2D Geometry Questions and Answers

While driving from his home to his workplace, Chris has to pass through two traffic lights. The general probability of getting a red signal at the first traffic light (event A) is 36%. The general probability of getting a red signal at the second traffic light (event B) is 25%. The probability of Chris getting a red signal at both traffic lights is 9%. In this scenario, A and B are ______ events.

Type the answer in the box. If necessarry, use /for the fraction bar. Give your answe in reduced form. A card is drawn at a random from a well-shuffled deck of playing cards. The probability that the card drawn is an ace or a red card is

Find all the complex roots. Leave your answer in polar form with the argument in degrees. The complex fifth roots of 3. Zo=(cos+isin) (Simplify your answer, including any radicals. Type an exact answer, using radicals as needed. Type any angle measures in degrees.) z₁=(cos+isin) (Simplify your answer, including any radicals. Type an exact answer, using radicals as needed. Type any angle measures in degrees.) z2=(cos+isin) (Simplify your answer, including any radicals. Type an exact answer, using radicals as needed. Type any angle measures in degrees.) z3=(cos+ i sin) (Simplify your answer, including any radicals. Type an exact answer, using radicals as needed. Type any angle measures in degrees.) z4=(cos+ i sinº) (Simplify your answer, including any radicals. Type an exact answer, using radicals as needed. Type any angle measures in degrees.)

Question) Identify what type of conic section, or if they are just straight lines, are the quadratic shapes below. Transform to the main axis. Express x¹ = [X₁ X₂] in terms of new coordinates y¹ = [y₁ Y₂]. a) 7x₁²+ 6x1x2 + 7x₂² = 200 b) 9x₁² - 6x1x2+ X₂² = 40

Select the correct answer.An experiment consists of rolling a six-sided die to select a number between 1 and 6 and drawing a card at random from a set of 10 cards numbered 1, 2, 3.... 10. Which event definition corresponds to exactly one outcome of the experiment? A. Both numbers are 5s. B. Neither number is a 5. C.The sum of the numbers is 3. D. One of the numbers is a 3.

If the endpoints of AB have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB? A. (5,3) B. (4,5) C. (5,5) D. (4,3)

Equations of Circles When center is (0, 0): x² + y² = r² when center is not (0, 0): (x - h)² + (y - k)² = r² Write the equation of a circle with center (0, 0) and a radius of 15.

A circle is centered at the point (-3, 2) and passes through the point (1,5). The radius of the circle is ___ units. The point (-7,__) lies on this circle.

What is the radius of the circle x² + y² + 16 = 9x?

What is the center of the circle x² + y² - 36 = 16x? Simplify any fractions. _____ , ______

The point Q lies on the segment PR. Find the coordinates of Q so that PQ is 3/5 of PR Coordinates of Q:(______)

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.

Select the correct answer. You pick a card from a shuffled pack and draw a king. You put it back in the pack, shuffle, and then pick another card. This time you draw a queen. How are the two events of picking a king and picking a queen related? A. dependent B. independent C. codependent D. mutually exclusive

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?