Don completes the square for the equation x^2 + 6x + 3 = 0. Which of the following equations reveals the vertex of the parabola?

Answers

Answer 1

Answer: x² + 6x + 3 = 0

y = x² + 6x + 3
y - 3 = x² + 6x

6x ⇒ 6x / 2x = 3 ⇒ 3² = 9

y - 3 + 9 = x² + 6x + 9
y + 6 = (x+3)²
y = (x+3)² - 6

vertex of the parabola is (x+3)²

y = (x+3)(x+3) - 6
y = x(x+3)+3(x+3) - 6
y = x² + 3x + 3x + 9 - 6
y = x² + 6x + 3

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A football stadium holds 52,000 fans. A college student is doing research and determines that on any given game day, the home team has five times as many fans as the visiting team. In order to help the student in his research, he represents the number of home team tickets as H and the visiting team’s tickets as V.

Answers

This problem is asking us to make an algebraic equation or representation of the situation. First we have to assign the variables which is already given in the problem. H is the number of the home team and V is the visiting team. Since the problem states there are the home team has five times as manyfans as the visiting team, then it can be represented as:

H = 5V
Also, H + V = 52,000. H and V can then be solves by solving the 2 equations simultaneously. The results are 43,333 and 8,667.

Simplify
2x7.5+2x11
thanks!

Answers

2 · 7.5 + 2 · 11 = 15 + 22 = 37

Suppose you want to represent a triangle with sides 12 feet, 16 feet, and 18 feet on a drawing where 1 inch = 2 feet. How long should the sides of the triangle be in inches?The sides of the triangle on the drawing should be _____.

Answers

Answer: The sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches.

Step-by-step explanation:

Given: A triangle with sides 12 feet, 16 feet, and 18 feet on a drawing where 1 inch = 2 feet.

Then, 1 feet of original triangle = $(1)/(2)$ inch on drawing.

Now, the sides of the triangle on the drawing are:-

12 feet = $(1)/(2)*12=6\text{ inches}$

12 feet = $(1)/(2)*16=8\text{ inches}$

12 feet = $(1)/(2)*18=9\text{ inches}$

Hence, the sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches.

the sides of the triangle would be 6 inches, 8 inches, and 9 inches long

Haley's softball team has a phone tree in case a game is cancelled. The coach calls three players. THen each of those players call three players, and so on how many players will be notified during the third round of calls

Answers

Answer:

Step-by-step explanation:

If we follow the amount of players called,

Coach called three/3

Players called three/3

Three players called three/3

And make it into a equation, 1 x 3 = 3

Those three people call three more: 3 x 3 = 9

Those nine people call three more: 9 x 3 = 27

A water sprinkler has a range of 5meters. The jet of water from the sprinkler sweeps out at an angle of 85degrees as the nozzle turns. What is the area watered by the sprinkler?