Answer:
Add 9 to each side of the equation.
Step-by-step explanation:
To complete the square, we need to add (b/2) ^2 to each side, where b is the coefficient of the x terms.
The coefficient of the x terms is -6
so we need to add (-6/2) ^2 = (-3)^2 = 9.
Add 9 to each side of the equation.
Answer: The team won 47 games.
Step-by-step explanation: The total games played was 84, and that means all games added together, but victories and losses. If the games they lost is called X, and the team won 10 more games than it lost, then it means the games they won is X + 10.
To find the value of wins and losses, we can now express both properly as;
X + (X +10) = 84
2X + 10 = 84
Subtract 10 from both sides of the equation
2X = 74
Divide both sides of the equation by 2
X = 37.
If the number of games won is X + 10, then games won is derived as
Wins = X + 10
Wins = 37 + 10
Wins = 47
The team won 47 games
<h3>
Answer: 35.5</h3>
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Explanation:
The triangles are identical. So this means that the triangle on the left has the horizontal portion of 50 ft, and the other sides are x ft (where x is a placeholder for a number).
Add up the sides for the either triangle. We have x+x+50 = 2x+50. This expression is the perimeter of one triangle. The perimeter of both triangles is simply us doubling that expression
combined perimeter of 2 triangles = 2*(perimeter of one triangle)
combined perimeter of 2 triangles = 2*(2x+50)
combined perimeter of 2 triangles = 2*(2x)+2*(50) ... distribute
combined perimeter of 2 triangles = 4x+100
We're told that the combined perimeters total 242 ft, so this means 4x+100 must equal 242
Solve for x
4x+100 = 242
4x+100-100 = 242-100 ... subtract 100 from both sides
4x = 142
4x/4 = 142/4 ... divide both sides by 4
x = 35.5
note: 35.5 feet = 35 feet, 6 inches because 1/2 ft = 0.5 ft = (0.5*12) inches = 6 inches
A because inverse is the opposite order so instead of -3/1 or 5/1 it becomes 1/-3 and 1/5
Answer:
B (√6)/4
Step-by-step explanation:
The smallest multiplier that will make the denominator of the fraction into a perfect square is 2, so you have ...
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Answer choice D is also a correct rationalization of the denominator, but is not simplified as far as it can be. √24 = 2√6, so a factor of 2 can be cancelled from numerator and denominator, giving answer choice B.
