Question: What value of c will complete the square below (
) and make the expression a perfect square trinomial?
Answer: c = 225
Step-by-step explanation:
Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)². In the presented trinomial, we can immediately identify that <u>a = x, and b² = c</u>, but we need to find the numerical value of 
.
To do this, note that the middle term, or <u>2ab, corresponds with (is equal to) 30x</u>. We know that a = x, and thus, <u>2ab = 2bx</u>. Now, 2bx and 30x are corresponding terms; thus, <u>2bx = 30x</u>.
Dividing by 
on both sides gives us <u>b = 15</u>. Therefore, c = b² = 15² = 225. (As a squared binomial, this would be (x + 15)² as a = x and b = 15.)
Cost of 1 lemon = 15/2 = 7.5 cents
Cost of 60 lemons = 7.5 * 60 = 450 cents or $4 50
Answer:
The solution set is (6,3)
Step-by-step explanation:
Begin by multiplying equation 1 by 2. You'll see why in a moment
2y = 2*(1/2) x
2y = x
Substitute this value into equation 2.
2y + 4y = 18 Combine like terms on the left
6y = 18 Divide both sides by 6
6y/6 = 18/6 Do the division
y = 3
To solve for x just use the top equation
y = 1/2x
3 = 1/2x Multiply by 2
3*2 = x
x = 6
Step-by-step explanation:
It's 27
Your welcome!!!!
Answer:
Answer: 042
Step-by-step explanation:
The fourth clue eliminates 7, 3 and 8 as possibilities, the fifth clue means that 0 is the correct number but in the wrong position. The third clue indicates that the right digits, including the 0, are in the wrong place. That means the 0 must be the first number of the code.
Based on the first and second clues, the 6 must be eliminated as a possibility because it’s in the same place in both clues, but one clue says it’s in the right place and the other clue says it’s in the wrong place. So by looking at the first clue, we can determine that 6 and 8 are both eliminated (the 8 due to the fourth clue), meaning that the 2 is right and in its place.
The final number can be solved using the second clue. Because the digit remaining to be solved is the second digit, the answer must be 4 and not 1. The digit is right but in the wrong place, so it can’t be 1, which is already in the middle, so it must be 4, meaning the full answer is 042.
