When simplified completely, the product of a monomial and a binomial is ______ a trinomial. Always Never Sometimes

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• Certainly! Here's a clear explanation and the steps to form the equation and solve it: A) To write an equation, we need to define the variables for the number of dimes and quarters. Let's call the number of dimes 'd'. Since the number of quarters is 8 less than the number of dimes, we can call the number of quarters 'd - 8'. Now we know that the value of a dime is $0.10 and the value of a quarter is $0.25. To find the total value of the dimes and quarters, we multiply the number of each coin by its value and add these amounts together to equal $4.30. The equation representing the total value is: 0.10d (value of the dimes) + 0.25(d - 8) (value of the quarters) = $4.30 B) To solve for the number of dimes, clear the decimals from the equation by multiplying every term by 100: 10d + 25(d - 8) = 430 Now distribute the 25 through the parentheses: 10d + 25d - 200 = 430 Combine like terms: 35d - 200 = 430 Add 200 to both sides to solve for 35d: 35d = 630 Now divide by 35 to solve for d: d = 630 / 35 d = 18 There are 18 dimes in the jar.