Fiona has a recipe for a pint of sweet iced tea that calls for 8 teaspoons of sugar and 2 teaspoons of lemon juice. The ratio of teaspoons of sugar to teaspoons of lemon juice is 8:2.What is the ratio of THREE pints of sweet iced tea?

Given:

The ratio of teaspoons of sugar to teaspoons of lemon juice of one pint of sweet iced tea is 8:2.

To find:

The ratio of THREE pints of sweet iced tea.

Solution:

For a pint of sweet iced tea that calls for 8 teaspoons of sugar and 2 teaspoons of lemon juice.

So, for three pints of sweeet iced tea,

Sugar = 3 × 8 = 24 teaspoons

Lemon juice =  3 × 2 = 6 teaspoons

Now,

Therefore, the ratio of teaspoons of sugar to teaspoons of lemon juice of three pint of sweet iced tea is 24:6.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: