Question : A jet plane traveling at a constant speed goes 1200 miles : 2163518

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the expression is rational.

201) A jet plane traveling at a constant speed goes 1200 miles with the wind, then turns around and travels for 1000 miles against the wind. If the speed of the wind is 50 mph and the total flight took 4 hours, find the speed of the plane in still air.

A) 605 mph

B) 550 mph

C) 435 mph

D) 525 mph

202) A plane flies 450 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 25 mph, what is the speed of the plane in still air?

A) 205 mph

B) 190 mph

C) 200 mph

D) 225 mph

Simplify the complex fraction. Leave the answer in factored form when appropriate.

203) ((1/5)/(5/8))

A) (1/8)

B) (8/25)

C) (25/8)

D) 8

204) ((5/8)/(8/3))

A) (3/5)

B) (64/15)

C) (15/64)

D) (5/3)

205) ((5/3)/(1/6))

A) 10

B) (18/5)

C) (1/10)

D) (5/18)

206) ((8/11)/7)

A) (77/8)

B) (4/9)

C) (8/77)

D) (8/11)

207) ((12/7)/3)

A) (36/7)

B) 4

C) (4/7)

D) (7/4)

208) ((1/a) + 1/(1/a) - 1)

A) 1 - a²

B) (a/1 - a²)

C) 1

D) (1 + a/1 - a)

209) ((9/x² - 16) - (10/x + 4)/(11/x² - 16) - (7/x - 4))

A) (9x - 40/11x - 28)

B) (-31 - 10x/7x - 39)

C) (-10x + 49/-7x - 17)

D) (-10x - 49/-7x - 17)

210) ((-3/x + 3) + (5/x + 5)/(5/x + 5) - (-3/x + 2))

A) (-(x + 2)/x + 3)

B) (2x² + 4x/2x² - 23x + 75)

C) (2x² - 34x + 60/2x² - 31x + 75)

D) (2x² + 4x/8x² + 49x + 75)

211) ((7/5r - 1) - 7/(7/5r - 1) + 7)

A) (2 + 5r/5r)

B) (5r/2 - 5r)

C) (2 - r/r)

D) (2 - 5r/5r)

212) ( (x⁵/2y⁸)/(x²/y⁶))

A) (x³/2y¹⁴)

B) (x³/y²)

C) (x³/2y²)

D) (x⁷/2y¹⁴)

Simplify the expression, using only positive exponents in your answer.

213) (m-1 + z-1/m-1 - z-1)

A) (z + m/z)

B) (z + m/m)

C) (z + m/z - m)

D) (z - m/z)

214) (x^-2/x^-2 - y^-2)

A) (y/y² - x²)

B) (y²/y² + x²)

C) (y² - x²/y²)

D) (y²/y² - x²)

215) (x^-6 + y^-6/x^-1 + y^-1)

A) (y⁶ + x⁶/x⁵ + y⁵)

B) (y⁶ + x⁶/x⁵y⁶ + x⁶y⁵)

C) (1/x + y)

D) (1/x⁵ + y⁵)

216) (x^-2 - 36y^-2/10y - 60x)

A) (y² + 6x/10x²)

B) 10x - 60y²

C) (x + 6y/10x²y)

D) (y + 6x/10x²y²)

Solve.

217) A commuter travels to work, driving a distance d at speed r. At the end of the day, she returns home and drives the same distance 6 mph faster, at a speed r + 6. Her average speed for the round trip can be represented by the expression (2d/(d/r) + (d/r + 6)). Simplify this expression.

A) (r(r + 6)/r + 3)

B) (r(r + 3)/r + 6)

C) (1/r + 3)

D) (dr(r + 6)/dr + 3)

218) The fixed monthly payment required to amortize a loan of L dollars over a term of n months at an annual interest rate of r is given by ((Lr/12)) ÷ [1 - (1 + (r/12))^-n]. Write this expression as a complex fraction.

A) (1 - (Lr/12)/(1 + (r/12))^-n)

B) (Lr/(1 - (1 + (r/12))^-n/12))

C) ((Lr/12)/1 - (1 + (r/12))^-n)

D) (Lr/12 - (1 + (r/12))^-n)

219) The total current flowing through a particular circuit is given by (V/(1/R) + (1/R - 8)), where V represents voltage and R represents resistance. Simplify this expression.

A) (V/R(R - 8))

B) (VR(R - 8)/2(R - 4))

C) VR(R - 8)

D) (V(R - 8)/2(R - 4))

220) If two light bulbs have resistances R₁ and R₂, then their combined resistance R is given by the complex fraction R = (1/(1/R₁) + (1/R₂)). Evaluate this formula when R₁ = 50 ohms and R₂ = 90 ohms. Round to the nearest tenth of an ohm.

A) 32.1 ohms

B) 50.01 ohms

C) 140 ohmsohm

D) 0.031 ohms