To solve these problems, we must remember the distributive property. This property states that a coefficient being multiplied by a polynomial in parentheses is equal to the sum of the coefficient times each of the separate terms. Using this knowledge, let's begin with number 21:
-(4x + 17) + 3(7-x)
To begin, we should distribute the negative sign through the first set of parentheses and the coefficient of positive 3 through the second set of parentheses.
-4x - 17 + 21 - 3x
Next, we must combine like terms, or add/subtract the constants terms and the variable terms in order to create a more concise expression.
-7x + 4 (your answer)
Now, we can move on to question 22 and solve it in a similar manner:
7(2n-8) - 4(12 - 8n)
Again, we will distribute the coefficients through the parentheses. However, keep in mind that the coefficient in front of the second set of parentheses is actually a NEGATIVE 4, so we must distribute the negative as well.
14n - 56 - 48 + 32n
Next, we will combine like terms (add the n terms together and subtract the constant terms).
46n - 104
Now, we can solve problem 23:
8 + 2(5f - 3)
We will again distribute through the parentheses:
8 + 10f - 6
Combine like terms after that:
10f + 2
Therefore, your answers for the three problems are as follows:
21) -7x + 4
22) 46n - 104
23) 10f + 2
Hope this helps!
Answer: D
Step-by-step explanation:
The opposite sides of a rectangle are equal, so we can write the following equations:
2x = 3y + 5 ...........(1)
x = 2y + 2 .............(2)
Multiply equation (2) by 2, to get:
2x = 4y + 4 ...........(3)
The right hand sides of equations (1) and (3) are equal, so we can write:
3y + 5 = 4y + 4
which gives y = 1 as the solution.
Plugging y = 1 into equation (2), we find the x = 4.
So the full solution is: x = 4, y = 1.
If you meant 1,000 then there would be 227 voters Candidate A can expect to receive.
If you meant 10,000 then there would be 2267 voters Candidate A can expect to receive.
