The product of two positive numbers is 750. The first number is 5 less than the second number. The equation x(x – 5) = 750 can be used to fi

Question

The product of two positive numbers is 750. The first number is 5 less than the second number. The equation x(x – 5) = 750 can be used to find x, the value of the greater number. What is the value of the greater number? 15 25 30 50

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Maria 1 week 2021-09-10T11:09:29+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T11:10:36+00:00

    Answer:

      30

    Step-by-step explanation:

    You can try the answer choices to see what works.

      15·10 ≠ 750

      25·20 ≠ 750

      30·25 = 750 . . . . the larger number is 30

      50·45 ≠ 750

    0
    2021-09-10T11:10:57+00:00

    Answer:

    The value of the greater number is 30.

    Step-by-step explanation:

    We need to find the values of x that satisfy the equation :

    x(x-5)=750

    Working with the equation ⇒

    x(x-5)=750

    x^{2}-5x=750

    x^{2}-5x-750=0

    Given an equation with the form

    ax^{2}+bx+c=0

    We can use the quadratic equation to find the values of x

    x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a} and

    x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}

    With a=1\\b=-5\\c=-750 we replace in the equations of x1 and x2 ⇒

    x1=\frac{-(-5)+\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=30

    x1=30 is a solution of the equation x^{2}-5x-750=0

    Now for x2 ⇒

    x2=\frac{-(-5)-\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=-25

    x2=-25 is a solution of the equation x^{2}-5x-750=0

    Given that both numbers are positive ⇒

    x>0 and (x-5)>0\\x>5

    Therefore, x2 is not a possible value for the greater number

    The greater number is x1=30

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