An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.

let

x  = one integer

y = another integer

x = 5y - 3

If the product of the two integers is 36, then find the integers.

x * y = 36

(5y - 3) * y = 36

5y² - 3y = 36

5y² - 3y - 36 = 0

Solve the quadratic equation using factorization method

That is, find two numbers whose product will give -180 and sum will give -3

Note: coefficient of y² multiplied by -36 = -180

5y² - 3y - 36 = 0

The numbers are -15 and +12

5y² - 15y + 12y - 36 = 0

5y(y - 3) + 12 (y - 3) = 0

(5y + 12) (y - 3) = 0

5y + 12 = 0      y - 3 = 0

5y = - 12           y = 3

y = -12/5

The value of y can not be negative

Therefore,

y = 3

Substitute y = 3 into x = 5y - 3

x = 5y - 3

x = 5(3) - 3

= 15 - 3

= 12

x = 12

Therefore,

(x, y) = (12, 3)

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3, 12

Step-by-step explanation:

Et x and y be the required integers.

Case 1: x = 5y - 3...(1)

Case 2: xy = 36

Hence, (5y - 3)*y = 36

Hence, the required integers are 3 and 12.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.