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1.We have a rectangle of dimensions $x - 2$ by $2x + 5$ such that its area is $8x - 6$. What is the value of $x$?

 

2.The equation  describes the height (in feet) of a projectile launched from the surface of Mars at 51 feet per second. In how many seconds will the projectile first reach 108 feet in height?

 

thanks for helping btw :D

i struggle a lot

 Jul 31, 2022
edited by Gordn  Jul 31, 2022
 #1
avatar+124676 
+2

(x - 2) ( 2x + 5)  = 8x - 6

 

2x^2 - 4x + 5x - 10 = 8x -6

 

2x^2 + x -10 =  8x - 6       rearrange as

 

2x^2 - 7x - 4  = 0

 

(2x + 1) ( x - 4)  =  0

 

The second factor set = 0  is what we want 

 

x - 4 =  0 

 

x  = 4

 

cool cool cool

 Jul 31, 2022
 #2
avatar+28 
+1

thxs :D

 Jul 31, 2022
 #3
avatar+124676 
+1

Welcome....!!!

 

BTW -  no equation shown for the second one

 

 

cool cool cool

CPhill  Jul 31, 2022
 #4
avatar+28 
+1

o holld up

 Jul 31, 2022
 #5
avatar+28 
+1

-6t^2 + 51t

 Jul 31, 2022
 #6
avatar+124676 
+2

OK

 

We have that

 

-6t^2 + 51t    =   108         divide through by -3

 

2t^2  - 17t  =  -36

 

2t^2 - 17t + 36 =  0      see if we  can  factor   (you could use the Q Formula but I like to  factor, if possible )

 

(2t - 9) ( t - 4)  =  0

 

2t - 9  = 0                                 or            t  - 4   =  0

2t = 9                                                       t = 4 sec

t = 9/2 sec = 4.5 sec

 

It first reaches 108 ft  at 4 sec

 

 

cool cool cool

 Jul 31, 2022

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