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anygoal [31]
3 years ago
8

5x+2=5x+2 has how many solutions?

Mathematics
1 answer:
tigry1 [53]3 years ago
8 0
It has 1 solution i believe
You might be interested in
Create a list of steps, in order, that will solve the following equation 1/4(x+5)^2-1=3
julia-pushkina [17]

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

6 0
3 years ago
Please help I'm begging
Elina [12.6K]
The figure is made up of a cone and a cylinder.

Diameter = 16 ft
radius = 16÷2 = 8ft

Volume of the cone = 1/3bh
Volume of the cone = \frac{1}{3}  \pi  r^{2} h
Volume of the cone =  \frac{1}{3} \pi 8^{2}(6) = 402.12

Volume of the cyclinder = bh
Volume of the cylinder = \ \pi r^{2} h
Volume of the cylinder = \ \pi 8^{2}(4) = 1206.37

Total = 402.12 + 1206.37 = 1608.49 cubic feet

6 0
3 years ago
If you understand, please put the answer!
il63 [147K]

Step-by-step explanation:

3-8 is diagnal 7-2 is also 7-2 is the answer

8 0
3 years ago
PLEASE HELP MEEEEE!!!!!!!
OverLord2011 [107]

Answer:

  1. Cheese: 4\frac{3}{8}  
  2. Milk: 1\frac{2}{3}  
  3. Pasta: 6\frac{1}{4}

Step-by-step explanation:

Cheese:

  1. 1\frac{3}{4} = \frac{7}{4}  
  2. Set up a proportion: \frac{\frac{7}{4} }{4} = \frac{x}{10}  
  3. Cross multiply, then divide: 10 × 7/4 = 17.5, 17.5 ÷ 4 = 4.375
  4. 4.375 = 4\frac{3}{8}  

Milk:

  1. Set up a proportion: \frac{\frac{2}{3} }{4} = \frac{x}{10}  
  2. Cross multiply, then divide: 10 × 2/3 = 6\frac{2}{3}, 6\frac{2}{3} ÷ 4 = 1\frac{2}{3}  

Pasta:

  1. 2\frac{1}{2} = \frac{5}{2}  
  2. Set up a proportion: \frac{\frac{5}{2} }{4} = \frac{x}{10}  
  3. Cross multiply, then divide: 10 × 5/2 = 25, 25 ÷ 4 = 6.25
  4. 6.25 = 6\frac{1}{4}  

I hope this helps!

4 0
3 years ago
A bakery has 2,160 loaves of whole-wheat bread in July. In all, the bakery SOLD 9000 loaves THIS MONTH. What percent of the loav
Bumek [7]
24% because you would make a ratio like x/100= 2,160/9000. So basically the x is the percentage you need, 100 is just an easy factorable percent, and 2,160 is the wheat bread and 9000 is all the bread. Basically what you do with this ratio is you cross multiply. This means you multiply 2,160 by 100 and divide by 9000 and that’s your percent
3 0
3 years ago
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