Julie collects dimes and quarters. She has a total of 98 dimes and quarters in a jar. She counted the money and found out she has $14.90 in the jar. How many dimes and quarters does she have?

64 dimes and 34 quarters.

Step-by-step explanation:

Let d represent the amount of dimes and q represent the amount of quarter Julie has.

She has in total 98 coins. Therefore:

Each dime is worth 0.10 and each quarter is worth 0.25. Together, they are worth in total $14.90. Therefore:

We have a system of equations. We can solve this using substitution.

First, we can multiply the second equation by 100 to simplify. So:

From the first equation, we can subtract q from both sides:

Substitute this into the second equation:

Distribute:

Combine like term:

Subtract:

Therefore:

So, Julie has 34 quarters.

Returning to our first equation:

Substitute:

Therefore:

Thus, Julie has 64 dimes and 34 quarters.

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.