Two angles form a linear pair if they have the same vertex, they share one side, and their interiors do not intersect. \(\displaystyle \angle FBC\) has vertex \(\displaystyle B\) and sides \(\displaystyle \overrightarrow{BF}\) and \(\displaystyle \overrightarrow{BC}\); \(\displaystyle \angle FBA\) has vertex \(\displaystyle B\), shares side \(\displaystyle \overrightarrow{BF}\), and shares no interior points, so this is the correct choice.

A line segment is named after its two endpoints in either order; \(\displaystyle \overline{AD}\) is the segment with endpoints \(\displaystyle A\) and \(\displaystyle D\), so it can also be named \(\displaystyle \overline{DA}\). 

Two angles are vertical if they have the same vertex and if their sides form two pairs of opposite rays. The correct choice will have vertex \(\displaystyle C\), which is the vertex of \(\displaystyle \angle FCB\). Its rays will be the rays opposite \(\displaystyle \overrightarrow{CF }\) and \(\displaystyle \overrightarrow{CB}\), which, are, respectively,  \(\displaystyle \overrightarrow{CG }\) and \(\displaystyle \overrightarrow{CD}\), respectively. The angle that fits this description is \(\displaystyle \angle DCG\). 

To find where two lines intersect, simply set them equal to each other and solve for \(\displaystyle x\). Then plug the resulting \(\displaystyle x\) value back in to one of the equations and solve for \(\displaystyle y\).

\(\displaystyle \small -\frac{1}{3}+7=3x+7\)

Add \(\displaystyle \frac{1}{3}x\) to both sides and subtract \(\displaystyle 7\) from both sides to isolate our like terms:

\(\displaystyle \small 0=3\frac{1}{3}x\)

So, \(\displaystyle x=0\) must be true for where these lines intersect. Next, plug \(\displaystyle 0\) back in for \(\displaystyle x\) in one of our original equations:

\(\displaystyle \small \small f(x)=3(0)+7=7\)

So, the \(\displaystyle y\) value of our intersection is \(\displaystyle 7\).

This makes the coordinate of our intersection \(\displaystyle (0,7)\).

You can check your answer by plugging in the point you calculated into both equations. Both equations will be true when \(\displaystyle x\) is equal to \(\displaystyle 0\) and \(\displaystyle y\)—in this case, \(\displaystyle f(x)\) and \(\displaystyle g(x)\)—is equal to \(\displaystyle 7\).

The perimeter is the sum of the measures of the sidelengths.

Knowing that the hexagon is regular only tells you the six sides are congruent; without the measure of any side, this does not help you. 

Knowing only that each of the six sides measures 10 cm is by itself enough to calculate the perimeter to be

\(\displaystyle 6\times 10=60\ cm\).

The answer is that Statement 1 is sufficient, but not Statement 2.

This figure can be seen as a smaller rectangle cut out of a larger one; refer to the diagram below.

We can fill in the missing sidelengths using the fact that a rectangle has congruent opposite sides. Once this is done, we can add the lengths of the sides to get the perimeter:

\(\displaystyle P = 10 + 3 + 15 + 7 + 25 + 10 = 70\) feet.

The perimeter \(\displaystyle P\) of any figure is the sum of the lengths of its sides. Since we have a rectangle with a length of \(\displaystyle 20cm\) and a width of \(\displaystyle 5cm\), we know that there will be two sides of length \(\displaystyle 20cm\) and two sides of width \(\displaystyle 5cm\). Therefore:

\(\displaystyle P=20cm+20cm+5cm+5cm\)

\(\displaystyle P=40cm+10cm\)

\(\displaystyle P=50cm\)

In order to find the perimeter \(\displaystyle P\) of the right triangle, we need to know the lengths of each of its sides. While we are given two sides - the base \(\displaystyle (a)\) and the height \(\displaystyle (b)\) - we do not know the hypotenuse \(\displaystyle (c)\). There are two ways that we can find \(\displaystyle c\), the first of which is the direct application of the Pythagorean Theorem: 

\(\displaystyle a^{2}+b^{2}=c^{2}\)

\(\displaystyle 5^{2}+12^{2}=c^{2}\)

\(\displaystyle 25+144=c^{2}\)

\(\displaystyle 13=c\)

We could have also noted that \(\displaystyle 5:12:13\) is a common Pythagorean Triple and deduced the value of \(\displaystyle c\) that way.

Now that we have all three side lengths, we can calculate \(\displaystyle P\):

\(\displaystyle P=5cm+12cm+13cm\)

\(\displaystyle P=30cm\)

Starting with the knowledge that we are dealing with an octagon, an 8-sided figure, we calculate the perimeter \(\displaystyle P\) by adding the lengths of all 8 sides. Since we also know that each side measures \(\displaystyle 15cm\), we can use multiplication:

\(\displaystyle P=8\times15cm\)

\(\displaystyle P=120cm\)

A pentagon is a 5 sided shape. We are given that two sides are 5 inches each.

Side 1 = 5inches

Side 2 = 5 inches

The next two sides are each 1.5 times bigger than the smallest two sides.

\(\displaystyle \small 5*1.5=7.5\)

Side 3 =Side 4= 7.5 inches

The last side is twice the size of the smallest side, 

Side 5 =10 inches

Add them all up for our perimeter:

5+5+7.5+7.5+10=35 inches long