If a * b = a - 3b and a # b = 2a + 3b, evaluate the expression (4 * 3) # 5.
If y # y = 2x + 3y and x * y = 5x + 4y, evaluate the expression 2 # (4 * 3).
Please help! Try to explain how I should solve these - don't just give me the answer. These problems showed up in my math book, and my teacher didn't teach us how to do those in the lesson. And, first of all, what does # mean in a problem like this? Thank you.
hmm...interesting. sorry to say, I still don't get this! thank you for your help, though, Bob.
my math teacher ending up explaining this today (after he took a homework completion grade - of course I hadn't been able to do the problem!)and then I just checked and read your explanation, and I still don't get it. can somebody please help?
4*3=4-3*3=-5 according to the rules.
-5#5= 2*-5 + 3*5 or 5 according to the rules.
# is the symbol for an unknown math operator, defined as a#b=2a + 3b
To solve these expressions, we need to understand the operations represented by the symbols * and #.
In the given expressions, the symbol * represents a binary operation defined as a * b = a - 3b. This means that to find the result of a * b, you subtract 3 times the value of b from a.
On the other hand, the symbol # represents another binary operation defined as a # b = 2a + 3b. This operation involves multiplying a by 2 and b by 3, and then adding the two results together.
Let's start with the first expression, (4 * 3) # 5.
Step 1: Evaluate (4 * 3) using the * operation.
Using the * operation, we substitute a = 4 and b = 3 into the expression a * b = a - 3b. So, (4 * 3) = 4 - 3(3) = 4 - 9 = -5.
Step 2: Evaluate (-5) # 5 using the # operation.
Using the # operation, we substitute a = -5 and b = 5 into the expression a # b = 2a + 3b. So, (-5) # 5 = 2(-5) + 3(5) = -10 + 15 = 5.
Therefore, (4 * 3) # 5 = 5.
Now, let's move on to the second expression, 2 # (4 * 3).
Step 1: Evaluate (4 * 3) using the * operation.
Using the * operation, we substitute a = 4 and b = 3 into the expression a * b = a - 3b. So, (4 * 3) = 4 - 3(3) = 4 - 9 = -5.
Step 2: Evaluate 2 # (-5) using the # operation.
Using the # operation, we substitute a = 2 and b = -5 into the expression a # b = 2a + 3b. So, 2 # (-5) = 2(2) + 3(-5) = 4 - 15 = -11.
Therefore, 2 # (4 * 3) = -11.
Keep in mind that the symbols * and # represent arbitrary mathematical operations defined in these particular questions. Their meaning could be different in other contexts, so it's important to carefully read the given definitions.