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Ira Lisetskai [31]
2 years ago
9

The 373 students who listed soccer as their favorite sport were 13 more than three times the number of students who listed baske

tball as their favorite sport. How many students chose basketball as their favorite sport? Write this as an equation.
Mathematics
1 answer:
wariber [46]2 years ago
6 0
373-13=360
360 divided by three equal to 120
So 120 children chose basketball
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Step-by-step explanation:

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Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.
skad [1K]

5-2x2=-15

Two solutions were found :

                  x = ± √10 = ± 3.1623

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    5-2*x^2-(-15)=0

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (5 -  2x2) -  -15  = 0

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  20 - 2x2  =   -2 • (x2 - 10)

Trying to factor as a Difference of Squares :

3.2      Factoring:  x2 - 10

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 10 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  3  :

 -2 • (x2 - 10)  = 0

Step  4  :

Equations which are never true :

4.1      Solve :    -2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2      Solve  :    x2-10 = 0

Add  10  to both sides of the equation :

                     x2 = 10

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 10  

The equation has two real solutions  

These solutions are  x = ± √10 = ± 3.1623  

Two solutions were found :

                  x = ± √10 = ± 3.1623

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3 years ago
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