2D Geometry Questions and Answers

What is the radius of the circle x² + y² + 11x + 30 = 0? Write your answer in simplified, rationalized form.

Graph the circle x² + y² - 2y = -21 + 12x. Plot the center. Then plot a point on the circle. If you make a mistake, you can erase your circle by moving the second point onto the first.

The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $12 per pound. The manager wishes to mix 70 pounds of the $12 coffee to get a mixture that will sell for $8 per pound. How many pounds of the $6 coffee should be used?

Graph the circle 3x² + 3y² - 48 = 0. Plot the center. Then plot a point on the circle. If you make a mistake, you can erase your circle by moving the second point onto the first.

Donna is making candles in the shape of a cylinder. She needs to determine how many cubic centimeters of wax she needs. Use the button or 3.14 in your computation. Round your answers to the nearest tenth as needed. If the radius of each candle is 5 cm and the height of each candle is 10 cm (a) How much wax is needed for one candle? ____ cubic cm (b) How much wax is needed for 60 candles? ____ cubic cm

Solve using the quadratic formula. 2r²+8r - 1 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. r= or r=

The equation of a parabola is y = x² + 4x + 12. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions.

TV screens are measured on the diagonal. If we have a TV-cabinet that is 58 inches long and 46 inches high, how large a TV could we put in the space (leave 2-inches on all sides for the edging of the TV)? Round your answer to the nearest tenth. The screen can measure up to____inches on the diagonal.

The equation of a parabola is y = x² + 8x + 8. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions.

The equation of a parabola is y = x² - 8x + 24. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions.

The equation of a parabola is y = x² - 10x + 25. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions.

Solve using the quadratic formula.8n² - 8n - 1 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. n=_____or n= ______

The equation of a parabola is y = x² - 6x + 14. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions.

Solve using the quadratic formula. -5y² - 6y = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. y = or y=

The equation of a parabola is y=-3x²-(3x) + 38. Write the equation vertex form. Write any numbers as integers or simplified proper or improper fractions.

Solve using the quadratic formula. 2x² + 4x + 2 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. X = or x =

What is the focus of the parabola y = -(7x²)? Simplify any fractions. (___, ____)

Show that given 15 points in a rectangle with length 3 meters and width 1 meter, there exists two points that are at most 1/√2 apart.

What is the focus of the parabola y = (-5x²) - 6? Simplify any fractions. (____ ,____)

The equation of a parabola is y = x² - (6x) + 1. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fraction.

What is the focus of the parabola y=8x²? Simplify any fractions.

What is the directrix of the parabola y = 3x² - 1? Simplify any fractions.

What is the focus of the parabola y = -(3x² )+ 1? Simplify any fractions.(___, ___)

What is the focus of the parabola y=-3x² - 5? Simplify any fractions. (____ , ____)

What is the focus of the parabola y = 3x² + 6? Simplify any fractions.

What is the directrix of the parabola y = -(3x²)? Simplify any fractions.

What is the directrix of the parabola y =6x²?

What is the directrix of the parabola y = (6x² )- 2? Simplify any fractions.

What is the focus of the parabola y = 4x² + 3?

What is the directrix of the parabola y = -6x²? Simplify any fractions.

What is the directrix of the parabola y = 3x² + 2?

Solve the traveling salesman problem for the graph below by finding the total height of all Hamilton circuits and determining a circuit with minimum total weight.

What is the directrix of the parabola y = 10x²?

What is the directrix of the parabola y = -9x²? Simplify any fractions.

What is the axis of symmetry of the parabola y = 6x² - 5?

Write, in radians, the related angles (remaining family members) from 0 to 2π for each of the following angles. a) 3π/13 b) 0.89 (correct to two decimal places)

Of all the soft drink consumers in a particular sales region, 30% prefer Brand A and 70% prefer Brand B. Of all these soft drink consumers, 20% prefer Brand A and are female. and 40% prefer Brand B and are female. What is the probability that a randomly selected consumer is female, given that the person prefers Brand A? A. 0.18 B. 0.21 C. 0.34 D. 0.67

The general form of the equation of a circle is Ax² + By² + Cx+ Dy+ E= 0, where A =B≠0. If the circle has a radius of 3 units and the center lies on the y-axis, which set of values of A. B. C. D. and E might correspond to the circle?

in a group of 55 people, 33 are coffee drinkers and 12 are tea drinkers. Assuming that no one in this group drinks both tea and coffee, what is the probability that a person picked at random from the group does not drink tea or coffee? A)3/5 B)2/5 C)7/11 D)2/11

250 employees in an organization were surveyed about their hair color and height. The data collected probability that the person is taller than 180 centimeters and has black hair? A 0.257 B. 0.351 C. 0.360 D. 0.116

What type of triangle is formed by joining the points D(7, 3), E(8, 1), and R4,-1)? A. equilateral triangle B. isosceles triangle C. right triangle D. acute scalene triangle E. obtuse scalene triangle

The probability of a randomly selected employee of a company being male is 60%. The probability of the employee being less than 30 years old is 70%. If the probability of the employee being less than 30 years old given that the employee is a male is 40%, what is the probability that the employee is a male, given that the employee is less than 30 years old? A. 0.34 B. 0.42 C. 0.55 D. 0.69 E. 0.71

Given hexagon JKLMNO - hexagon PQRSTU, LK =15, JO=22, and QR=4, find the scale factor from JKLMNO to PQRSTU. Give your answer in decimal form rounded to the nearest hundredths. Keep in mind, is the figure getting smaller or bigger? Figures getting smaller would have a scale factor less than 1. Figures getting larger would have a scale factor greater than 1.

The general form of the equation of a circle is 7x² + 7y²-28x+42y-35 = 0. The equation of this circle in standard form is________ the centre of the circle is at the point _____and its radius is _____units

Of all the yoga students in a particular area, 20% study with Patrick and 80% study with Carl. We also know that 8% of the yoga students study with Patrick and are female, while 66% of the students study with Carl and are female. What is the probability that a randomly selected yoga student is female, given that the person studies yoga with Carl? A. 0.35 B. 0.56 C. 0.69 D. 0.83

Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is found that 10% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming on weekdays and are female. The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is

A point on the line segment is chosen at random. What is the probability it is between 18 and 27?

Select the correct answer from the drop-down menu. The probability that Jane will go to a ballgame (event A) on a Monday is 0.73, and the probability that Kate will go to a ballgame (event B) the same day is 0.61. The probability that Kate and Jane both go to the ballgame on Monday is 0.52. From the given scenario, we can conclude that events A and B are

The Breaker's Manufacturing Company makes 80% of a particular sensor, the Cartin Company makes 15% of them, and the Flutes Company makes the other 5%. The sensors made by Breaker's have a 4% defect rate, the Cartin sensors have a 6% defect rate, and the Flutes sensors have a 9% defect rate. If a sensor is randomly selected from the general population of all sensors, what is the probability that it is defective, given that it was made by Breaker's? A.0.04 B. 0.05 C. 0.15 D. 0.80

Select the correct answer from the drop-down menu. A machine needs two of its gears replaced. You find two gears, one manufactured 5 years ago and the other manufactured 10 years ago. The specification sheet says that the chance of gear failure is 5% after 5 years and increases to 8% after 10 years. If the gears on the machine are not linked to each other, the probability that both replacement gears will fail is____