PLEASE HELP ASAP!: Solve for a and b 6a-b=-5 4a-3b = -8
1 answer:
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For this case, the first thing we must do is define variables:
p: plane speed
w: wind speed
With the wind in favor, the speed is:
With the wind against the speed is:
Rewriting both equations, we have the following system of equations:
Then, solving the system of equations (graphically for example), we have the solution is:
Therefore, jet stream's speed:
Answer:
A) p + w = 960; p - w = 600; jet stream's speed = 180 km / h
p: plane speed
w: wind speed
With the wind in favor, the speed is:
With the wind against the speed is:
Rewriting both equations, we have the following system of equations:
Then, solving the system of equations (graphically for example), we have the solution is:
Therefore, jet stream's speed:
Answer:
A) p + w = 960; p - w = 600; jet stream's speed = 180 km / h
Answer:
see explanation
Step-by-step explanation:
(9)
Expand and simplify right side and compare coefficients of like terms on left side.
(x - 2)(x² + ax + b) + c
= x³ + ax² + bx - 2x² - 2ax - 2b + c
= x³ + x²(a - 2) + x(b - 2a) - 2b + c
compare with
x³ + 2x² - 3x + 4
x² terms
a - 2 = 2 ( add 2 to both sides )
a = 4
x terms
b - 2a = - 3 ← substitute a = 4
b - 8 = - 3 ( add 8 to both sides )
b = 5
constant terms
- 2b + c = 4 ← substitute b = 5
- 10 + c = 4 ( add 10 to both sides )
c = 14
Thus a = 4, b = 5 and c = 14
-------------------------------------------------
(10)
Since both functions cross the x- axis at - 2 then (- 2, 0) satisfies both, that is
f(- 2) = + a(- 2)³ + b(- 2)² + 36(- 2) + 144 = 0, that is
- 16 - 8a + 4b - 72 + 144 = 0
- 8a + 4b + 56 = 0
- 8a + 4b = - 56 → (1)
and
g(- 2) = + (a + 3)(- 2)³ - 23(- 2)² + (b + 10)(- 2) + 40 = 0, that is
- 16 - 8(a + 3) - 92 - 2(b + 10) + 40 = 0
- 16 - 8a - 24 - 92 - 2b - 20 + 40 = 0
- 8a - 2b - 112 = 0
- 8a - 2b = 112 → (2)
Subtract (1) from (2) term by term
- 6b = 168 ( divide both sides by - 6 )
b = - 28
Substitute b = - 28 into (2)
- 8a + 56 = 112 ( subtract 56 from both sides )
- 8a = 56 ( divide both sides by - 8 )
a = - 7
Thus a = - 7 and b = - 28
The solution to the statement 4 + (-4) is correctly given by the third number line.
- The solution given by plot 1 is : (-4) + (-4) as both arrows points 4 units to the left.
- The solution given by plot 2 is : ( 4 + 4) as both arrows points 4 units to the right.
- The solution given by plot 3 is (4) + (-4) as one arrow points 4 units to the left and the other points 4 units to the right.
- The solution given by the plot 4 is (-4 + 8) as one arrow points 4 units to the left and the other points 8 units to the right.
Therefore, the Number line which shows the solution 4 + (-4) is the third number line.
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