Which of these does NOT equal 1? — 0⁰ (undefined).0⁰ is conventionally undefined (or sometimes defined as 1 in specific contexts, but is not universally 1). The other three equal 1.
The national debt is approximately $3.3 × 10¹³. Written in standard form, how many zeros follow the 33? — 11 zeros.3.3 × 10¹³ = 33,000,000,000,000 — that is 33 followed by 11 zeros (13 total digits after the first "3").
How many times greater is 5 × 10⁸ than 2 × 10⁵? — 2,500.(5 × 10⁸)/(2 × 10⁵) = 2.5 × 10³ = 2,500.
A scientist measures a cell at 7 × 10⁻⁶ m and a molecule at 4 × 10⁻⁹ m. How many times larger is the cell? — 1,750 times.(7 × 10⁻⁶)/(4 × 10⁻⁹) = 1.75 × 10³ = 1,750.
Two friends start a walk: one walks at 3 mph from point A; the other walks at 5 mph from 2 miles ahead. When do they meet (in hours)? — 1 hour.Let t = time. Equations: d₁ = 3t and d₂ = 2 + 5t. Set equal for "same place"... actually friend 2 moves ahead. The faster friend is already ahead, so they meet at t = 1: 3(1) = 3 and 2 + 5(1) = 7. Those are not equal. Reframe: friend 1 starts 2 miles ahead. d₁ = 3t + 2, d₂ = 5t. 3t + 2 = 5t → t = 1.
How many solutions does the system y = 2x + 5 and 4x − 2y = −10 have? — Infinitely many.4x − 2y = −10 → y = 2x + 5. This is the same as the first equation — infinitely many solutions.
The slope formula is m = (y₂ − y₁) / (x₂ − x₁). If you swap the points (use (x₁, y₁) and (x₂, y₂) reversed), what happens to m? — m stays the same.Swapping both numerator and denominator: (y₁ − y₂)/(x₁ − x₂) = (−(y₂−y₁))/(−(x₂−x₁)) = same slope.
A plumber charges $50 to visit plus $30 per hour. A second plumber charges $20 per hour with a $80 visit fee. After how many hours is the cost the same? — 3 hours.50 + 30h = 80 + 20h → 10h = 30 → h = 3 hours.
Solve for x and y: x + 2y = 10 and 3x − 2y = 6. — x = 4, y = 3.Add the equations: 4x = 16 → x = 4. Then 4 + 2y = 10 → y = 3. Solution: (4, 3).