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nadezda [96]
3 years ago
9

Create a list of steps, in order, that will solve the following equation 1/4(x+5)^2-1=3

Mathematics
1 answer:
julia-pushkina [17]3 years ago
6 0

Answer:

either x = -1, or x = - 9

Step-by-step explanation:

given   \frac{1}{4} (x+5)^{2} -1=3

add one to both sides   \frac{1}{4} (x+5)^{2} =4

im not sure which one comes first. either you multiply both the x and the 5 in the parenthesis by \frac{1}{4}. or you square x and 5

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :   1/4*(x+5)^2-(4)=0  

Step by step solution :

Step  1  :

           1 /4

Equation at the end of step  1  :

  1                  

 (— • (x + 5)2) -  4  = 0  

  4                  

Step  2  :

Equation at the end of step  2  :

 (x + 5)2    

 ———————— -  4  = 0  

    4        

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

        4         4 • 4

   4 =  —  =  ———

        1            4  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+5)2 - (4 • 4)     x2 + 10x + 9

———————     ———————  =  ——

       4                        4      

Trying to factor by splitting the middle term

3.3     Factoring  x2 + 10x + 9  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +10x  its coefficient is  10 .

The last term, "the constant", is  +9  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 9 = 9  

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   10 .

     -9    +    -1    =    -10  

     -3    +    -3    =    -6  

     -1    +    -9    =    -10  

     1    +    9    =    10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  9  

                    x2 + 1x + 9x + 9

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+1)

             Add up the last 2 terms, pulling out common factors :

                   9 • (x+1)

Step-5 : Add up the four terms of step 4 :

                   (x+9)  •  (x+1)

            Which is the desired factorization

Equation at the end of step  3  :

 (x + 9) • (x + 1)

 —————————————————  = 0  

         4        

Step  4  :

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 (x+9)•(x+1)

 ——————————— • 4 = 0 • 4

      4      

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  (x+9)  •  (x+1)  = 0

Theory - Roots of a product :

4.2    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 :

4.3      Solve  :    x+9 = 0  

Subtract  9  from both sides of the equation :  

                     x = -9

Solving a Single Variable Equation :

4.4      Solve  :    x+1 = 0  

Subtract  1  from both sides of the equation :  

                     x = -1

Supplement : Solving Quadratic Equation Directly

Solving    x2+10x+9  = 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

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√2 times √800 anyone know?
jeka94

\sqrt{2}  \times  \sqrt{800}

\sqrt{2}  \times 20 \sqrt{2}

\sqrt{2}  \times  \sqrt{2}  =  \sqrt{4}  \:  = 2

20 \times 2 = 40

therefore \:  \:  \:  \sqrt{2}  \times  \sqrt{800} = 40
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3 years ago
Round 3.44570830811 to the nearest hundred-thousandth,
Alika [10]

Answer:

3.44571

Step-by-step explanation:

look at the number to the right of the decimal. if the number is higher than or is 5 round the number up, but if the number is less than 5 it will stay the same.

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2 years ago
More evaluation that I need help on p.s you do not need to explain your work because I just need the answer
makvit [3.9K]

Your answer is C) 1/9

lol I just solved the other answer sorry but people are going to try and take free points so I needed to give an answer to show that someone did something. Hope I helped anyway. You don't need to mark brainliest, but I'd appreciate it if you did.

<h2>-^_^-</h2>
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3 years ago
Shelby made $200 from selling candy bars. Large, x, candy bars sell for $4 each and smaller, y, candy bars sell for $2 each. Wri
babymother [125]

Answer:

The Equation is

4x+2y= 200

Then total number of candy bars is

X+Y

Step-by-step explanation:

Shelby made $200 from selling x at $4 each and y at $2 each.

Let's have in mind that x is the number of large candy bars

And y is the number of small candy bars

The equation is simple

The amount it was sold is going to be the coefficient of the numbers we don't Know...

So

Equation is

4x+2y= 200

Then total number of candy bars is

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3 years ago
The exam scores (out of 100 points) for all students taking an introductory Statistics course are used to construct the followin
ella [17]

Answer:

The inter quartile range is 55

Step-by-step explanation:

<u>Interquartile range</u>:-

<u>Definition</u>:-

The inter quartile range is the difference between the upper (Q3) and lower(Q1) quartiles, and describes the middle  50% of values when ordered from lowest to highest.

Interquartile range = higher quartile - lower quartile

given data 50.25.80.10

write the ascending order 10 25 50 80

Step:-1

Median:- The median is obtained by first arranging the data in ascending or descending order and applying the following rule.

If the number of observations is odd, then the median is

({\frac{n+1}{2} })^{th}observations

Step2:-

The median is obtained by first arranging the data in ascending or descending order and applying the following rule.

If the number of observations is even, then the median is ({\frac{n}{2} })^{th}

({\frac{n+1}{2} })^{th}

In given data the number of observations is '4'(even)

If the number of observations is even, then the median is ({\frac{n}{2} })^{th}

({\frac{n+1}{2} })^{th}

median is ({\frac{4}{2} })^{th} is 2 observations and ({\frac{4+1}{2} })^{th} is 2.5 observations.

so we have to select average of these two observations.

therefore the median is '3' observation

median of the given data = 50

<u>Step:3</u>

Interquartile range = higher quartile - lower quartile

                                  = 80-25

                                  =55

3 0
3 years ago
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