I have 54 coins in my pocket; some of them are quarters and the rest are nickels. In total, the coins are worth $6.10. How many of each coin do I have?

17 quarters, 37 nickels

Step-by-step explanation:

We just have to set up a system of equations

quarters are x

and nickels are y

x+y=54

0.25x+0.05y=6.10

now we can get ready to substitute

x=54-y

substitute it in

0.25(54-y)+0.05y=6.10

simplify/evaluate

13.5-0.25y+0.05y=6.10

-0.2y=-7.4

y=37

plug it back in

x+37=54

x=17

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following