Let's solve your inequality step-by-step.<span>−10≤<span><span>2x−4</span><8</span></span><span><span>−10+4</span>≤<span><span><span>2x−4</span>+4</span><8+4
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(Add 4 to all parts)<span>−6≤<span>2x<12</span></span><span><span>−62</span>≤<span><span>2x2</span><122
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(Divide all parts by 2)<span>−3≤<span>x<6</span></span>
Based on the given above, collection of books of Nathan and Jason can be translated into the following equations:
6J + 1/3N = 134
1/3 J + N = 31; J = Jasons and N=Nathan
Solving two equations with two unknowns simultaneously,
Jason = 21 books and Nathan = 24 books
Answer:
x = 387
Step-by-step explanation:
The wind acts in the opposite direction to the plane when the time is longer.
The wind acts in the same direction as the plane when the time is shorter.
Equation
d = r*t
Givens
- d = 1720
- x = plane's speed
- y = wind speed
- t1 = 5 hours
- t2 = 4 hours.
Substitution
- d = (x + y) * t
- 1720 = (x + y) * 4
- 1720 = (x - y) * 5
Since the two distances are the same, you can equate the right hand sides.
- (x + y) * 4 = (x - y)*5 Remove the brackets.
- 4x + 4y = 5x - 5y Add 5y to both sides
- 4x + 4y + 5y = 5x - 5y + 5y Combine all the terms.
- 4x + 9y = 5x Subtract 4x from both sides
- 9y + 4x - 4x = 5x - 4x Combine
- 9y = x
Now use one of the given equations with the distance
- 1720 = (x + y)*4 Substitute 9y for x
- 1720 = (9y + y) * 4 Combine
- 1720 = 10y * 4 Multiply the right
- 1720 = 40y Divide by 40
- 1720/40 = 40y/40 Do the division
- 43 = y y = wind speek
- 9y = x x = 9*y
- 9*43 = x
- x = 387 miles per hour.
Use the Pyth. Theorem to calculate the total distance flown by the plane in 3 1/2 hours:
d = sqrt(750^2 + 750^2) = 750sqrt(2) miles
Now divide this distance by the total time (3 1/2 hours):
750sqrt(2) miles
---------------------- = 303 miles per hour average
3.5 hours
