A collection of dimes and nickels has a total value of two dollars and contains 31 coins. How many dimes are there in the collection?

There are 9 dimes in this collection.

Step-by-step explanation:

Dimes are 10¢; nickels are 5¢.

d + n = 31

0.1d + 0.05n = 2

In this system of equations, d represents the amount of dimes in this collection and n represents the amount of nickels in this collection.

1. Isolate n in the first equation.

n = -d + 31

2. Substitute this value into the other equation to find the value of d.

0.1d + 0.05(-d + 31) = 2

0.1d - 0.05d + 1.55 = 2

0.05d + 1.55 = 2

0.05d = 0.45

d = 9

If you'd like to know how many nickels are in the collection, just subtract the amount of dimes from the total number of coins in the collection.

31 - 9 = 22

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.