Geometry Questions

Find the angle between the vectors u 6i 6j v i 3j 5k The angle between the vectors is 0 Round to the nearest hundredth as needed radian s

Nora leans a 24 foot ladder against a wall so that it forms an angle of 76 with the ground How high up the wall does the ladder reach Round your answer to the nearest hundredth of a foot if necessary

5 In the diagram below a plane intersects a square pyramid parallel to its base Which two dimensional shape describes this cross section 6 A solid metal prism has a rectangular base with sides of 4 inches and 6 inches and a height of 4 inches A hole in the shape of a cylinder with a radius of 1 inch is drilled through the entire length of the rectangular prism Find the volume of the entire rectangular prism Find the volume of the cylinder 4 in 4 in What is the approximate volume of the remaining solid in cubic inches 6 in

A person is standing at the edge of the water and looking out at the ocean see figure The height of the person s eyes above the water is h 1 7 m and the radius of the Earth is R 6 38 x 106 m a How far is it to the horizon In other words what is the distance d from the person s eyes to the horizon Note At the horizon the angle between the line of sight and the radius of the earth is 90 b Express this distance in miles a Number i Units 90 Horizon

find the area of segment coloured in red A D 400m A B 340m B D 260m triangle is above centre point G A weat wosk

m 1 N L Find the measure of each marked angle in the figure when m1 3x and m2 2x 10 2 u m t C O S

Find the volume of the solid 20 5 in 7 in 21 2 cm 6 cm 4 cm 22 11 24 ft 4 ft

B a 80 b 120 16z 12 E 2z 4 D c 12 d 141

9 Which is mVXU a 15 W a 105 b 120 9x 18 X V T 15x U 3x 21 c d 122 5 126

anu 0 H Not drawn to scale Given m HJF 84 are shown Which statement if true would help prove that quadrilateral FGHJ is inscribed in Circle O and why a m JFG 84 for a quadrilateral inscribed in a circle adjacent angles are congruent b m JFG 96 for a quadrilateral inscribed in a circle adjacent angles are supplementary c m FGH 84 for a quadrilateral inscribed in a circle opposite angles are congruent d m FGH 96 for a quadrilateral inscribed in a circle opposite angles are supplementary

12 What is m XYZ a 83 166 b 979

16 Write the equation of a circle with center M 7 10 and radius 2 a x 10 y 7 4 b x y 7 10 4 c x 7 10 4 d x 7 10 2

14 Which statement below correctly relates BDC and ZBAC B A a ZBDC and ZBAC are complementary ZBDC and ZBAC are supplementary b c ZBDC and ZBAC are congruent d It is impossible to determine a relationship between ZBDC and ZBAC

ven the following sets find the set A n BUC U 1 2 3 8 A 1 2 4 6 B 1 2 3 C 1 2 3 4 5

The circle in the figure below has a radius of r and center at C The distance from A to B is x Redraw the figure below label as indicate in the problem and then solve the problem If C 70 and x 27 find r Round your answer to the nearest whole number r Xx D B X A

could be used to show that Circle A is similar to Circle B 2 and radius 1 0 0 and scale hat sequence of transformations a a translation of the center 5 units to the right and 2 units up then a dilation with center 0 0 and scale factor 3 b a translation of the center 5 units to the right and 2 units down then a dilation with center 113 C a translation of the center 5 units to the left and 2 units up then a dilation with center 5 2 and scale factor 3 d a translation of the center 5 units to the left and 2 units up then a dilation with center 5

what is the equation for the parabola with a focus f 0 16 7

3 The central angle of a circle measures 97 and intercepts a minor arc What is the measure of its major arc a 83 b 97 C 187 d 263

6 What is BD a 7 5 b 8 5 4 C d

b Let T x y 4x y 1 x y2 represent the temperature on the xy plane Sketch the leve curves for T 2 1 0 1 2

4 Which of these arcs has a measure of 134 7 201 g 2 46 c EG d DH

Find the area of the polygon 17 kite 26 18 regular pentagon 19 regular decagon C

1 Factor completely 3 x 3 x 2 1 b 3 x 3 x 3 3x 9 x 2 a C 3x 3x18

Find the lateral area of each regular pyramid 7m 7 m 17 7 m 15 ft 12 ft 12 ft 12 ft ANS

Find the surface area of ench regular pyramid 21 ft 9 5 cm 12 ft 5 cm 12 ft 9 cm Ans S A ANS S A

Find the lateral area of each cone 2 A 20 cm 57 9 cm 10 m 2 m ANS L A bi

3 Use the quadratic formula to solve x 2x 3 2

What is the difference between factoring and solving

8 Factor completely 5a b 20a b5

7 Solve the following quadratic equation a x 4 11 b x 4 21 c x 8 21 x 5 8x

8 Factor completely 5a4b 20a b5

9 Factor completely 21m5n 7m n

Tor Analysis Using the Quadrat 2a nd the line that contains the error explain the error and then solve the problem correctly Line 1 Line 2 Line 3 Line 4 Line 5 X x2 5x 24 x 5x24 0 a 1 b 5 c 24 5 5 4 1 24 2 1 5 25 96 X X 2 5 71 2

3 Solve for x 1 Marton Ex 4 3 2

A solid with surface area 50 units is dilated by a scale factor of k to obtain a solid with surface area 200 units2 Find the value of k

2 The curve r 4 sine is rotated about the x axis Find the area of the resulting surface

a The slope of the line is 1 3 Simplify your answer b Interpret the slope For every 3 unit change in x the change in y is unit s Simplify your answer

This prism has a right triangle for a base What is the volume of the prisma The volume is cubic units 4 A 8 5 D B

solve the following equation for 0 where 0 0 180degree sec 20 3degree csc 20 51degree

7 4 A 1 Solve for angle C Show your work 11 6 C B 15 2

Note type any negative numbers without a space between the sign and the number ex 17 Do NOT include commas for spacing between sets of three digits ex 250000 include a 0 before the decimal point when necessary ex 0 2 Here is a graph of y sin 0 y sin 0 A 0 71 1 b For which angles 0 does sin 0 Your answers should be of the form 3pi 4 or pi 2

A rotation takes P to Q What could be the measure of the angle of rotation in radians Select all that apply KA 214

Rob and his brother are riding in the same car on a Ferris wheel which has a diameter of 40 feet Once the Ferris wheel starts they feet before the ride stops to let more people on What is the measure of the associated central angle for the travel a distance of T arc they traveled The central angle measures

Find the slope of the line if it is defined The line through 6 9 and 3 9

Use the Law of Sines to find all triangles if 109 b 13 5 c 10 5 Round to two decimal places As in the text a a B b and y c are angle side opposite pairs If no such triangle exists enter DNE in each answer box Enter the values for an acute triangle solution Y degrees degrees a Enter the values for an obtuse triangle solution Y degrees a degrees a Question Help Video

the parallelogram to answer each of the following questions a Find the height b Find the area of the parallelogram 3 2 The triangular prism below has a base area of 25 units and a height of 5 9 units Find its volume 3 In right triangle MTH shown below mZH 90 HT 8 and HM 5 a Which figure is formed if triangle MTH is continuously rotated around MH 7 b Determine and state to the nearest tenth the volume of the three dimensional solid formed by rotating triangle MTH continuously around MH M 5 DI H 4 What is the volume of a hemisphere that has a diameter of 12 6 cm to the nearest tenth of a cubic centimeter 8

1 Use the parallelogram to answer each of the following questions a Find the height 5

1 Bob wants to measure the building and decides to use a mirror to do so He stands away from the building and looks into the mirror on the ground moving away or closer to the mirror until he can see the top of the building in the mirror His friend measures the distance between the building and the mirror and the mirror and Bob They draw the following picture to demonstrate the distances Solve for the height of the building 5 ft Cong s by prop of reflections Line of sight 10ft Mirror 100ft h Building Right angle with the ground

3 The image comes from www startplayingtennis com You are playing tennis are are ready to serve the ball You hit the ball at a height of 8 You are standing on the baseline 39 from the 3 5 net Where will the ball land on the other side of the net 8 tennis player

2 A man who is 6 feet tall stands in front of a flagpole His shadow is 10 feet long and the distance from the flagpole to the tip of his shadow is 85 ft How tall is the flagpole 6 ft ft