+0

# help pls

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256
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+30

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
+128732
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(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

Jul 31, 2022
#2
+30
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thxs :D

Jul 31, 2022
#3
+128732
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Welcome....!!!

BTW -  no equation shown for the second one

CPhill  Jul 31, 2022
#4
+30
+1

o holld up

Jul 31, 2022
#5
+30
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-6t^2 + 51t

Jul 31, 2022
#6
+128732
+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

Jul 31, 2022