2D Geometry Questions and Answers

0 38 If the measure of angle A is 75 and the measure of angle C is 25 in a triangle ABC what is the measure of angle B

A window has the shape of a parabola above and a circular arc below Find the area of the window 10 7 10 ft 6 34 Use the dotted line as your y axis and the solid gray line as the x axis Find the distance from the z axis to the top of the circle Write the equation of the circle Write the equation of the parabola feet

y Find the value of the variable 450 450 y 60

Find the value of each variable Express in simplest radical for 5 14 X ly

Find the value of each variable Express in simplest radical form 1 30 60 30 X y

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For both of the following problems identify the function whose level curve is the surface described and use it to solve the integration problem a Integrate f x y z 22 over the hemisphere given by the equation x y z 4 for z 0 Hint If you choose the circle x2 y 4 as R note that z 0 in R and plug that into the integral in that instance Answer 0 b Integrate f x y z x y z over the portion of the plane 2x 2y z 2 that lies within the first octant which means x y z 0 Hint If you choose the triangle in the x y plane as R note that 20 here so you can plug that into f in that instance Answer 1

A rapid transit service operates 189 trains along five routes A B C D and E The number of trains assigned to each route is based on the average number of daily passengers per route given in the following table Use Webster s method to apportion the trains The standard divisor is 58 13 Route A B C D E Average Number of Passengers 1098 1349 1548 1514 5478 Route Number of apportioned trains A

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For each of the following graphs obtain a lower bound L A for the area enclosed by the curve by adding the areas of the squares enclosed completely by the curve Then obtain an upper bound U A for the area by adding the areas of the squares enclosed either partially or completely by the curve Notice the squares in the first graph are 1 by 1 squares and the squares in the second graph are 1 2 by 1 2 squares a L A b U A 2 1 0

2 In the adjacent figure x xOy is an angle Ox B C perpendicular to Ox and Oy perpendicular to O Oy A is a point of Ox and B is a point of Ox such that OA OB C is a y X point of Oy and D is a D point of Oy such that OC OD 1 Compare angles AOD and BOC 2 Prove that AD BC y 3 points 3 points

Find an equation for the conic section with the given properties The ellipse with vertices V1 1 9 and V 2 1 11 and foci F1 1 7 and F2 1 9

Two golf balls are hit into the air at 80 feet per second 60 mi hr making angles of 39 and 53 with the horizontal If the ground is level estimate the horizontal distance traveled by each golf ba The ball hit at 39 travels about feet Round to the nearest integer as needed

Given ABCD is a parallelogram BEAC and DF 1 AC Prove ABEC ADFA Step 1 try Statement ABCD is a parallelogram BE AC DF 1 AC Type of Statement B E F C Re Gi

Ron Prentice bought goods from Shelly Katz On Sept 12 Shelly gave Ron a time extension on his bill by accepting a 2 700 8 190 day note On Dec 16 Shelly discounted the note at Roseville Bank at 8 Use Days in a year table What proceeds does Shelly Katz receive Note Use 360 days a year Do not round intermediate calculations Round your answer to the nearest cent Proceeds received

The capacity of an elevator is either 20 children or 15 adults If 14 children are currently in the elevator how many adults can still get in Your AncwoK

se the method of cylindrical shells to find the volume generated by rotating the region bounded by y e y 0 x 0 and x 1 about the y axis olume

The graph of y f bx is a horizontal compression of the graph of y f x if b The graph of y f bx is a horizontal compression of the graph of y f x if b 1

vide Write your answer in simplest f 75 5 6 s 1 3

Multiply Write your answer in simplest form 3 1 3 1

Multiply Write your answer in simplest form 2c 23c 12 2c 5 2c 5 C 12

Divide Simplify your ans 17p 2 17p 8np

Divide Write your answer in simplest fo 1 n n 1

Multiply Write your answer in simplest form 12s s 1 s 2 3s 1 8s 16s

the excluded value for y 4 x 4

What is the excluded value for y X 6

Multiply Write your answer in simplest form u 14u3 49u 18u 6 4 7

Divide Write your answer in simplest 3p 13p 12 3p 2p 2 P 3 4p p

Multiply Write your answer in simplest form 3g 4g 4 9 2 9 2 2 g 11g12

Simplify Express your answer as a single fraction in simplest form X 5x 33x 10 6x 10

vide Write your answer in simplest for 2d 5 2d 10d 2d 5 2d

Divide Write your answer in simplest form 6q 7q 7q 5 29 2 12914q3 109

Simplify Express your answer as a single fraction in simplest form 3 2 2 3w 2w 14

Multiply Simplify your answer 10s 3su 6u

Simplify Express your answer as a single fraction in simplest form z 4 7z 6z 7

Simplify Express your answer as a single fraction in simplest form 2c C 2 C 2 c

Multiply Write your answer in simplest form 8 7 3w 4 5w2

Simplify Express your answer as a single fraction in simplest form P 2p 12p 24 4p 8

Simplify Express your answer as a single fraction in simplest form b 5b b 2

Simplify Express your answer as a single fraction in simplest form a 9 a 10

Sketch the graph of the following between x CSC X 4 and x 4 Y

Determine the number and type of solutions of a quadratic funct B Determine the a coefficient of a quadratic function Calculate the y intercept of a parabola

6 Solve using the quadratic formula 2 8z 7 There are four parts to this questions labeled A D Part A Write the given equation in the form ar b c 0 Part B Identify the values of a b and c a Part C C Evaluate the discriminant 2 4ac Enter the value of the discriminant Because the discriminant is Part D there solutions Substitute values into the quadratic formula and solve round answers to the nearest hundredth The exact solution s in simplest radical form are x 2a and the approximate solutions are x and x

5 Solve using the QUADRATIC FORMULA SMALLEST NUMBER FIRST ROUND TO THE NEAREST HUNDREDTH 4x 4 z H

5 Solve the quadratic equation by completing the square x 4x 3 0 Ax 2 7 6 x 2 7 x 4 7 D x 4 7

Use the Quadratic Formula to solve these equations Write your answers as complex numbers in the form a bi x 4x 13 0

Which of the equations below is the QUADRATIC FORMULA bb2 4ac A x 2a B 62 4ac b c x 2a p q D x 2

14 Use the imaginary number i to match the expressions given in the first column as a complex number Simpify all radicals 16 DRAG DROP THE ANSWER 3i 21 21

Find the sum of the real parts of the complex numbers 22 5i and 10 8i Then find the sum of their imaginary parts Sum of real parts Sum of imaginary parts i

3 a Part A In a direct variation equation y 15 when x 5 Write a direct variation equation that shows the relationship between x and y A y B Y 2838 y 2x Dy 3x b Part B Solve the equation of direct variation to determine the value of y when x 10 y wwwww www