Lyla grew 16 flowers with 2 seed packets. how many seed packets does lyla need to have a total of 40 flowers in her garden? assume the relationship is directly proportional. seed packets

Lyla needs 5 seed packets to have 40 flowers in her garden

Step-by-step explanation:

* Lets explain the direct proportion

- Direct proportion is the relationship between two variables when

 their ratio is equal to a constant value

- If m and n are in direct proportion m ∝ n , then m = kn, where

 k is constant

- We can write the direct proportion as m/n = k

* Lets solve the problem

- Lyla grew 16 flowers with 2 seed packets

- The relationship between the number of flowers and the number

 of the seed packets is direct proportional

∴ F ∝ P , where F is the number of the flowers and P is the number

 of the seed packets

∵ F = kP

∵ F = 16 when P = 2

∴ 16 = k(2)

- Divide both sides by 2

∴ k = 8

- Substitute the value of k in the equation

∴ F = 8P

Lets find how many packets does Lyla need to have 40 flowers

∵ F = 40

∴ 40 = 8P

- Divide both sides by 8

∴ P = 5

∴ Lyla needs 5 seed packets to have 40 flowers in her garden

Step-by-step explanation:

(x-4)2-28=8

Two solutions were found :

x = 10

x = -2

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (x-4)^2-28-(8)=0

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2-8x-20

The first term is,  x2  its coefficient is  1 .

The middle term is,  -8x  its coefficient is  -8 .

The last term, "the constant", is  -20

Step-1 : Multiply the coefficient of the first term by the constant   1 • -20 = -20

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   -8 .

     -20    +    1    =    -19

     -10    +    2    =    -8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  2

                    x2 - 10x + 2x - 20

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-10)

             Add up the last 2 terms, pulling out common factors :

                   2 • (x-10)

Step-5 : Add up the four terms of step 4 :

                   (x+2)  •  (x-10)

            Which is the desired factorization