Sam has some pennies, dimes and nickels in his pocket which total 52 cents. He has two more nickels than dimes and three times as many pennies as nickels. How many of each coin does he have?

Step-by-step explanation:

Let the amount of pennies be x

amount of dimes be y

amount of nickels be z

If it all totaled 52, then x+y+z = 52

If he has two more nickels than dime, then;

z = y + 2

y = z-2

If he has three times as many pennies as nickels;

3x = z

x = z/3

Subtitute the funcion in original function;

z/3 + (z-2) + z = 52

z + 3z - 6 + 3z = 156

7z - 6 = 156

7z = 162

z =

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.