Determine the value of x if the sequence 2x-1; 3x+1; 7x-1; is a geometric sequence

x=0 or x=3

Step-by-step explanation:

Since it is a geometric sequence, that means term divided by previous term is the same number. Let's call that number, r.

That means we have:

(3x+1)/(2x-1)=r

(7x-1)/(3x+1)=r

Since both of the ratios are the same, then we have

(3x+1)/(2x-1)=(7x-1)/(3x+1)

Cross multiply:

(3x+1)(3x+1)=(2x-1)(7x-1)

Distribute:

9x^2+3x+3x+1=14x^2-2x-7x+1

Combine like terms:

9x^2+6x+1=14x^2-9x+1

Subtract 1 on both sides:

9x^2+6x=14x^2-9x

Subtract 14x^2 on both sides

Add 9x on both sides

-5x^2+15x=0

Factor -5x:

-5x(x-3)=0

-5x=0 when x=0 since -5(0)=0

x-3=0 when x=3 since 3-3=0

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.