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Nonamiya [84]
2 years ago
12

Your friend says that the absolute value equation | 3x+8 |-9=-5 has no solution because the constant

Mathematics
1 answer:
sineoko [7]2 years ago
3 0

Answer:

Incorrect

Step-by-step explanation:

We are given the equation:

\displaystyle \large{|3x+8|-9=-5}

Add both sides by 9.

\displaystyle \large{|3x+8|-9 + 9=-5 + 9} \\ \displaystyle \large{|3x+8|=4}

When we want to tell if the absolute equation has solutions or not, we have to simplify in this form first: or isolate the absolute sign.

\displaystyle \large{ |ax + b|  = c}

If c ≥ 0, the equation has solutions.

If c < 0, the equation does not have solutions.

Therefore, it does not always matter if the constant on right side is in negative because if there is a number on the left side then there is a chance that the equation has solutions.

From |3x+8| = 4 is equivalent |3x+8|-9=-5 and the right side is 4 which is positive.

Hence, the equation does have a solution!

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3 years ago
An airplane travels 6111 kilometers against the wind in 9 hours and 7911 kilometers with the wind in the same amount of time. Wh
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Answer:

Speed of the plane in still air: 779\; {\rm km \cdot h^{-1}}.

Windspeed: 100\; {\rm km \cdot h^{-1}}.

Step-by-step explanation:

Assume that x\; {\rm km \cdot h^{-1}} is the speed of the plane in still air, and that y\; {\rm km \cdot h^{-1}} is the speed of the wind.

  • When the plane is travelling against wind, the ground speed of this plane (speed of the plane relative to the ground) would be (x - y)\; {\rm km \cdot h^{-1}}.
  • When this plane is travelling in the same direction as the wind, the ground speed of this plane would be (x + y)\; {\rm km \cdot h^{-1}}.

The question states that when going against the wind (v = (x - y)\; {\rm km \cdot h^{-1}},) the plane travels 6111\; {\rm km} in 9\; {\rm h}. Hence, 9\, (x - y) = 6111.

Similarly, since the plane travels 7911\; {\rm km} in 9\; {\rm h} when travelling in the same direction as the wind (v = (x + y)\; {\rm km \cdot h^{-1}},) 9\, (x + y) = 7911.

Add the two equations to eliminate y. Subtract the second equation from the first to eliminate x. Solve this system of equations for x and y: x = 779 and y = 100.

Hence, the speed of this plane in still air would be 779\; {\rm km \cdot h^{-1}}, whereas the speed of the wind would be 100\; {\rm km \cdot h^{-1}}.

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Step-by-step explanation:

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