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Simplify the following expression: -4 of [2 ÷ 84 ÷ 7 - 1]
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Step-by-step solution
21 stepsEvaluate the expression inside the innermost parentheses.
Substitute this value back into the expression.
"of" means multiplication. Perform divisions from left to right.
Substitute this result back into the brackets.
Perform the final multiplication.
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2.
The value of the expression is .
Define the two-digit number using its digits.
Let the tens digit be and the units digit be .
The number can be represented as .Formulate equations based on the given conditions.
Condition 1: The product of the digits is 20.
Condition 2: When the digits are reversed, the new number is greater than the original number by 9.
The reversed number is .Simplify the second equation.
Subtract and from both sides:
Divide by 9:
From (2), we can express in terms of :
Substitute the expression for into equation (1).
Rearrange into a quadratic equation:
Solve the quadratic equation for .
Factor the quadratic equation:
Possible values for are or .
Since is a digit of a positive two-digit number, it must be a positive integer between 1 and 9.
Therefore, .Find the value of using .
Form the original two-digit number.
The number is .
Verify the conditions.
Product of digits: (Correct).
Reversed number: 54.
Difference: (Correct).The number is .
Rewrite the first term using the exponent rule .
Substitute this back into the original equation.
Factor out the common term .
Express 625 as a power of 5.
Substitute back into the equation.
Use the exponent rule on the left side.
Since the bases are equal, equate the exponents.
Solve for .
The solution for is .
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