Let A be the number of Dimes & B the number of Quarters, the linear equation is as follows:
A.D+B.Q=2.05
Answer:
Plane Speed (x) = 378 mph
Step-by-step explanation:
Equation
d = r * t
Givens
With the wind
- d = 1680 miles
- t = 4 hours
- r = x + y
Against the wind
- d = 1680
- t = 5 hours
- r = x - y
Equation
The distances are the same, so you can solve for x in terms of y and then deal with the actual distance.
(x + y)*4 = (x - y)*5 Remove the brackets on both sides
Solution
- 4x + 4y = 5x - 5y Subtract 4x from both sides
- 4y = -4x + 5x - 5y Combine
- 4y = x - 5y Add 5y to both sides
- 5y + 4y = x
- x = 9y
Solution part 2
Now take one of the distance formulas and solve for x first then y.
- (x - y)*5 = 1680 Substitute 9y for x
- (9y - y)*5 = 1680 Subtract on the left
- 8y * 5 = 1680 Multiply on the left
- 40y = 1680 Divide by 40
- y = 1680/40
- y = 42 That's the speed of the wind.
- (x - y)*5 = 1680 Substitute the wind speed for y
- (x - 42)*5 = 1680 Divide both sides by 5
- (x - 42) = 1680 / 5 Do the division on the right
- (x - 42) = 336 Add 42 to both sides.
- x = 336 + 42
- x = 378 mph Plane's speed
Answer:
(2)
Step-by-step explanation:
Let f(x) = y → f-¹(x) = f(y) = x, f(y) is the inverse of f(x)
Thus,
=> -x³ - 9 = y
=> - y - 9 = x³
=> (-y - 9)^(1/3) = x
=> f(y) = x
Inverse is (-y-9)^(1/3)
Replacing the variable, inverse is (-x-9)^(1/3)
Option (2)
From the given equations below,
(1) 6x + 6y = 7.50
(2) 10x + 5y = 8.75
Solving for the values of x and y simultaneously gives an answer of x = 0.5 and y = 0.75.
Thus, the cost of apples and oranges are $0.5 and $0.75, respectively.
