Part 2) What's the perimeter of a regular heptagon if one side measures 3 inches?
we know that
The number of sides in a regular heptagon is equal to
so
The perimeter is equal to
where
a is the length side
in this problem
substitute
therefore
the answer Part 2) is the option
B. 21 in.
Part 3) A polygon that has all sides the same measure and all angles the same measure is called what?
we know that
When all angles are equal and all sides are equal, is a polygon that is equiangular and equilateral, so, is called a regular polygon
therefore
the answer part 3) is the option
C. Regular polygon
Part 4) The gazebo in the park is an octagon. Each side of the gazebo is 4 feet long. What is the perimeter of the gazebo?
we know that
The number of sides in a octagon is equal to
so
The perimeter is equal to
where
a is the length side
in this problem
substitute
therefore
the answer Part 4) is the option
D. 32 feet
Part 5) Which of the following best describes a plane?
we know that
--The edge of a desk is a piece of a straight or curved line.
-- A curve in a road is a piece of a curved line.
-- The intersection of two walls is a piece of a straight line
therefore
the answer Part 5) is the option
A. The surface of a flat table
Part 6) Two angles are supplementary. The first angle measures 40°. What's the measurement of the second angle?
we know that
Two angles are supplementary if the sum of their angles is equal to degrees
so
Let
x------> the measure of the second angle
therefore
the answer Part 6) is the option
C. 140°
Part 7) In order for a button to fit through its buttonhole, the hole needs to be the size of the button's diameter. What size buttonhole is needed for a button with a circumference of 9.42 centimeters?
we know that
The circumference is equal to
where
D is the diameter
solve for D
therefore
the answer Part 7) is the option
C. 3 centimeters
Part 8) The Pentagon in Washington DC is immense in size, with each outside wall 921 feet in length. What is the perimeter of the Pentagon?
we know that
The number of sides in a pentagon is equal to
so
The perimeter is equal to
where
a is the length side
in this problem
substitute
therefore
the answer Part 8) is the option
D. 4,605 ft.
I'm assuming you need to find the solution to this system of equations (where the lines intersect).
We can use the substitution method to solve this system. Take the value of from the second equation and substitute it into the first:
Add to both sides of the new equation:
Now add to both sides of the equation:
Divide both sides by :
Now let's solve for by substituting the known value of into the first equation:
Simplify using subtraction:
This means our solution is:
Answer:
x = 3, y = 1
Step-by-step explanation:
Solve the following system:
{y = x - 2 | (equation 1)
y = 7 - 2 x | (equation 2)
Express the system in standard form:
{-x + y = -2 | (equation 1)
2 x + y = 7 | (equation 2)
Swap equation 1 with equation 2:
{2 x + y = 7 | (equation 1)
-x + y = -2 | (equation 2)
Add 1/2 × (equation 1) to equation 2:
{2 x + y = 7 | (equation 1)
0 x+(3 y)/2 = 3/2 | (equation 2)
Multiply equation 2 by 2/3:
{2 x + y = 7 | (equation 1)
0 x+y = 1 | (equation 2)
Subtract equation 2 from equation 1:
{2 x+0 y = 6 | (equation 1)
0 x+y = 1 | (equation 2)
Divide equation 1 by 2:
{x+0 y = 3 | (equation 1)
0 x+y = 1 | (equation 2)
Collect results:
Answer: {x = 3, y = 1
B √1.3
C √1.4
D √1.5