Answer : 153 miles
Explanation : first take 134.29 & subtract the 14.95 base fee which give you 119.34 . now divide 119.34 by 78 which gives you 1.53. so he drove 153 miles.
equation : 14.95+ 0.78x = 134.29 . to double check just multiply 153 x 0.78 and add $14.95 which gives us the total of $134.29
Answer:
x=3
y=-2
Step-by-step explanation:
2x - 5y = 16
3x + 2y = 5
Solve for x in the first equation.
2x - 5y = 16
2x = 16 + 5y
x = (16 + 5y)/2
x = 8 + 5/2y
Put x as 8 + 5/2y in the second equation and solve for y.
3(8+5/2y) + 2y = 5
24+15/2y + 2y = 5
24 + 19/2y = 5
19/2y = 5-24
19/2y = -19
y = -2
Put y as -2 in the first equation and solve for x.
2x - 5(-2) = 16
2x +10 = 16
2x = 16-10
2x = 6
x = 3
Answer with step-by-step explanation:
Equation: x × 4 = y
This equation is true because if you look at the graph, multiply 4 by each x length and you will get the y length.
Hope this helped!
You do the implcit differentation, then solve for y' and check where this is defined.
In your case: Differentiate implicitly: 2xy + x²y' - y² - x*2yy' = 0
Solve for y': y'(x²-2xy) +2xy - y² = 0
y' = (2xy-y²) / (x²-2xy)
Check where defined: y' is not defined if the denominator becomes zero, i.e.
x² - 2xy = 0 x(x - 2y) = 0
This has formal solutions x=0 and y=x/2. Now we check whether these values are possible for the initially given definition of y:
0^2*y - 0*y^2 =? 4 0 =? 4
This is impossible, hence the function is not defined for 0, and we can disregard this.
x^2*(x/2) - x(x/2)^2 =? 4 x^3/2 - x^3/4 = 4 x^3/4 = 4 x^3=16 x^3 = 16 x = cubicroot(16)
This is a possible value for y, so we have a point where y is defined, but not y'.
The solution to all of it is hence D - { cubicroot(16) }, where D is the domain of y (which nobody has asked for in this example :-).
(Actually, the check whether 0 is in D is superfluous: If you write as solution D - { 0, cubicroot(16) }, this is also correct - only it so happens that 0 is not in D, so the set difference cannot take it out of there ...).
If someone asks for that D, you have to solve the definition for y and find that domain - I don't know of any [general] way to find the domain without solving for the explicit function).
