In triangle abc centroid d is on median am. ad= x + 3 and dm= 2x - 1. find am. options: a. 5/3 b. 3 1/2 c. 7 d. 8

Option C is correct.

Value of AM = 7

Explanation:

Given: In  centroid D is on the median of AM.

AD = x+3 and DM= 2x-1.

In a ΔABC , a segment AM is the median to side BC.

The centroid D, on AM is the point of intersection of all 3 medians of the triangle divides the median in the ratio 2:1, where AD:DM = 2 : 1 .

Also, we can say that: AD=2DM

Substitute the value of AD and DM to solve for x:

Use Distributive property on right hand side; ()

x+3 = 4x-2

Subtract x from both sides of an equation:

Simplify:

3 = 3x-2

Add 2 both side of an equation:

3+2 = 3x-2+2

Simplify:

5 = 3x

⇒

Now, find the length of AM:

AM = AD+DM = x+3+2x-1

AM = 3x+2                       ......[1]

Substitute the value of in [1];

AM =

Therefore, the value of AM is 7.

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.