Solving Equations & Angles
-4m + 2 = 6m + 12
Solve.
m = -1
1. Inscribed: Vertex is on the circumference of a circle; has chords for arms.
2. Central: Vertex is at the centre of the circle; has radii for arms.
A hexagon has equal side lengths of 52m. A line going from the middle of a side to the centre of the hexagon measures to be 44m. What is the area of the hexagon?
A = 6864 m2
If a right pyramid and a prism have equal bases and heights, how many pyramids can fit inside the prism?
3
Tigger is about to jump off of a staircase that is shaped like a right triangle. He calculates that the distance from where he is and to where he will land is 5m, while being 5m above the ground. If he were to fall diagonally, what distance would he cover after falling to the ground?
He would cover a distance of 7.1m.
Any '/' indicates a fraction:
(a + 5)/3 = (3 - a)/7
Solve.
a = -13/5
b) What term is used to describe the angle value of these two angles?
b) Congruent
A rectangle with side lengths of 15 cm and 10 cm also has a semi-circle attached on top of one of its 15 cm sides. If the radius is 7.5 cm, what is the perimeter of the whole shape? Round to 2 decimal places.
PSemi-Circle = 47.124 cm
PRectangle = 35 cm
PTotal = 82.12 cm
A cube has a side length of 1 cm. What is the surface area?
SA = 6 cm2
If Tigger is chasing his tail in a circular motion, how many circles would he have created if each circle is 100 cm in circumference, and he traveled 10000 cm in total?
100 circles
The side lengths of a triangle are 10x-4, x-8, and x+20.
a) Determine a simplified expression for the perimeter.
b) If the perimeter is 660 cm, use your simplified expression to determine the value of x. If applicable, round to 2 decimal places.
a) P = 12x+8
b) x = 54.33
A midsegment is a line that starts at the midpoint on the side of a triangle and ends at another side at 90 degrees.
False
What is the term for polygons that are made up of multiple similar shapes?
Composite Shapes
Tigger is forced into his enclosed, rectangular-prism shaped carrier. In order to ensure he doesn't suffocate, he tries to calculate the surface area of the 3D shape. He measures 10 cm for the length, 20 cm for the width, and 100 cm for the height. What is the surface area of the carrier?
The surface area is 6400 cm2.
Within a circular environment, if Tigger shoots two lasers out of one of his eyes and it creates a central angle of 50 degrees, what is the value of the inscribed angle in front of Tigger?
25 degrees
If two equilateral triangles are arranged in an hourglass figure (one right-side up and the other upside down, touching at their vertexes), and the opposite angles in the middle are both 60 degrees, what must be the values of the other 2 angles in both triangles?
60 degrees
a) What is the point of intersection between 3 medians called?
b) What does the median of a triangle do to its area?
a) Centroid
b) Bisects the area
A trapezoid, with only one diagonal side, has side lengths of 14x-4 (top), 20x+16 (bottom), and 6x (vertical side). These side lengths do not include the length of the diagonal side. Determine the area of the shape.
A = 102x2 + 36x
A square pyramid has a base length of 10 cm, and a slant height of 12 cm. What is the height of the pyramid? (Hint: The height reaches down exactly to the middle of the square base, perpendicularly.)
h = 10.91 cm.
Tigger dreams of a fish telling him that a transversal going through two parallel lines creates an F pattern, with one angle being 72 degrees, while the other is unknown. He wakes up and tries to figure out the missing angle value. What must this angle value be?
72 degrees
a) What two conditions must be true in order to classify a polygon as a convex polygon?
b) How many triangles fit within a polygon with 999 sides?
c) What do all exterior angles add up to?
a) All interior angles must be less than 180 degrees; Any straight line going throughout the shape should, at most, cross 2 sides.
b) 997 triangles
c) 360 degrees
Tigger is 20 years younger than Mr. Carson. If the sum of their ages is 10000, what are each of their ages?
Let x represent Mr. Carson's age.
T: x - 20
C: x
x-20+x = 10000
2x - 20 = 10000
2x = 10020
x = 5010, T = 4990
Therefore, Mr. Carson is 5010 years old, while Tigger is 4990 years old.
True or False:
The Pythagorean Theorem is used to describe the relationship between the lengths of an oblique triangle. The square of the hypotenuse is more than the sum of the squares of the legs.
False.
It describes the relationship between the lengths of a right triangle. The square of the hypotenuse is equal to the sum of the squares of the legs.
Sphere cats come in packages of three. The radius of each sphere cat is 3 cm. The height of the package (long, rectangular prism) is 18 cm, and the square base side length is 6 cm. How much air is in the package?
308.70 cm3 of air is in the package
BONUS QUESTION:
Tigger looks down at a piece of plastic bag from the top of a building at an angle of depression of 20 degrees. From the plastic bag's point of view, what is the angle of elevation to Tigger?
20 degrees