Geometry Questions

Jan is constructing an inscribed circle in a triangle What is the center of this circle called orthocenter centroid circumcenter incenter

Which of the following is NOT true of a perpendicular bisector it bisects a segment to construct it we have to draw two arcs using each of the endpoints as centers to construct it we have to draw two arcs using the intersection points as centers it forms a right angle with the segment

the line passeng through your answer Dietermine the slope of the given points worite exact simplified form 212 615 and 7 2 2 5

1 point D C B If the measure of arc AB is 64 degrees what is the measure of angle ADB 128 degrees 32 degrees 90 degrees 64 degrees

1 point A Solve for x x 5 O x 10 x 2 x 4 42 10 E B X D

E 00 11 D 43 45 Is segment CE tangent to circle D Why or why not No this doesn t look like a right triangle Therefore the segment is not tangent by the converse of the Perpendicular Tangent Theorem Yes this looks like a right triangle Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem Yes the Pythagorean Theorem holds true so it is a aright angle Therefore the segment is a tangent by the converse of the Perpendicular Tangent T e converse of the Perpendicular Ta No Pythagorean theorem does not hold true so it s not a right angle Therefore the segment is not tangent by t

33 35 24 24 A X 24 8 2 45 y 10 X 34 36 d 60 C 3 Fe Jo a 24

17 1 point Which of the following is NOT used in geometric constructions pencil protractor compass ruler

0 1 point Nate is constructing a tangent line to a circle he drew from a point outside the circle Once he has the circle and the point drawn what is his next step connect the center of the circle to the point outside the circle label the points where the arc intersects the circle construct a perpendicular bisector construct rays from the point through the points of intersection

1 point Which of the following constructions must you know how to do in order to construct a circumscribed circle for a given triangle duplicating a line segment angle bisector inscribed quadrilateral perpendicular bisector

1 point Laurie is constructing an angle bisector She sketched her angle then opened her compass to a radius length less than the length of the rays that make up the angle What should be her next step draw an arc using the vertex as the center draw a ray from the point of intersection to the vertex label the point of intersection of the two arcs mark the points of intersection

b If a 11 solve for b and c b 11 3 c 22 Ob 11 c 11 2 b 11 c 22 b 5 5 c 11

Given any two side lengths in a right triangle what is used to find the third side length sine tangent Pythagorean Theorem cosine

1 point A meteorologist measures the angle of elevation to her weather balloon as 33 degrees A radio signal from the balloon indicates that it is 1601 meters diagonally from her location How high is the weather balloon above the ground Round to the nearest hundredth 1342 71 feet 871 97 feet 1039 70 feet

10 1 point 60 Solve for x 2 2 2 2 3 1 30

Solve for u an 4 O A OB V 30 2 U A u 8 v 6 v 6 B u 4 C u 4 D u 8 v 23 v 2 3

POSSIBLE POINTS each pair of solids determine if their volumes are the same or different If the volumes are different identify the solid with the greatest volume Explai ur reasoning 1 A prism and a pyramid have the same height The pyramid s base has 3 times the area of the prism s base 2 A pyramid and a cylinder have bases with the same area The cylinder s height is 3 times that of the pyramid 3 A cone and a cylinder have the same height The cone s radius is 3 times the length of the cylinder s radius

4 17 mi 16 m 17 m 5 D X 25 4 m 9 6 m 12 m

An ellipsoid is a 3D shape whose cross sections are ellipses A whispering gallery is a room with a half ellipsoid ceiling If one person whispers from one focus another person can hear them clearly from the other focus Suppose a whispering gallery has 5 foot walls A cross section of the ceiling can be modeled by the ellipse shown below centered at the origin with a horizontal major axis If the maximum height of the ceiling is 20 ft and the width of the room is 50 ft write the equation of the ellipse 201 50 5

What set of reflections would carry trapezoid ABCD onto itself 1 point A BO T 9 2 C Ox axis y x y axis x axis Ox axis y axis x axis Oy x x axis x axis Oy axis x axis y axis x axis T D 3 2 27

Suppose h x is a linear function and the points points 2 4 and 5 13 lie on the graph of h x Complete the following tasks 1 Calculate the slope of the function using the two points provided 2 Substitute either of the points and the slope into slope intercept form and solve for b 3 Write the slope intercept form of the function

earthquake intensity measured by 1 lo x 10 m lo is reference intensity and M is magnitude An earthquake measuring 6 1 on the Richter scale is 125 times less intense than the second earthquake What would the Richter scale measure be for the second earthquake

Exercise 7 3 2 Find the direction and length of each principal axis of the hyperbola given by the equation below and sketch its graph 7x 48x1x2 7x3 25

lete the information on the unit 63 tartos mont wan Th 33 k 511 G TE 77 le 16pts 27t 312 3 5 57t 44T 51 dongtag wens glad of wolad mergan 23 TE 0 1 311 0 1 ME SACEN T 5TE 72 7 TU This alt 11m 2 T 1 0 3 sjo aroddi arize

earning Activity 28 Jace Find the surface area of following 4 m 18 m 5 m 6 cm 2 cm 8 cm 4 cm 6 cm

A circle of radius 12 units is divided into 8 congruent slices 1 What is the area of each slice 2 What is the arc length of each slice square units T units

Find the volume of this object Use 3 for Volume of a Cylinder V r h 4 ft 9 ft 5 ft 5 ft 5 ft Volume of a Rectangular Prism V lwh V ft

3 the area of each regular polygon Leave your answer in simplest form 2 10 8 8 3 13 12 4 10 6 8 3 11 16

1 A diver jumps from a cliff into the water below The path of the diver is given by the function f x t 4t 12 where f is the height of the diver above water level in metres after t seconds Hassan calculated the following average rates of change in the height of the diver over the following intervals 1 1 1 st 2 AROC 1m s ii 2 st 3 AROC 1m s iii 3 st 4 AROC 3m s Based on these values which of the following statements is FALSE about this situation a The AROC from 3 to 4 seconds is a smaller negative value therefore it implies that the diver is slowing down as it gets closer to the ground b The AROC from 1 to 2 sec is that same as the AROCI for 2 to 3 sec and since the first AROC is positive and the second is negative it implies that a maximum height was reached in the middle at 2 seconds c The diver was at first increasing in height and then decreasing to the AROCS changing from positive values to negative values

point In a basketball drill two players start at the same spot on the court One player runs 6 feet down the court and the other player runs 4 5 feet across the court in a direction perpendicular to the first player What is the distance that one player must pass the ball for it to reach the other 6 5 feet 7 5 feet 4 feet 8 feet Da

Determine an equation for the sinusoidal function given 2 45 0 M 135 180 225 270 315 360 45 J 9 0

Which of the following exponential functions grows at the slowest rate Select one O a y 2 O b y 0 5 O c y e O d y 5

1 point Inverse tangent is used to find a missing angle measure when we are given the opposite side hypotenuse opposite side adjacent side adjacent side hypotenuse same side other side and the

4 What inverse trig function can be used to find the measure of angle A tan 1 Cos 1 12 none sin 1

X 12 Solve for X Y 13 Y Round to the nearest tenth X 30 degrees Y 60 degrees X 67 4 degrees Y 22 6 degrees X 60 degrees Y 30 degrees X 22 6 degrees Y 67 4 degrees

A function is defined by f x 3x where x 0 Find f x Select one O a 3 x 1 O b O d 3x x 1

Solve the following exponential equations 4 4x 16 Select one O a x 4 O b OC O d x 2 X 2 x 4

Find the sum of the infinite Geometric Series 25 5 1 1 12 15 Round to the nearest hundredth if necessary M

Find the sum S 6 K 1 Select one O a 728 O b 364 OC 364 O d 346 3 k 1

Solve the following exponential equation 9 2x 1 27 x 0 Select one O a 1 O b 1 O C 2 d 2

Solve the following equation x log 1 2 16 Select one O a 4 O b 2 O C 2 O d 4

Choose the graph of In x 1 Select one O a O b O C 10 10 10 20 10 0 10 20 10 0 10 20 10 0 10 10 10 20 20 20

onvert the following to the exponential form 2 log 5 25 Select one O a 30 1 O b 52 25 O c 53 125 O d 35 243

olve the following equation e 3x 9 elect one O a 0 459 O b 0 327 OC 0 237 O d 0 732

The function f x 3 demonstrates Simplify the following log 2 x 8 log2x4 Select one O a log2x linear degression linear growth exponential decay quadratic increase exponential growth logarithmic growth

mplify the following log 2 x log 2 x 4 elect one a log x b c d 4 log2x 8 log 2x 2log 2x

the following graph of a function modeling damped harmonic motion Find the equation for the function pictured in terms of y and 1 Assume that a factor of e provides the desired damping effect and that the graph has no vertical or horizontal shifts 4 2 2 Enable Zoom Pan t

y 2 x find the value of y elect one a 1 4x b 4x C 22x d 24x

onvert the following to logarithm form 4 16 lect one a log 42 16 b log 2 16 4 O c log 4 16 2 O d log 16 4 2

Find a 8 of a geometric sequence if the first few terms of the sequence are given by 1 3 9 27 Select one O a 2 187 O b 7 880 OC 1 934 O d 3 405