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1. The ratio of $x+2$ to $2x+2$ is equal to the ratio of $4x+3$ to $7x+3$. What is the product of all real x which satisfy this statement? 2. The ratio of $x+2$ to $2x+2$ is equal to the ratio of $4x+3$ to $7x+3$. What is the product of all real x which satisfy this statement?

 

2. The equation $y = -4.9t^2 + 42t + 18.9$ describes the height (in meters) of a ball tossed up in the air at 42 meters per second from a height of 18.9 meters from the ground, as a function of time in seconds. In how many seconds will the ball hit the ground?

 May 1, 2021
 #1
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1.      (x + 2)  / ( (2x + 2)   =   (4x + 3)  / ( 7x + 3)      cross-multiply

 

(x + 2) ( 7x + 3)  =  ( 2x + 2) ( 4x + 3)     simplify

 

7x^2 + 17x  + 6   =  8x^2  +  14x   + 6            

 

7x^2  + 17x  = 8x^2  +  14x      rearrange   as

 

x^2  -  3x  =  0

 

x ( x -  3)  =  0

 

x = 0  is one solution.....so....the product   of all real solutions  must  be    0

 

cool cool cool

 May 1, 2021
edited by CPhill  May 1, 2021
 #2
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Thank you for the first answer but can someone please answer the 2nd question?

Guest May 1, 2021

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