Simplify the following expression: -4 of [2 ÷ 84 ÷ 7 - 1]

Step 1: Evaluate the expression inside the innermost parentheses. (-4 + -9 + 15) = (-13 + 15) = 2 Step 2: Substitute this value back into the expression. -4 of [2 ÷ 84 ÷ 7 - 1] "of" means multiplication. Perform divisions from left to right. 2 ÷ 84 = (2)/(84) = (1)/(42) (1)/(42) ÷ 7 = (1)/(42 × 7) = (1)/(294) Step 3: Substitute this result back into the brackets. -4 × [(1)/(294) - 1] -4 × [(1)/(294) - (294)/(294)] -4 × [-(293)/(294)] Step 4: Perform the final multiplication. (4 × 293)/(294) = (1172)/(294) Step 5: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2. (1172 ÷ 2)/(294 ÷ 2) = (586)/(147) The value of the expression is (586)/(147). --- Step 1: Define the two-digit number using its digits. Let the tens digit be t and the units digit be u. The number can be represented as 10t + u. Step 2: Formulate equations based on the given conditions. Condition 1: The product of the digits is 20. t × u = 20 (1) Condition 2: When the digits are reversed, the new number is greater than the original number by 9. The reversed number is 10u + t. 10u + t = (10t + u) + 9 Step 3: Simplify the second equation. 10u + t = 10t + u + 9 Subtract u and 10t from both sides: 9u - 9t = 9 Divide by 9: u - t = 1 (2) From (2), we can express u in terms of t: u = t + 1 Step 4: Substitute the expression for u into equation (1). t × (t + 1) = 20 t^2 + t = 20 Rearrange into a quadratic equation: t^2 + t - 20 = 0 Step 5: Solve the quadratic equation for t. Factor the quadratic equation: (t + 5)(t - 4) = 0 Possible values for t are t = -5 or t = 4. Since t is a digit of a positive two-digit number, it must be a positive integer between 1 and 9. Therefore, t = 4. Step 6: Find the value of u using u = t + 1. u = 4 + 1 = 5 Step 7: Form the original two-digit number. The number is 10t + u = 10(4) + 5 = 45. Step 8: Verify the conditions. Product of digits: 4 × 5 = 20 (Correct). Reversed number: 54. Difference: 54 - 45 = 9 (Correct). The number is 45. --- Step 1: Rewrite the first term using the exponent rule a^m+n = a^m × a^n. 5^2x+2 = 5^2x × 5^2 5^2x+2 = 25 × 5^2x Step 2: Substitute this back into the original equation. 25 × 5^2x - 20 × 5^2x = 625 Step 3: Factor out the common term 5^2x. (25 - 20) × 5^2x = 625 5 × 5^2x = 625 Step 4: Express 625 as a power of 5. 625 = 5^4 Step 5: Substitute 5^4 back into the equation. 5 × 5^2x = 5^4 Step 6: Use the exponent rule a^m × a^n = a^m+n on the left side. 5^1+2x = 5^4 Step 7: Since the bases are equal, equate the exponents. 1 + 2x = 4 Step 8: Solve for x. 2x = 4 - 1 2x = 3 x = (3)/(2) The solution for x is (3)/(2). Last free one today — make it count tomorrow, or type /upgrade for unlimited.