Answer:
The domain of the function is R i.e. any real value.
Step-by-step explanation:
The given figure is a graph on the coordinate plane of the function
Now, the domain of a function means that the values of x (Independent variable) for which the function is valid i.e. the y values are real.
It is clear from the equation given above that for any real value of x there will be a real corresponding value of y.
Therefore, the domain of the function is R i.e. any real value. (Answer)
Answer:
<h2>8. D) 2x + 8</h2><h2>9. C) 6x + 32 = 158</h2><h2>10. 50 ft</h2>Step-by-step explanation:
Look at the picture.
9. The perimeter of the rectangle l × w:
P = 2l + 2w
Substitute l = 2x + 8 and w = x + 8:
P = 2(2x + 8) + 2(x + 8) <em>use the distributive property</em>
P = (2)(2x) + (2)(8) + (2)(x) + (2)(8)
P = 4x + 16 + 2x + 16 <em>combine like terms</em>
P = (4x + 2x) + (16 + 16)
P = 6x + 32
10. Solve the equation:
6x + 32 = 158 <em>subtract 32 from both sides</em>
6x = 126 <em>divide both sides by 6</em>
x = 21
Put the value of x to the expression 2x + 8:
2(21) + 8 = 42 + 8 = 50
Answer:
Step-by-step explanation:
<u><em>Horizontal Major Axis:</em></u>
<u><em>Vertical Major Axis:</em></u>
So these two expressions are essentially the same with the only difference being the location of "a" and "b". The length of the major axis will be "2a" and the length of the minor axis will be "2b". The way I remember this is because when you have the horizontal major axis the "a" value is in the denominator of the (x-h) and I think of "x" as a horizontal value, since it moves a point horizontally. When you have a vertical major axis the "a" value is in the denominator of (y-k) and I think of "x" as a vertical value, since it moves a point vertically.
So just by looking at the graph, you can easily determine that the eclipse has a horizontal major axis. This can be further proven, since the distance from the origin on the right side is 28, and the distance from the the top to the origin is only 20.
So you could set up an equation to solve for a, since 2a = length of major axis, but since we're given the two points, the "a" value is really just the length from the origin to the right/left side, and combining these together you get the value of 2a/major axis, but you don't have to do that. So by looking at the graph you'll see the distance from the origin to the right side is 28. This means "a=28"
You can do the same thing here for the "b" value, and since the top is 20 units away from the origin, "b = 20"
So now let's set up the equation:
Square the values in the denominator