Answer:
<h3>x = 5</h3>
Step-by-step explanation:
f(x) = 2(x + 6)
f(x) = 22
thereofre we have the equation:
2(x + 6) = 22 <em>use distributive property</em>
2x + 12 = 22 <em>subtract 12 from both sides</em>
2x = 10 <em>divide both sides by 2</em>
x = 5
The greatest common factor is 18
Take a better pic and i will explain in comment
Step-by-step explanation:
when a line intersects with 2 (or more) parallel lines. then, of course, the intersection angle is the same with every of the intersected lines. otherwise they would not be parallel.
so,
7x - 10 = 60
7x = 70
x = 10
Answer:
Step-by-step explanation:
Let x be the number of 2 coins and y be the number of 5 coins. Let z be the number of 10 coins she exchanged. Then, we have the first equation

Since she has one 5 coin less than 2 coins, then y=x-1. So we get the equation
which is equivalent to
If we add 5 on both sides and factor out on the right by 5 we get

We can solve for x and get
Since x represents the number of 2 coins, we must have that x is an integer. That is, we cannot have, for example 1.5 2 coins. Since 7 doesn't divide 5, we must have that 7 divides 2z+1. That is, the value of z is such that the number 2z+1 is multiple of 7. That is 2z+1 = 7p where p is an integer.
If that is the case, then
x = 5p, then y = 5p-1. By having 2z+1 = 7p, we are forcing that p is an odd integer, so we have infinite solutions. For each value of p that is an odd integer, then x=5p and y=5p-1 is a solution to the problem