Answer:
5 hours and 48 minutes
Step-by-step explanation:
The equation for finding average speed is:
Let x represent the distance for both the journey from Riley's college to home and back. We can use one variable to represent this because both distances are the same.
We also know that the total round trip took 12 hours. Let y represent the time it took for Riley to drive from college to home. Therefore the time it takes for Riley to drive from home to college is 12 - y.
Using this information, we can set up a system of equations.
<h3>Setting up a System of Equations</h3>
Multiply both sides of the first equation by "y" and both sides of the second equation by "12 - y".
Since both 65.1y and 835.2-69.6y are equivalent to x, we can set them equal to each other.
Now, we have to solve the equation for time or "y".
<h3>Solving for Time</h3>
Add 69.6y to both sides
Divide both sides by 134.7
This is the time it took for Riley to drive from college to home, therefore the time it took for Riley to drive from home back to college is:
5 hours and 48 minutes
Answer:
they're flipped
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
An inverse variation is where the product of inputs and outputs is constant. This means x*y is always the same number.
A is not a solution since it has 3*-4 = -12 and -2*4 = -8. It's not the same.
B is not a solution since it has 2*8 = 16 and 3*12 = 36. It's not the same.
C is a solution since 12*4 = 48 and 8*6 = 48 and 4*12 = 48 and 3*16 = 48. It's the same.
D is not a solution since it has 1*6 = 6 and 2*4 = 8. It's not the same.
Step-by-step explanation:
Both equations have a term in them, so if we subtract the second equation from the first, it will eliminate those terms, allowing us to solve for the remaining terms:
Finally, we can plug this value for into either of the two original equations to solve for :
This means the solution to the system of equations is .
Please see the attached figure. This is how you draw a hyperbola. Its general formula is:
(x-h)²/a² - (y-k)²/b² = 1, where
(h,k) is the center
a is the semi-major axis
b is the semi-minor axis
The given equation is
(x+4)²/16 - (y+3)²/25 = 1
So, from the general form we can deduce that,
Center(-4,-3)
a = 4
b = 5
So, the first point we can plot is the centerpoint. Next, you draw the two intersecting lines. Their slopes are +/- b/a. Thus, it corresponds to +/- 5/4. Using this slope, we can find the equation of the two lines by using the slope and the center.
-3 = +5/4 (-4) + b ---> b= 2
-3 = -5/4 (-4) + b ---> b= -8
So, you plot the equations y=5/4x + 2 and y = -5/4 x -8 by assigning values of x and plotting them against y. Then, the vertex of the hyperbolas are 4 units from the center, denoted by the green dots. The hyperbola is shown in the next picture.