<h2>A.</h2>
So let's break down this sentence (Let n = unknown number):
- "A number is doubled and then 1 is added to it"; Remember that double means multiplied by 2. With this sentence, we can determine that "2n + 1" is a part of the equation.
- "The answer is divided by 5, and then increased by 16"; The "answer" they refer to is "2n + 1" from the prior sentence. Since this is divided by 5 and <em>then</em> added by 16, we can determine that
is a part of our equation. - "The final result is 18"; This means that the prior part of the equation is equal (=) to 18. <u>With this info, our full equation is
</u>
<h2>B.</h2>
Now, let's solve our prior equation found in A. To solve for the unknown number, n, we need to isolate the variable onto 1 side of the equation. Firstly subtract both sides by 16 to cancel out the + 16 on the left side:
Next, multiply both sides by 5 to cancel out the division on the left side:
Next, subtract both sides by 1 to cancel out the + 1:
Lastly, divide both sides by 2 to cancel out the multiplication:
<u>In short, the number is 9/2 or 4.5.</u>
Answer:
y - 2x = 3
Step-by-step explanation:
y = 2x + 3
-2x -2x
y - 2x = 3
We manipulate the given equation in order to solve for EC. We do this by cross multiplying.
The resulting equation will be:
EC = (4 x 3)/5
EC = 12/5 = 2.4
Additionally, the side-splitter theorem works for this problem since DE and AC are parallel to each other, therefore splitting the remaining two sides into proportional segments.
First, we should answer two simple questions.
1. How many ways can we travel from a-b?
2. How many ways can we travel from b-c?
This is given in the problem - because there are 7 roads connecting a to b, there are 7 ways to get from a-b. Because there are 6 roads from b-c, there are 6 ways to get from b-c.
Now that we understand this, we can use some logic to figure out the rest of the problem. Let's think about each case.
Let's go from a-b. We'll choose road 1 of 7. Now that we are in b, we have 6 more choices. This means that there are 6 ways to get to from a-c if we take road 1 when we go to b.
If we take any road going from a-b, there will be 6 options to get from b-c.
So, we can just add up the number of options because we know that there are 6 routes per road from a-b. This is simply 7*6 = 42. So, there are 42 ways to travel from a to c via b.
