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📰 Question: What two-digit positive integer is one less than a multiple of 5 and also one less than a multiple of 7? 📰 Solution: Let $x$ be the integer. Then $x \equiv -1 \pmod{5}$ and $x \equiv -1 \pmod{7}$. This implies $x + 1$ is divisible by both 5 and 7, so $x + 1 = \text{LCM}(5, 7) = 35$. Thus, $x = 34$. $\boxed{34}$Question: A retired engineer designing a robotic arm observes that the sum of two gear rotation speeds $ a $ and $ b $ is 10, and the sum of their squares is 58. What is $ a^3 + b^3 $? 📰 Solution: We are given $ a + b = 10 $ and $ a^2 + b^2 = 58 $. We want to find $ a^3 + b^3 $. 📰 Social Stratification 1691893 📰 What Is Sharecropping 9742208 📰 Hotels In Manchester 4160920 📰 Yojimbo Price Ffx 7185027 📰 You Wont Believe What I Saw In Ig Storiesclick To Unlock The Secret 6173760 📰 Spider Woman Unleashed Unbelievable Powers That Will Blow Your Mind 3629731 📰 Ways To Earn Money Fast 4517945 📰 Game Changing Sports Quotes Every Fan Should Know Boost Your Passion Instantly 5265320 📰 This Black And White Picture Will Make You Stop And Thinkyou Wont Look At Old Photos The Same Way 1255089 📰 Whats The Federal Tax Rate In 2024 Protect Your Money Before Its Gone 8392178 📰 How To Redeem Airline Miles 7717390 📰 Bills Vs Chiefs Score 6038251 📰 Endnote Secrets Total Newbies Are Ignoring Endsite Stunner 5259980 📰 Southwest Fly To Orlando 3245328 📰 Discover The Secret Behind How Cubicasa Can Make Or Break Your Creations 5990103