2D Geometry Questions and Answers

Decide whether each statement is true or false. If a statement is true, say which of Euclid's five postulates apply to it, then write the converse and contrapositive statements, and then decide which of these statements are true (it may help to rewrite the statements in "if-then" form). If it is false, give a counterexample or explain why. a. A triangle can be drawn from any three points that are not on the same line. b. A square can be drawn from any four points not on the same line. c. When two lines intersect, the four angles they make add to 360 degrees. d. There is only one parallel line to any given line.

A triangle has sides of length 5 cm and 6 cm. What can you say about the length of the third side? Choose the correct answer below. A. A third side cannot be found to complete this triangle. B. The side is shorter than 11 cm but not necessarily longer than 1 cm. C. The side is longer than 5 cm and shorter than 6 cm. D. The side is longer than 5 cm but not necessarily shorter than 6 cm. E. The side is longer than 1 cm and shorter than 11 cm. F. The side is shorter than 6 cm but not necessarily longer than 5 cm, G. The side is longer than 1 cm but not necessarily shorter than 11 cm. H. No conclusion can be made about the other side

Definition: Two n x n matrices A and B are said to be similar if there exists an invertible n x n matrix P such that A = PBP-¹. Let A, B and C be arbitrary n x n matrices. If A and B are similar and B and C are similar, prove that A and C are also similar. In your proof, you must explicitly state any properties or theorems you have used.

The following equation is an equation of an ellipse, find the radii of this ellipse. 7x1²-8 x1 x2 + 13x₂² = 1. Answer: Note: Enter the radii as a maple list [a, b], use sqrt to enter square roots, i.e., to enter 1/√2 type

Graph the expression on each side of the equals symbol to determine whether the equation might be an identity. (cscθ+ cot θ) (1 - cos θ) = sin θ It is not an identity. It is an identity.

Find the length of an arc intercepted by a central angle 0 in a circle of radius r. r = 24.09 cm, θ=10/9π radians A. 168.2 cm B. 42.1 cm C. 84.1 cm D. 26.8 cm

The height of a high tide is 12 m, and the height of the low tide is 2 m. If high tide occurs at 10 am, and then again at 4 pm. Find an equation that models the height of tide (m) with respect to time, where t=0 is 12 midnight.

Find the circumference and area of a circle with the radius 3.5 feet. Use 22/7 for T.

Medical insurance status-covered (C) or not covered (N)-is determined for each individual arriving for treatment at a hospital's emergency room. Consider the chance experiment in which this determination is made for two randomly selected patients. The simple events for this chance experiment are O₁ = (C, C), meaning that the first patient selected was covered and the second patient selected was also covered, O₂ = (C, N), O₁ = (N, C), and O₁ = (N, N). Suppose that probabilities are P(O₂) = 0.81, P(O₂) = 0.09, P(O3) = 0.09, and P(0₁)=0.01. b. Define B as the event that the two patients have the same coverage status. i. What simple events are in the event B? ii. Calculate P(B).

The line has an equation of y=2x intersects the curve y²=8x, Determine the centroid of the area from the x-axis. A. 5 B. 4 C. 2 D. 3

Identify the vertex and the y-intercept of the graph of the function. y=-0.25(x-4)²-2 1. vertex, (-4, 0); y-intercept, -6 2. vertex, (2,-4); y-intercept; -6 3. vertex, (-2, 4); y-intercept, -6 4. vertex, (4,-2); y-intercept, -6

consider o.n. Oxy, a circunference of equation (x-1)² (4 + 2)² = 25. which of the following equations define a tangent line to this circunference? (A) X= A (B) x = S (c) y=-2 (D) y 3

Construct a square inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a square inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings.

Alaina has a spherical balloon that has a diameter of 18 centimeters. Rahim has a spherical balloon that holds twice as much air as Alaina's balloon. What is the diameter of Rahim's balloon?

A large clock has a minute hand 1.5 meters long. At the start of each hour, the tip of the minute hand touches the top of the clock, and on the half hour, it touches the bottom of the clock. At 4:50 PM, how far is the tip of the minute hand above the bottom of the clock?

Starting with the graph of f(x) = 3ˣ, write the equation of the graph that results from (a) shifting f(x) 1 units downward. y = ___________ (b) reflecting f(x) about the y-axis. y = ___________ (c) shifting f(x) 4 units left. y = ___________

In Euclidean geometry, a regular hexagon of side s is inscribed in a circle of radius s. On the sphere, there exists a regular pentagon of side s inscribed in a circle of radius s, but for only one value of s. What is s?

A quadrilateral with opposite sides congruent and all angles equal to 90° is called a: A. trapezoid B. pentagon C. rectangle

A square is called a polygon. A. concave B. isosceles C. regular D. irregular

Find the sum of the interior angles of a regular octagon.

A regular quadrilateral is also called A. a square B. a pentagon C. a nonagon D. an octagon

A population numbers 12,000 organisms initially and decreases by 2% each year. Suppose P represents population, and t the number of years of growth. Write an exponential model to represent this situation. P =

Percent Markdown A shirt was originally priced at $30. The store is having a 35% off sale. How much will you pay for the shirt after the discount (not including tax)? Round your answer to the nearest cent A $30 shirt marked 35% off will cost $ before tax

Out of 270 racers who started the marathon, 245 completed the race, 20 gave up, and 5 were disqualified. What percentage did not complete the marathon? Round your answer to the nearest tenth of a percent.

Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. 645 m2; 740 m2 668 m²; 740 m² 645 m²: 812 m² 668 m²; 704 m²

Linear Application The equation V = 27.8 +1.9x gives the value (in thousands of dollars) of an investment after a months. Interpret the Slope in this situation.

Find the volume of a square pyramid with base edges of 48 cm and a slant height of 26 cm. 768 cm3 23,040 cm3 11,520 cm3 7,680 cm³

Find the volume of the cylinder in terms of π. 60.8 m3 57.76 m3 438.98 m3 115.52 m3

Find the volume of the given prism. Round to the nearest tenth if necessary. 580 ft3 488 ft3 576 ft3 567 ft3

4. We describe locations on the Earth using latitude and longitude 8. Using these coordinates, we describe a location A on the Earth with A = (A,θA). Las Vegas, for example, has coordinates (36° N, 115° W), or (36°, -115°). Prove the distance formula cos(|AB|/R) = sin A sin b + cos A cos B cos(A - B), where R is the radius of the Earth. Hint: Look at ΔABN where N is the North pole.

Solve: -6c+7= 11. Write your answer as an integer, proper fraction, or mixed number in simplest form. C =_________ Question Help: Video 1 Video 2 Submit Question

The circumference of a circle is 64cm. Find the diameter, the radius,and the length of an arc of 190°. 64 cm; 128 cm; 16.9 cm 64 cm; 32 cm; 33.8 cm 32 cm; 64 cm; 16.9 cm 128 cm; 32 cm; 185 cm

A triangle has side lengths of 12 cm,35 cm, and 37 cm. Classify it asacute, obtuse, or right. 0 acute O right 0 obtuse

A triangle has sides of lengths 24, 143, and 145. Is it a right triangle?Explain. no; 24² + 143² # 145² no; 24² + 143² = 145² yes; 24² + 143² = 145² yes; 24² + 143² # 145²

A kite has diagonals 5.8 ft and 6 ft.What is the area of the kite? O 5.9 ft² O 23.6 ft² O 34.8 ft² O 17.4 ft2

The volume of a rectangular pyramid is 216 units. If the length of the rectangular base measures 6 units and the width of the rectangular base measures 12 units, find the height of the pyramid.

What is the volume, in cubic inches, of a cylinder with a height of 7 inches and a base radius of 2 inches, to the nearest tenths place?

What is the diameter of a hemisphere with a volume of 5078 m³, to the nearest tenth of a meter?

What is the volume of a cylinder, in cubic feet, with a height of 5 feet and a base diameter of 10 feet? Round to the nearest tenths place

The length of a rectangle is inches and the width is 4 inches.What is the ratio, using whole numbers, of the length to the width? O 30:19 O 30:38 O 15:19 O 19:30

2. Given the general term tn = 3n+ 5, which is the first four terms of the sequence? A 3, 5, 7, 9 B 1, 3, 5, 7 C 8, 11, 14, 17 D 5, 8, 11, 14

Red and grey bricks were used to build a decorative wall. The number of red bricks5 number of grey bricks was 2. There were 224 bricks used in all. How many red bricks were used? O 64 O 160 O 44.8 O 32

8. Determine the number of terms in each sequence. a) -14, -6, 2, 10, ..., 58

9. Determine the sum of each series. a) 400 +420 + 440 + ... +620 th= a +(n-1)d 620=400+ (n-1) 20 220 =(n-1) 20 11 = n-1 n = 12; b) 3+6+ 12+ 24 +48 +...+1536

You are reducing a map of dimensions 2 ft by 3 ft to fit to a piece of paper 8 in. by 10 in. What are the dimensions of the largest possible map that can fit on the page? 8 in. by 10 in.

ZJ and Mare base angles of isosceles trapezoid JKLM.If m/J = 18x+8, and m/M = 11x + 15, find m/K. 0 26 O 77 01 O 154

The sizes of three of the interior angles of a quadrilateral are 65°, 35, and 60°. What is the measure of the fourth angle of the quadrilateral?

Name the smallest angle of ΔABC. The diagram is not to scale. Two angles are the same size and smaller than the third. ∠C ∠B ∠A

DEFG is a rectangle. DF = 5x - 3 and EG = x + 5. Find the value of x and the length of each diagonal. x=2, DF = 7, EG = 12 x=2, DF=7, EG=7 x=2, DF = 6, EG=6 x = 1, DF = 6, EG = 6

Use less than, equal to, or greater than to complete this statement: The sum of the measures of the exterior angles of a regular 9-gon, one at each vertex, is the sum of the measures of the exterior angles of a regular 6-gon, one at each vertex. cannot tell less than equal to greater than