Mario is constructing a square dart board. it will consist of a smaller square centered in a larger square. the smaller square measures $4$ inches on each side. the ratio of the area of the smaller square to the area of the entire dart board is $\frac 49$. how long is the side of the larger square?

6 inches.

Step-by-step explanation:

Let a represent side length of larger square.

We know that area of square is square of its side length, so area of the larger square will be .

The area of smaller square would be .

We will use proportions to solve our given problem.

Cross multiply:

Take square root:

Since the length cannot be negative, therefore, the side length of larger square is 6 inches.

54

step-by-step explanation:

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.