The ratio of white marbles to blue marbles in Olivia's bag is 2 to 5. If there are more than 50 marbles in the bag, what is the minimum number of marbles that can be in the bag?

Step-by-step explanation:

the distributing ratio is 2:5.

that means for every 2 white marbles there must be 5 blue marbles.

so, we are taking about "groups" or multiples of 7 (2+5 = 7).

now, even 7×7 = 49 is too small.

but the next multiple of 7 (7×8 = 56) is now big enough to include at least 50 marbles.

so, in order to keep the 2:5 ratio strictly in place, the minimum number of marbles in the bag is 56.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17