2D Geometry Questions and Answers

Consider a triangle ABC with the features c=65 meters and m∠B= 23. Find the values of side length b for which there would be zero, one, or two possible triangles for this situation. a) For what values of b would there be ZERO possible triangles? b) For what values of b would there be ONE possible triangle? c) For what values of b would there be TWO possible triangles?

Find the radius of a circle with a diameter of 38 cm.

Graph the parabola. y=-3x² +24x-44

In ΔABC, LC is a right angle and m∠A = 40°. Which list shows the sides in order from longest to shortest? AB, BC, AC BC, AB, AC AC, BC, AB AB, AC, BC

A triangle has sides with lengths of 12 feet, 12 feet, and 16 feet. Is it a right triangle? yes no

A rhombus has diagonals of 5 and 7. Find the length of its sides.

Given: Rectangle ABCD Prove: AC=BD

If the perimeter of a rectangle is 30 cm and the area is 50 square cm, then what are the dimensions of the rectangle? The width, or shorter side is _______cm The length, or longer side is ________cm

Given that the area of an equilateral triangle is 331 cm², find its perimeter. The perimeter of the triangle is Give your answer to 2 decimal places.

Write 2/7 as a decimal rounded to the nearest tenth.

Write 2.012 as a mixed number and as an improper fraction. Write your answers in simplest form.

Write 1.15 as a mixed number and as an improper fraction. Write your answers in simplest form.

(a) An angle measures 51°. What is the measure of its supplement? (b) An angle measures 33°. What is the measure of its complement?

(a) 43.7 is what percent of 9.2? (b) What is 55% of 19.6?

A pail holds 2 3/4 gallons of water. How much is this in cups? Write your answer as a whole number or a mixed number in simplest form. I

Write 67/11 as a decimal rounded to the nearest hundredth.

Find the least common denominator (LCD) of and 4/15 and 9/10.

A rirg shaped region is shown below. Its inner diameter is 38 m, and its outer diameter is 50 m. Find the area of the shaded region. Do not round any intermediate steps. Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas.

The circumference of a circular garden is 138 feet. What is the radius of the garden? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas.

The circumference of a circular field is 310 yards. What is the radius of the field? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas.

A ring-shaped region is shown below. Its inner radius is 7 cm, and its outer radius is 10 cm. Find the area of the shaded region. Do not round any intermediate steps. Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas.

What is the y-intercept of the line that has a slope of -4 and passes through the point (4, -6)? (A)-10 (B)-6 (C)8 (D) 10

Determine the equation of the circle that is centered at (0, 0) and passes through the point (3,-7).

The size of a laptop is determined by the diagonal of its screen. If a 11- inch laptop has a screen that is 7.3 inches tall, how wide is the screen? The screen is __ inches wide.

The center of a circle of radius 3 in. is at a distance of 50 in. from the center of a circle of radius 27 in. There are two circles that do not touch, four segments, and five labeled points. What is the exact length (in inches) of common internal tangent AB? (Hint: Use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.) in

Three of the four angle measures in a quadrilateral are 90, 90, and 125. Find the measure of the fourth angle.

If two sides of a triangle have the following measures, find the range of possible measures for the third side. 12, 8 5, 16 2,7 44, 38 21, 22 81, 100

If two triangles are congruent, which of the following statements must be true? Check all that apply. A. The corresponding sides of the triangles are congruent. B. The triangles have the same shape. C. The triangles have the same size. D. The corresponding angles of the triangles are congruent.

1. Parallel Line Construction: For this part of the assignment you will construct a parallel line through a given line and point. First, draw a segment (AB) and point C on your paper. Next, construct a line through point C that is parallel to AB. Label all points and lines used in the construction. 2. Perpendicular Line Construction: For this part of the assignment you will construct a perpendicular line to a given segment that passes through a given point. First, draw a segment (AB) on your paper. Draw a point (C) above that line. Construct a perpendicular line through segment AB and point C. Label all points. and lines used in the construction.

The vertices of the transformed figure are L' (0, 15), M (-15, -15), and N' (18, -6), and the original figure are L (0, 5), M (-5, -5), and N (6, -2). Find the scale factor used in this transformation. 3 2 5 -3

Find the scale factor, if the point A (2, 6) is dilated to A' (8, 24). 4 1/4 2 1/2

What is the perimeter of the ellipse defined by the equation: 36x^2 + 4y^2 = 144?

Consider the following planes. x+y+z= 9, x + 3y + 3z = 9 (a) Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (x(t), y(t), z(t)= (b) Find the angle, in degrees rounded to one decimal place, between the planes.

Select the correct answer. The vertices of a hyperbola are at (-5, -2) and (-5, 12), and the point (-5, 30) is one of its foci. What is the equation of this hyperbola? A. (y-5)^2 /24^2 - (x+5)^2 / 7^2 =1 B. (x+5)^2 /24^2 - (y-5)^2 / 7^2 =1 C. (x+5)^2 /7^2 - (y-5)^2 / 24^2 =1 D. (y-5)^2 /7^2 - (x+5)^2 / 24^2 =1

Select all the possible names for the figure below parallelogram quadrilateral square rhombus trapezoid isosceles trapezoid

Point R divides EF in the ratio 1:5. If the coordinates of Eand Fare (4, 8) and (11,4), respectively, what are the coordinates of Rto two decimal places? A. (4.66, 7.62) B. (6,6.86) C. (5.17,7.33) D. (9.83, 4.67)

Find x so that the triangle with vertices A=(-4, 3, -2), B=(-6. -1, -9), and C-(-9, 7, x) has a right angle at A. x=_________

5. If (ACBD)=-1, and M is the midpoint of AB show that 1/CA CB+ 1/DA DB=1/MA MB

Determine whether each statement is true or false. a. The Poincaré Incidence Plane is an example of an affine plane.

If P and Q are points and the Ruler Postulate is assumed to be true, prove the following. a. PQ ≥ 0 b. PQ = 0 if and only if P = Q C. PQ = QP

Follow these steps to construct a diagram: 1. Draw a circle with center A that takes up most of the visible view. 2. Create four well-spaced points on circle A. Label them B, C, D, and E, in clockwise alphabetical order. 3. Create two chords, BD and CE, and mark F as their point of intersection. 4. Measure and record BF, CF, DF, and EF. Also record m<CFB. 5. Draw four line segments, AB. AC. AD, and AE. (To highlight them for later use, try making these line segments different colors by changing the object properties.) 6. Label the central angles CAB and LEAD, and display their measures.

Find the parametric equation of a plane perpendicular to a given straight line passing through point P. I want to know how to solve both problems (1) and (2). (1) P(-2, 1, 7), *=x-4 /2 = y-2 /-3 = z /-5 (2) P(1, 1, -2), x-2/-3= y-3/-2 = -z-1

Enter the standard graphing form of the horizontal parabola for the given vertex and directrix. Vertex: (4,-4) Directrix: x = 4 - 1/-12

For an arc length s, area of sector A, and central angle 0 of a circle of radius r, find the indicated quantity for the given value. r=2.32 in, θ=pi/2 s=?

Given: a circle with a center O and a straight line with a point M on it (they do not intersect). Construct a circle tangent to the given circle and tangent at point M to the given line.

Smog is a general term used to describe pollutants in the air. A smog alert is usually issued when the air quality index is greater than 50. Air quality can vary throughout the day, increasing when more cars are on the road. Consider a model of the form 1= 30 sin (15(t - 4)) + 25 Where I is the value of the air quality index and t measures the time after midnight, in hours. a.What is the period of the modelled function? Explain why this makes sense. b.Determine the maximum, minimum and amplitude. c.What is the value of the air quality index at 6am?

What is the most specific name of the quadrilateral formed by the coordinates (-2,0), (-1,5), (0,4)(-3,1)? select one: O Rectangle O Parallelogram O Square O Rhombus

A line segment has an endpoints at (-5, 1), and (5,6). What is the location of the point that divides the segment in a ratio of 4:6? Select one: O (4,5.5) O (3,5) O (-3,2) O (-1,3)

A line segment has an endpoints at (4.25, 19) and (8, -1). What is the location of the point that divides the segment in a ratio of 1:4? O (3,7.25) O (5.75, 11) O (5,15) O (-6.5,7)

A line segment has an end points at (-5, 1) and (5,6). What is the location of the point that divides the segment in a ratio of 2:8? Select one: O (-1,3) O (3,5) O (-3,2) O (4,5.5)