Geometry Questions

Find the standard form of the equation of the hyperbola with the given characteristics Vertices 14 0 foci 7 0

Han invests 13 000 into a fund that combines stocks and bonds The return varies from year to year The balance at 5 year intervals is given in the table below The goal of this exercise is to find constants a and b such that the model y ae best fits the data In order to do that we apply the natural logarithm to both sides of the model This yields In y n a and using properties of logarithms weet T lex be and the problem now reduone to finding the Pcjwey In y In a In ee In y In a bt If we let Y In y c In a and c b the problem now reduces to finding the linear fit Y q c the set of dats points Part b t 0 5 10 15 20 25 y Balance 1 000 13 14 5 16 18 2 19 9 22 3 5 10 FLO 18 31 115 11451 lec16 In 1821 In 199 Find the cheskydecompcation of S and store in U Soke thener system w me sing the backataah command Solve the langur system cw using the backslash command Compute the best fit use 25 2231 art a The sectors and y have already been created for you Compute the sector by evaluating the natu ofy note that the natural logam entered a lng in MATLAB Create the mote X for the rear Create the tor 2 Create the magic I Plot the date pents and upper case Use o to plot points by the original data polts Use Lindth 2 und is that you por Use Inestyle and color the line back gure by tyckig hold off Computand where and are the values you found in part 4 Se the wi coobies a widespectively Ente figure to open a new gu plot the original data points and lower cass no toplot points

8 GARDENING A gardener uses a grow light to grow vegetable indoors If m 1 8x and m 2 7x 4 what is m 1 M21 8X 7 1846 11

13y 17 1 2 3 Given m27 38 and mz10 102 find the measure of each missing angle 4 3 5 6 29 x 3 15x 7 9 10 12 11 8 7 m 13 14 16 15

This is just a practice with some of the applications Please make sure you study all of the vocabulary for the unit too A large portion of the quiz is based off of the vocab Find the value of each variable 1 Note pl m P m 120 Co e d a b C d e

9 m2 DJP 10b 54 find the following D 3b 3 K 5b 27 P b mzDJK m DJP

A property is bing transported through a fluidat steady state trough a content cros sectional area at point the concentration is 278 x 10 amount of roperty m and 1 50 x 10 at point 2 t a distanceof 20 m away Thedificity depends on concentraion l as 8 0 150 1651 a calculate the teadystate fut if he two points were separated by 35 m but with he same concentrations How does the flux vary with the distance between the points Calculate the steady state fut if the concentration at point 2 was 150 x 10 amount of property using the right stance 20 to do the way with he diference in concentration b

Complete the proof of the identity by choosing the Rule that justifies each step sec x tan x 1 To see a detailed description of a Rule select the More Information Button to the right of the R Statement sec x tan x 1 tan x tan x Rule Rule

A1 November 21 03 m2SUT 34 Find mz1 Find x if m2 4x 5 and A2 m151 A3 Find BD T A4 Solve for x 12 1 1 21 16 15 35

20 21 8 40 Q 43 75 For 19 21 find the values of x and y 19 Jo 77 96 R 1 y 35 2 xo st 4 S 3 64 7 5 6 mz1 mz2 mz3 m24 x x x m25 mz6 m27 m28 y y y

Section 5 1 Worksheet 1 The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles For 2 5 classify the triangle by its sides and by its angle measures 2 X 3 M For 8 For 6 and 7 classify AABC by its sides Then determine whether it is a right triangle 6 A 2 3 B 6 3 C 2 7 7 A 3 3 B 6 9 C 6 3 Classify by sides Is it a right triangle N find m21 Then classify the triangle by its angles 78 319 4 J Classify by sides Is it a right triangle mz1 Classify by its angles 5 B A

Geometry 9 3x RE mz1 40 Classify by its angles 64 75 Exterior 30 10 2x mz1 38 For 12 14 find the measure of the exterior angle Hint you may need to find x first 12 13 14 Classify by its angles Exterior For 15 17 find the measure of each acute angle by finding x first 15 16 2x 2 45 3x 2 11 m21 17 60 Classify by its angles 60 3x 6 Exterior x 7 11x2 24 2x 18

The dimensions of a rectangular duct with grooved seam are height h 18 inches width w 28 inches length 3 5 ft M 3 8 inch A Find in inches the value of the Length of the Stretchout L S 13 75 B Find in inches the value of the Width of the Strechout W S 70 75 MY F Xinches State your answer as a decimal value Do not ro Xinches

Determine the remaining sides and angles of the triangle ABC A 19 39 B 20 57 c 16 98 m C Question 8 7 1 23 Part 1 of 3

Solve the triangle a 8 103 in c 6 630 in B 78 63 What is the length of side b in Round to the nearest thousandth as needed What is the measure of angle A Round to the nearest hundredth as needed What is the measure of angle C O Round to the nearest hundredth as needed

Solve the triangle with the given parts a 25 3 m b 14 4 m c 14 3 m What is the degree measure of angle A 7 Round to the nearest tenth as needed

Solve the triangle What is the length of side a A 0 C 13 26 C 20 a Round to the nearest whole number as needed What is the measure of angle B B Round to the nearest degree as needed What is the measure of angle C 0 Round to the nearest degree as needed a B

K Solve the triangle shown to the right A B and C Round to the nearest tenth as needed 15 A 15 17 B

1 Find the area of the triangle using the formula A bh and then verify that Heron s formula gives the same result Use the formula A he area is 1 zbh

Determine the remaining sides and angles of the triangle ABC A 22 62 B 36 58 c 19 65 m C O Part 1 of 3

Solve each triangle ABC that exists A 38 a 3 4 c 14 3 Select the correct choice below and if necessary fill in the answer boxes within the choice OA There are two possible solutions for the triangle The measurements for the solution with the longer side b are as follows B C b The measurements for the solution with the shorter side b are as follows B C b Round to the nearest tenth as needed B There is only one possible solution for the triangle The measurements for the remaining angles B and C and side b are as follows B b C Round to the nearest tenth as needed C There are no possible solutions for the triangle

Consider circle E CD is the perpendicular bisector of segment AB B C What is the measure of the arc intercepted by ZACD A D 50 180 270 E 90 D B

f x 2 cos x 2 cos x xx 3x 7x The solution set for f x 0 in the interval 0 2x is 4 2 24 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed Find the solution set for f x 0 in the specified interval Choose the correct answer below OA The solution set of f x 0 is 0 OB The solution set of f x 0 is x 3x 22 3x 7x 4 2 2 OC The solution set of f x 0 is 0

Find the value of csc arccos Express numbers in exact form Use symbolic notation and fractions where needed Simplify your answer com

Find the standard form of the equation of the parabola with the given characteristics Vertex 7 6 directrix x 14

Find the x and y intercepts of the graph of the circle If an answer does not exist enter DNE x 10x y 2y 19 0 STEP 1 Consider the equation for the circle x 10x y 2y 19 0 Let y 0 Give the resulting equation below 10x 19 0 STEP 2 Solve your equation from Step 1 for x If one or more solutions exist these values are the x coordinates of the x intercepts of the graph of the circle Enter your answers as a comma separated list x x STEP 3 Consider once again the equation for the circle x 10x 2y 19 0 STEP 4 Solve your equation from Step 3 for y If one or more solutions exist these values are the y coordinates of the y intercepts of the graph of the circle Enter your answers as a comma separated list y 2y 19 0 Now let x 0 Give the resulting equation below STEP 5 Complete the problem by listing the x and y intercepts x intercepts x y smaller x value larger x value y intercept x y 1

Evaluate the given trigonometric function directly without first changing the radian measure to degree measur sec 4 3186 sec 4 3186 Round to four decimal places as needed

K Complete the statement y cos x means that x for 0 syst y cos x means that x for 0sys

Solve the equation for all exact solutions where appropriate Round approximate answers in degrees to the nearest tenth Write answers using the least possible nonnegative angle measures sin 0 cos 0 sin 0 0 Choose the correct answer below OA 270 n where n is any integer O B 0 OC 180 n where n is any integer O D 90 n where n is any integer

Determine the aplitude midline period and an equation involving the sine function for the graph shown below S 5 4 3 2 1 10 8 6 4 2 2 4 6 8 y c 1 2 3 X 5

Consider the following 25x 4 300x 40y 900 0 a Find the standard form of the equation of the ellipse b Find the center vertices foci and eccentricity of the ellipse Order your answers from smallest to largest x then from smallest to largest y If the ellipse is degenerate find its center then enter NONE in Centers Vertices Foci Eccentricity c Select the correct graph of the ellipse Use a graphing utility to verify your answer 10

A restaurant dining space and hallway is shown in the diagram below This area of the restaurant will have 12 foot ceilings b 1 m Step 1 Calculate the total volume of the dining area and hallway in cubic feet Assume a 6 4 m b 8 4 m and c 12 1 m Use 1 ft 0 3048 m for your conversion Remember to do the conversion for each dimension as we showed in class Round your answer to the nearest hundred not hundredth Volume of the space ft Step 3 The design of the duct work specifies an air speed of 275 ft min Use the formula airflow duct area x air speed MY NOTES Step 2 The design calls for 11 air changes per hour Calculate the total air flow in CFM cubic feet per minute needed to meet the air change requirements for the space Round to the nearest hundred CFM Airflow required CFM to find the duct area needed Round your answer to the nearest tenth duct area sq ft round ASK

Directions Show and explain mathematical work for ALL problems Part I Multiple Choice Each question is worth 2 points 1 As shown in the diagram below when hexagon ABCDEF is reflected over line 7 A B C D E F A E B D C C m Im B A E F F Under this transformation which property is not preserved a area b distance c orientation d angle measure

Match the equation with its graph 16 O O 10 10 5 y 10 5 5 10 y 10 10 5 10 5 10 5 5 5 5 y 5

Listen Classify each angle pair as corresponding alternate interior alternate exterior or consecutive interior angles 1 2 3 4 910 1112 56 78 13 14 15 16 Corresponding angles Alternate interior angles Alternate exterio

Amari Perform the following conversions Marks as indicated 1 A cone shaped fuel tank has the following dimensions D 37 6 in H 42 3 in SHOW YOUR WORK FOR THE FOLLOWING QUESTIONS 7 marks Use the formula for the volume of a cone to determine the A total capacity of the tank r D 2 O Student ID 101313077 Score

Use the diagram below showing the concrete floor of a building At a cost of 30 per cubic foot find the cost of having the floor poured Round your answer to two decimal places 50 ft 25 ft 6 in

Use the diagram below showing the concrete floor of a building At a cost of 30 per cubic foot find the cost of having the floor poured Round your answer to two decimal places 50 ft 25 ft 6 in

Solve Use 3 14 for Find the volume of the bushing shown below Round your answer to two decimal places 857 6 X in 6 in 8 in 16 in 24 in

L4L CA Math Geometry A Credit 3 Quiz Question 10 B In the figure below ZCAB LCAD What additional information would be enough to prove A ABC A ADC by the Side Angle S A B C II Pause Q Zoom D AB AD BC DC LABC LADC LBCA ZDCA

2023 What is true about line segments AD and BD A B C E D B Line segments cannot be proven congruent Line segments are congruent due to the side side side congruence postulate Line segments are congruent due to the side side angle congruence postulate Line segments are congruent due to the side angle side congruence postulate Illuminate Education Inc

Question 11 Which postulate or theorem can be used to prove that AABC ADCB A B A B C SSS SAS ASA D

6x 7 J M If JL 16 and KM is a perpendicular bisector of JL determine which of the following claims are True A JM 8 B JK LK 5x 3 L D LK 17 True True C JK 11 True True False False False False

Question 8 th B C 2x 41 S 61 Which of the following is the value of PQ A 46 67 D 91 3x 16 7x24 Pause Q Zoom 4

Question 9 Use the figure below to answer the following question B Given that AD and BC bisect each other at E which of the following justifies A ABE A DCE A SSS Postulate B C C D SAS Postulate Definition of Segment Bisector Definition of Congruent Triangles

D W X A Which additional information would be enough to prove that AXWY ADEC B C C D Y ZY ZD ZY ZE ZW LC ZW ZE

B O D mi 1 2 E 4 3 If m 22 78 which of the following angles also measure 78 Select THREE that apply A 23 5 6 8 7 24 25 26 a 27 b

Read the question and enter your response in the box provided Use the tools and your keyboard to construct your response In the diagram line I and line m are parallel m 4 7x 5 and m25 5x 27 Solve for 778 1 7 8 6 4 5 1 3 2

Given PIIQ and T is a transversal which of the following justifies 23 26 2023 A B C D 5 6 8 2 4 Q Corresponding Angles Postulate Alternate Interior Angles Theorem Consecutive Interior Angles Theorem Alternate Exterior Angles Theorem Illuminate Education TM Inc

Question 7 8 6 4 2 1 2 8 Question 7 Triangle ABC is reflected over the line y 1 to produce triangle A B C 6 4 N C 4 6 8 2 2 Pause A 2 4 1 8 A What will be the coordinates of B 2023 Illuminate Education Inc Q Zoom X