Geometry Questions

12 In a regular square pyramid the sides of the base measure s 10 cm each and the slant height measures 113 cm 2 points Find the volume of the pyramid V Bh where B is the base area s 10 h 1 13 2 11 5

3 Given kite ABCD with diagonal AC 10 cm m ABD 30 m ADB 45 Find the area of the kite 3 points B 30 E A C 45 D

5 Find the area of the 30 60 90 right AABC with AB 8 cm B 60 2 points 30

6 Find the area of the shaded region 2 points IC 12 18

8 Find the area of the regular hexagon whose sides have length s 8cm and apothem a 4 3 cm 2 points s 8cm

11 The lengths of sides of the triangular base are a 4 cm b 5 cm and c 7 cm s s aXs bs c to find the area of the triangle Use the Heron s Formula A a b c 2 b 2 points a

10 The volume of the right rectangular prism is V 270 cm Write a quadratic equation in terms of x Don t solve the equation 2 points x 3

9 Find the exact area of the sector Radius of the circle r 12 cm and m AOB 135 A 12 0135 2 points B

Please show your work No credit will be given for answers 1 Find the area of the rectangle ABCD if AB 30 cm AC 34 cm D 2 point C

2 Find the area of the ABCD if AD 10ft AE 6ft BE 7 ft 10 D 2 points h

1 Suppose we want to solve the cubic x Ax Bx C 0 To use our algorithm we make the substitution x u A 3 to get a cubic polynomial in u that has no square term This is called completing the cube We then use our algorithm to solve this cubic by using a circle centered at a b Solve for a and b in terms of A B and C 2 The length 2 cos 2 13 is a root of p x x ax x a 1 where a is the larger root of q x x x 3 What center a b should we use to solve the cubic Note that the center is constructible using

Shelby invests 300 in a bank account that earns a fixed 4 interest compounded annually The amount in the account after t years is given by f t 300 1 04 Graph this function on your calculator in an appropriate window Label each axis use an appropriate scale and label three points on the graph 3pt Please select file s Select file s Does f t have an inverse function Explain why using the graph 1pt Pick and write down one ordered pair of the inverse function and give its practical

A railroad bridge is built over a V shaped canyon If the supports are 2 feet long at each end the center support is 518 feet long and the supports increase in length by 4 feet with each support from 2 feet to 518 feet what is the total length of all the supports 67 078 ft O 67 082 ft 67 080 ft O 67 086 ft

For an object in an elliptical orbit around the moon the points in the orbit that are closest to and farthest from the center of the moon are called perilune and apolune respectively These are the vertices of the orbit The center of the moon is at one focus of the orbit A spacecraft was placed in a lunar orbit with perilune at a 89 mi and apolune at b 258 mi above the surface of the moon Assuming that the moon is a sphere of radius 1075 mi find an equation for the orbit of this spacecraft Place the coordinate axes so that the origin is at the center of the orbit and the foci are located on the x axis Round each answer to the nearest whole number x X apolune y2 b X 1 moon perilune

4T A sector with a radius of 6 cm has a central angle measure of i 9 radians r 6 cm 0 4T 9 What is the area of the sector

1 The ratio of the sides of a triangle is 2 6 7 If the perimeter of the triangle is 195 meters what is the length of the longest side

Solve the problem A forest ranger at Lookout A sights a fire at a bearing N35 W of her position Another ranger at Lookout B exactly 2 kilometers directly west of A sights t same fire at a bearing of N41 E How far is the fire from Lookout A Round your answer to the nearest 0 01 km O 1 35 km O 1 18 km O 1 56 km O 1 69 km

9 A lot for sale in a subdivision has the shape of the quadrilateral shown in the figure Find the area the lot rounded to two decimals 10 points 75 ft 800 40 ft 135f 128 ft

4 Identify Each Triangle by Side and by Angle Relations 42 3 AAE 4 VA A12 47 A11 A9 44 A10 A5 A1 A6 2 48 A3 10 12 a Equilateral b Isosceles Right c Acute isosceles d Obtuse Scalene e Obtuse Isosceles

1 What are the similarities and differences between finding the areas of Parallelograms Rectangles and Square BU Font Family AA A E

12 This shape is BEST described as being a n 13 Based on this type of triangle we know that y 14 Since the perpendicular bisector splits this into to two A s we can set up the folla x 80 X X 180 15 Find the measures of x and y y 180 degrees degrees

6 This shape is BEST described as being a n 7 Based on this type of triangle we know that y 8 Find the measures of x and y X y degrees degrees

3 Find the area of the following figure The units are in meters 10 A 12 m

2 This shape is BEST described as being a n 3 Based on this type of triangle we know that x 4 Set up an equation to solve for the missing angles x y 40 x y 5 Find the measures of x and y X y degrees degrees

Solve for x and find the perimeter of AABC x 3 D 4x 9 8 C B

9 This shape is BEST described as being a n X 30 10 Find the measures of x y and z y N Z degrees degrees degrees

9 The area of a rectangle is 15 square inches If the length of the rectangle is 2 more than the width find the length and width length width inches inches

11 Find the measures of x and y X y X 70 degrees degrees

8 Find the area of the following figure The units are in feet 12 14 49

7 Find the area of the following figure The units are in hectometers 2 10

4 Find the area of the following figure The units are in centimeters A 11 6 cm

2 Find the area of the following figure 13 yds A 12 yds yd 27 yds 27 yds 13 yds

Divide Check your answer If there is a remainder write the remainder over the divisor 2x 3 2x 2 6 x 2

When 6x 2 36x 32 is divided by a polynomial the quotient is 6x 6 and the remainder is 2 find the polynomial

Write parametric equations on a restricted interval for t to define the given graph Use only the given points when finding equations The parametric equations are x and y A for Osts 1 X G

9 How many paths are from A to B You can only travel South and East A

Write an equation that describes the following relationship y varies inversely as the cube root of x and when x 64 y 7 Y

S1 www analyzemath com 2 If the lenght of S2 is 80 feet find the radius of the circle Radius 2 feet 3 Find the Circumference of the circle

Write the vector in the form a b op 6 o 2 2 60 00 X

In 2021 an everything bagel from the Einstein Bros in Centennial Hall cost 0 89 In 2023 that same bagel cost 1 09 The linear function f t that models the price in dollars of an everything bagel t years after 2021 is Of t 0 89 0 1z Of t 0 89 0 1z Of t 1 09 0 1r Of t 1 09 0 12

A B A parallelepiped is determined by the vectors OA 2 2 5 OB 0 4 1 and oc 0 5 1 Based on the diagram calculate its volume

Write any fractions like this 5 2pi Here is the grapmorld sin wave High T Low B 2 High value 3 Low value 4 New Period Length 5 1 4 of Period 6 Value of interval A D the function y 2sin1 2 x 2pi 1 1 Origin horizontal vertical e g pi 2 E Given

1 Given sin A and cos B a Find the exact value of 1 cos A 7 and both A and B are in the Q1 2 sin B 1 5 points each b Using the values from above use a sum or difference identity to find the exact value of 3 points each 1 sin A B 2 cos A B

Using data and projections from 1950 to 2050 the number of women age 16 years and older in millions in a particular country s civilian labor can be modeled by the following where x is the number of years after 1950 y 0 00009x 0 00636x 1 043x 17 389 Use the model and a graphing utility to estimate when the number of women in the labor force reached 84 million The model projects the civilian labor force to be 84 million in Round up to the nearest year

The lot in the figure shown except for the house shed and driveway is lawn One bag of lawn fertilizer costs 15 00 and covers 5 000 square feet Use this figure to complete parts a and b below Note that the figure may not be to scale a Determine the minimum number of bags of fertilizer needed for the lawn 50 40 ft Drive House 2001 400 11 St

Let SinA 15 17 with A in Q11 and sinB 4 with Bin 5 Q111 find sinCA B cos A B and tean A B

hel 7 Since B is split by a line we must add the two parts of the angle together x 26 x 2 x3x Angle B x 3x 4x Angle A 2x 4 10 Find A B C by plugging in your answer from the last question in for x Angle B x 3x degrees degrees

Question 8 Points 2 Find the slant height of a regular pentagonal pyramid whose length of an edge is 6 cm and lateral surface area is 160 cm O 10 67 cm O 12 85 cm 9 45 cm 18 65 cm

Find the volume of the rectangular pyramid whose base is 3 m 6 m and whose height is 5 m 30 m 60 m O 90 m O 10 m

Question 3 A building in the shape of a square pyramid is washed for decoration The outside of the building is washed using one gallon of cleaning solution for each 100 square feet of surface The slant height of the pyramid is 125 ft Calculate the approximate number of gallons needed to wash the building if 50 ft is the side length of the base 84 O 125 O 150 Points 3 158