The symbol "<=" without quotes means "less than or equal to"
-6x + 2y <= 42
-6x + 2y + 6x <= 42 + 6x ... Add 6x to both sides
2y <= 6x + 42
2y/2 <= 6x/2 + 42/2 ... divide every term by 2
y <= 3x + 21
So the answer is choice D
Answer: 14ft
Step-by-step explanation: 12*5 = 60, 840/60 = 14ft
Placing the equation of the circle in standard-form, the correct statements are given as follows:
- The radius of the circle is 3 units.
- The center of the circle lies on the x-axis.
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
<h3>What is the equation of a circle?</h3>
The equation of a circle of center
and radius r is given by:
![(x - x_0)^2 + (y - y_0)^2 = r^2](https://tex.z-dn.net/?f=%28x%20-%20x_0%29%5E2%20%2B%20%28y%20-%20y_0%29%5E2%20%3D%20r%5E2)
In this problem, the equation is:
x² + y² - 2x - 8 = 0.
In standard-form:
x² - 2x + y² = 8
(x - 1)² + y² = 8 + 1²
(x - 1)² + y² = 9
Center of (1,0), on the x-axis, radius of 3, hence the correct statements are:
- The radius of the circle is 3 units.
- The center of the circle lies on the x-axis.
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
More can be learned about the equation of a circle at brainly.com/question/24307696
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Product means the answer to a multiplication problem.
So, A. 17 * n is the answer. 17n is also appropriate.
Given:
The diameter of the circle = 14 cm
To find:
The area of the circle.
Solution:
We have,
Diameter of the circle = 14 cm
We know that the radius of the circle is half of its diameter. So,
![r=\dfrac{14}{2}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7B14%7D%7B2%7D)
![r=7\text{ cm}](https://tex.z-dn.net/?f=r%3D7%5Ctext%7B%20cm%7D)
The area of a circle is:
![A=\pi r^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2)
Substituting
in the above formula, we get
![A=\dfrac{22}{7}\times (7)^2](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B22%7D%7B7%7D%5Ctimes%20%287%29%5E2)
![A=22\times 7](https://tex.z-dn.net/?f=A%3D22%5Ctimes%207)
![A=154](https://tex.z-dn.net/?f=A%3D154)
Therefore, the area of the circle is 154 square cm.