Identify the graph of the equation. what is the angle of rotation for the equation?
2xy – 9 = 0

The answer is hyperbola; 45° ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* 2xy - 9 = 0

∵ A = 0 , B = 2 , C = 0

∴ B² - 4 AC = (2)² - 4(0)(0) = 4 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* To find the angle of rotation use the rule:

- cot(2Ф) = (A - C)/B

∵ A = 0 , B = 2 , C = 0

∴ cot(2Ф) = 0/2 = 0

∴ 2Ф = 90°

∴ Ф = 45°

* The answer is hyperbola; with angle of rotation = 45°

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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