Given:
The system of equations is
To find:
The true statement about the given system of equations.
Solution:
The slope intercept form of a line is
Where, m is the slope and b is the y-intercept.
We have,
On comparing these two lines with slope intercept form, we get
Since the slopes of the lines are equal but the y-intercepts are different, therefore, the two lines are parallel and the system has no solution.
Therefore, the correct option is A.
The area of the shaded region is option first is correct.
It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.
It is required to find the shaded area (missing data is attached shown in the picture).
<h3>What is a circle?</h3>It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have a hexagon with a side length of 10 feet.
We know the area of the hexagon is given by:
where a is the side length.
⇒
We have the shortest length = x feet and from the figure:
2x = 10
x = 5 feet
The radius of the circle r = longer leg
feet
The area of the circle a = ⇒
The area of the shaded region = A - a
Thus, the area of the shaded region is
Learn more about circle here:
Given:
The vertex of a triangle MNP are M(-4, 6), N(2, 6), and P(-1, 1).
The rule of dilation is:
The image of triangle MNP after dilation is M'N'P'.
To find:
The coordinates of the endpoints of segment M'N'.
Solution:
The end points of MN are M(-4, 6) and N(2, 6).
The rule of dilation is:
Using this rule, we get
And,
The endpoints of M'N' are M'(-6, 9) and N'(3, 9).
Therefore, the correct option is B.