Answer: x=1
Step-by-step explanation:
You need to open up the parenthesis so you multiply every term inside the parenthesis by -7.
1. -7x + 14 + 1 = 15 -7x
2. Combine like terms -7x + 15 = 15-7x
The two sides of the equation are the same so that means that x=1
Answer:
Step-by-step explanation:
The segment joining an original point with its rotated image forms a chord of the circle of rotation containing those two points. The center of the circle is the center of rotation.
This means you can find the center of rotation by considering the perpendicular bisectors of the segments joining points with their images. Here, the only proposed center that is anywhere near the perpendicular bisector of DE is point M.
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Segment AD is perpendicular to corresponding segment FE, so the angle of rotation is 90°. (We don't know which way (CW or CCW) unless we make an assumption about which is the original figure.)
Answer:
The value of x = 9
Step-by-step explanation:
Angle Bisector Theorem
An angle bisector of a triangle would cut the opposite side into two segments that are proportional to the other two sides of the triangle.
Thus,

Cross Multiply the expression

Divide both sides by 20


Therefore, the value of x = 9
Answer:
The Brooks conjecture is true as the proportion of the area of a sector to the area of a circle is only dependent on the angle.
Step-by-step explanation:
The area of a sector for a radius r and an angle θ is given as

Whereas the area of a circle for a radius r is given as

Now the ratio is given as

Here as r is the radius of the circle and it is the same therefore the above ratio is simplified to

Here as π is constant the only variable here is θ. Thus according to Brooks conjecture when the angles are equal, the proportion of area of each sector relative to the area of the given circle is also equal is true.