Coordinate system Questions and Answers

Given A CBA DAB CAB DBA are Right Angles Prove BC AD B D 2 Complete the Two Column Proof Statement 1 CBA DAB 2 CAB DBA are Right Angles 3 CAB DBA 5 AABC ABAD 6 BC AD Reason 1 2 3 All Right Angl are 4 Reflexive Pro 5 6

Use y X Find the critical values Enter your answers as a comma separated list Find the critical points x y x y x y x x 5 36 and its derivative dx dy 5x x 3 x 5 36 relative maxima relative minima smallest x value Find the intervals on which the function is increasing Enter your answer using interval notation largest x value Find the intervals on which the function is decreasing Enter your answer using interval notation horizontal points of inflection Find the relative maxima relative minima and horizontal points of inflection If an answer does not exist ente x y DNE x y x y to find each of the following DNE DNE X X

Find the 3 cube roots of 64cis B 4

Write the standard form of the equation of the hyperbola subject to the given conditions 3 Vertices 2 1 6 1 Slope of the asymptotes The equation of the hyperbola in standard form is 00 0 0

Consider the following two loans for P 7 500 Loan A 5 year loan annual interest rate of 7 monthly repayments of 148 51 Loan B 3 year loan annual interest rate of 10 monthly repayments of 242 00 On which loan will you pay the least interest Select the correct answer below Loan A O Loan B

2 The measures of two supplementary angles are in the ratio 3 12 Find the measure of each angle 2 points X

In the figure for Exercises 21 to 24 RS is tangent to the circle at S See Theorem 6 3 7 21 Given Find RS 8 and RV 12 RT HINT Use the Quadratic Formula R T S Exercises 21 24 3

In Exercises 15 to 19 create drawings as needed

Problem 4 Jenny owns a bicycle with a chainring peddle gear with a radius of 7 inches The sprocket small gear at the center of the rear wheel has radius inches Finally the rear wheel has a radius of 20 inches If Jenny peddles at a rate of 1 revolution per second how fast will the bike be moving in feet per second

wen B CB FAB and CAB 90 rove AFBA ACBA Statement 1 FB CB 2 FAB and CAB 90 3 4 AFBA ACBA

In the figure below points T R X Y and Z lie in plane P Points and S do not lie in plane P For each part below fill in the blanks to write a true statement R a Another name for plane P is plane b and X are distinct points that are collinear c Y O O and are distinct points that are coplanar d Suppose line QT is drawn on the figure Then QT and 0 are distinct lines that intersect

stem of equations to solve the following problem any ounces of a 17 alcohol solution and a 33 alcohol solution must be combined to obtain 52 ounces of a 29 solution enter your answer opens in new window Jounces of 17 alcohol solution Jounces of 33 alcohol solution

Let L be the line given by 3 1 2 1 1 1 1 for t R 12 1 Show that the above line L lies on the plane 2x 3y 4z 1 0 12 2 Find an equation for the plane through the point P 3 2 4 that is perpendicular to the line 8 2 0 t 3 2 7

P 1 3 1 0 y In the xy plane above O is the center c circle and the measure of ZPOQ is a Q What is the cosine of a

Find the coordinates of a point on a circle with radius 20 corresponding to an angle of 170 x y Round your answers to three decimal places

5 pts It is know that a triangle has A 15 a 10 b 40 Solve the triangle giving all possible solutions

In the figure below points X Z Q R and S lie in plane P Points I and Y do not lie in plane P For each part below fill in the blanks to write a true statement T X Y Z Q R S P a Point Z and lineare coplanar b Suppose line ZY is drawn on the figure Then Z and are distinct lines that intersec c Another name for plane P is plane d and R are distinct points that are collinear

lain how to solve the following equations by reasoning about nur rations and expressions Do not use standard algebraic equation niques Specifically avoid things like subtract from both sides you would explain this to a student not me 18 36 x 20 36 348 926 x 350 17 x 48 50 984 17 31 x 47 62

Calculate the average rate of change of f x x x 3 on the interva 2 5 3 marks

Question 9 Points 2 Which of the following is NOT an example of circumscribed angle

Question 5 Points 1 A line which is perpendicular to a segment that passes through the segment s midpoint is called Oright angle O perpendicular bisector bisector

Find the value of x in the following figure C 25 O 50 O 90 O85 to O 20 B

11 Find the perimeter of the parallelogram if one set of parallel edges is 10 2 feet and the other set of parallel edges is 4 8 feet

3 Find the perimeter of a square whose side is 10mm Perimeter mm

factor of the dilation for transforming the circle C to C 10 C 8765432 7 2 C 10 9 8 7 6 4 3 2 1 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 27 O Translation 7 units to the left and 6 units down Scale factor enlargement ratio Translation 7 units to the right and 6 units up Scale factor enlargement ratio Translation 7 units to the right and 6 units down Scale factor enlargement ratio 2 com Ques 1 4 7 F 10

Circle A center 7 0 and radius 5 Circle B center 10 0 and radius 2 Which of the following transformation is performed from circle B to circle A to prove that the two circles are similar Translation 3 units left and scale factor Translation 3 units right and scale factor O Translation 3 units left and scale factor Reset bu enabled a this assessm Reset Questions 1 3

3 a Are any two regular pentagons similar b Are any two equiangular pentagons similar

Find a non trivial solution to the following homogeneous system of equations 4 3i x 4y 0 118i r 8 12i y 0 Enter your answers in the form a bi

nd integers that are upper and lower bounds for the real zeros of the polynomial Be sure the lower bound is the largest possil P x x2x x 9x 2 smaller value larger value

Solve the following equation for x in radians in the interval 0 2 sin x 1 2 Give the exact value radian angle measures when possible If needed give the approximate value to the nearest 2 decimal places You may select more than one answer

If 0 x 2 find all values of x that satisfy the following equation Select the correct answer below O x 4 and 5 x 5T and 75 O O O X X 5 7 19 18 18 18 4 5 10x 999 117 16 17 9 2 9 29 cos 3x 3 2

Plot the point whose polar coordinates are given Then find the Cartesian coordinates of the point a 6 47 x y 3 t x y c 5 x y

Consider a four year project with the following information initial fixed asset investment 500 000 straight line depreciation to zero over the four year life zero salvage value price 35 variable costs 26 fixed costs 200 000 quantity sold 80 000 units tax rate 25 percent How sensitive is OCF to changes in quantity sold Do not round intermediate calculations and round your answer to 2 decimal places e g 32 16

Suppose that 3x 2y t and x t cos 0 Find at ax t and at ax y

The quadrilaterals ABCD and JKLM are similar Find the length x of JK C X B D X 14 8 S M

y 2 tan 3x 2 1 Drag the movable black point to shift the function the red points to set the vertical asymptotes and the blue point at the correct set of coordinates You may click on a point to verify its coordinates Note that only one period of the function is shown Shift the given graph using the general form in order to ensure you are graphing the correct period Provide your answer below TE 211 3 5 11 3 4 3 2 2 1 4 1 2 0 0 71 3 T 2 1 21 3 IT

In Exercises 17 to 22 use proportions to solve each problem 17 A recipe calls for 4 eggs and 3 cups of milk To prepare for a larger number of guests a cook uses 14 eggs How many cups of milk are needed

32 A point of symmetry of the function f where f x a 3 4 b 3 5 c 3 4 d 3 4 x 3 4 is

Find the measure of 0 in the triangle Do not use a calculator 0 3 2 3 3

K Exercises 7 8 8 If LH and LJ are supplementary in HJKL are a ZK and LL necessarily supplementary also b LH and ZK necessarily supplementary

2 For the given model of the form x a Determine the value of p b Identify the focus of the parabola c Write an equation for the directrix Express numbers in exact simplest form x 4y 2 Part 0 3 4py Part 1 of 3

Z W X Exercises 3 4 4 In the drawing suppose that ZX is the perpendicul bisector of WY What type of quadrilateral is WXY

4 State how you know that ABDF is an isosceles triangle 2 points

A satellite dish has the shape of a parabola when viewed from the side The dish is 60 inches wide and 45 inches deep How far is the receiver from the bottom of the dish if the receiver is placed at the focus 3 4 45 in 45 m Receiver in 30 45 60 in 0 0 2 in 30 45

2 Given that the terminal side of the angle 0 in standard position passes through the point 3 5 Find the values of each of the 6 trigonometric functions for angle 0 and it s not necessary to rationalize any denominator a sin 0 b cos 0 c tan 0 d csc 0 e sec 0 f cot 0

Use the picture for the following two questions 08 4 How many common internal tangents can be drawn Internal 5 How many common external tangents can be drawn External

D 8 cm cm 8 cm 11 What is the measure of the radius of Circle O B cm 12 What is the measure of the diameter of Circle O

10 Name the following relationship between theses circles Disjoint circles O Tangent circles O Intersecting circles

11 If the following triangles are similar find x All drawings are not to scale 20 30 X The units are in inches X

A 6 0 8 D 2 2 32 6 1 b 6 2 C 2 2 B 6 0 00 6 8 10 X