The rectangle shown has a perimeter of 154 cm and the given area. Its length is 5 more than five times its width. Write and solv
e a system of equations to find the dimensions of the rectangle.
2 answers:
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It is given that the inequalities.
We need to determine the inequalities which have an open circle.
The graph will have an open circle only if it has the symbol < or > because it indicates that the boundary is not included.
<u>Option A</u>:
The inequality shows that it contains the boundary point 25.
Hence, the inequality does not have an open circle.
Hence, Option A is not the correct answer.
<u>Option B</u>:
The inequality shows that it contains the boundary point -2.5.
Hence, the inequality does not have an open circle.
Hence, Option B is not the correct answer.
<u>Option C</u>:
The inequality shows that it does not contains the boundary point 5.4
Hence, the inequality have an open circle.
Thus, Option C is the correct answer.
<u>Option D</u>:
The inequality shows that it does not contain the boundary point
Hence, the inequality have an open circle.
Thus, Option D is the correct answer.
<u>Option E</u>:
The inequality shows that it does not contain the boundary point 0
Hence, the inequality have an open circle.
Thus, Option E is the correct answer.
Answer:
The equation is that of ellipse withe angle of rotation 30° ⇒ answer (d)
Step-by-step explanation:
* Lets talk about the general form of the conic equations
- Ax² + Bxy + Cy² +D = 0 (center is the origin)
- A is the coefficient of x² , B is the coefficient of xy
C is the coefficient of y² , D is the numerical term
* Now we will study how to know the type of the graph of this equation
- If A and C have different signs (different values)
∴ The equation is that of an ellipse
- If A and C have different signs (different values)
∴ The equation is on a hyperbola
* Now look at the equation:
13x² + 6√3 xy + 7y² - 16 = 0
∵ A = 13 , B = 6√3 , C = 7 , D = -16
∵ A and C have same sign
∴ The equation is that of an ellipse
* Now lets find the angle of rotation by using the Rule:
- tan(2Ф) = B/(A - C) ⇒ Ф is the angle of rotation
- By using the value of A , B and C
∴ tan(2Ф) = 6√3/(13 - 7) = 6√3/6 = √3
∴ 2Ф =
∴ 2Ф = 60° ⇒ divide both sides by 2
∴ Ф = 30°
∴ The angle of rotation is 30°
∴ The equation is that of ellipse withe angle of rotation 30°
* The graph represent the ellipse
- The purple line represents the angle of rotation
Answer:
Frequency table
2,4,5,5,5,6,7,8,9,9,10,11,12,15
