which one of the following reasons does NOT explain why 4x+5y does not equal 9xy
    5·1 answer
  • What is 545 times 35
    5·2 answers
  • Y - 4= -8 (x - 1)<br> linear or nonlinear?
    7·2 answers
  • Geometry help please :)
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!