Answer
You can multiply the first equation by 4 and the second equation by 3.
You can multiply the first equation by 4/3.
You can multiply the first equation by 3.
Explanation
When solving a system of equations by elimination, you want to add or subtract the equations to "get rid" of a variable.
To do that, one of the variables in both equations have to have the same coefficient.
The first answer possible gives x the coefficient of 12 for both equations. You would get 12x+4y=52 and 12x-9y=39. You could subtract those equations to get 13y=13.
The second way gives x the coefficient of 4. You would multiply the first equation by 4/3 to get 4x+4/3y=52/3. You can subtract to get one variable, and then solve from there. Although, multiplying for 4/3 is annoying, so it's not suggested.
You can also "get rid" the the y. Multiply the first equation by 3 to get 9x+3y=39. You can add these equations. When you add 9x+3y=39 and 4x-3y=13 you get 13x=52.
There is infinitely many ratios which are equivalent to 5:9. As we know always we can write divide as fraction, so
. We can multiply nominator and denominator by the any number (but the same) and get another numbers but ratio will be the same, so equivalent.
For example
10:18,
15:27
Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
Answer: y=4x+8
Step-by-step explanation:
