In a cookie recipe, for every 3 cups of flour, 2 teaspoons of vanilla is needed. how many teaspoons are needed for 5 cups of flour

to find this answer we use proportional reasoning.

3 cups of flour:2 teaspoons of vanilla

3:2

if 5 cups of flour are used then we adjust the ratio to keep it proportional

the vanilla is 'x' because we don't know the value (yet)

5:x

then we set it up in an equation and solve

3/2=5/x

2 multiplied by 5 divided by 3     x=3.33

5:3.33

you need 3.33 teaspoons of vanilla for 5 cups of flour

10a^3+277a^2-132a-792

step-by-step explanation:

(2a+11)(5a-12)(foil)

=10a^2-24a+55a-132 =10a^2+31a-132

(10a^2+31a-132)(a+6)

=10a^3+60a^2+31a^2+186a^2-132a-792 =10a^3+277a^2-132a-792

i hope this is what you are looking for : )

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y