(x-5)(x+4) is the factored version of this trinomial so if either of those values in the parenthesis are in the answer bank, choose those.
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:
15-29= -14
(I need the explanation most importantly)
14+(-4) - 8 =10-8=2
(Explanation please)
-8.4 - (19.5.) = - 27.9, (just add them to each other and write -, because both have - in front of them)
(Explanation)
-15 + 8 - (-19.7) = - 7+19,7=12,7 (there is + and - so it will became - 7, and at next there is two - which will turn them into +)
(Explanation)
29.45 - 56.009 - 78.2=−104,759 (all you have to is to put them all together, and than make it 29.45 less, writing - in front of them)
(Explanation)
LAST ONE
45.9 - (-9.2) + 5= 45.9+9.2+5=55.1+5=60.1 (because when there is 2 minus next to each other it will became plus)
