Roberto uses 150 roses, 120 lilies, and 45 hydrangeas to make bouquets. Each bouquet has the same number of roses, the same number of lilies, and the same number of hydrangeas. i What is the maximum possible number of bouquets he can make? ii How many roses, lilies, and hydrangeas are in each bouquet?

(i) Maximum possible number of bouquets he can make = 15

(ii) There are 10 roses, 8 lilies and 3 hydrangeas in each bouquet.

Step-by-step explanation:

Given: Roberto uses 150 roses, 120 lilies, and 45 hydrangeas to make bouquets.

(i) Maximum possible number of bouquets he can make = HCF(150, 120 , 45)

Since , 150 = 2 x 3 x 5 x 5  , 120= 2 x 2 x 2 x 3 x 5 ,  45 = 3 x 3 x 5

HCF(150, 120 , 45) = 3 x 5 = 15

Now, Maximum possible number of bouquets he can make = 15

(ii)  Number of roses in each bouquet =

Number of lilies in each bouquet =

Number of hydrangeas in each bouquet =

Hence, there are 10 roses, 8 lilies and 3 hydrangeas in each bouquet.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180