Coordinate system Questions and Answers

How many radians is 45 degrees Oradians Oradians Oradians O radians

What is the area of a circle with a radius of 6 ft in terms of TT O 12 ft O 24 ft 6 ft 36 ft

What is the area of a circle with a radius of 13in rounded to the nearest tenth O 530 9 ft O 81 7 ft O 20 4 ft O 530 ft

Find the missing angle and arc measures for this figure E D BC ZARB EA A EB 30 100 R 50 B

Triangle Midsegment Theorem Theorem Theorem 6 2 Triangle Midsegment Theorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side DE is a midsegment of LABC DE AC and DE AC A Proof Example 2 p 331 Monitoring Progress Question 3 p 331 Ex 22 p 334 DE is the midsegment of AABC Find the value of x A ERROR ANALYSIS Describe and correct the error X B 5 10 E C DE BC so by the Triangle Midsegment Theorem Thm 6 8 AD DB and AE EC

Jse spherical coordinates to find the volume of the shown solid bounded below by the sphere p 2 cos and above by the cone z x y Z z x p 2 cos b Y

Parallelogram CDEF is shown What is m CDE F 10x 23 5r 7 E D

following rectangle is plotted on the coordinate plane below Plot the midpoint of the two diagonals of the rectangle y 3 2 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13

1 point What coordinate point is needed to to create a rhombus 10 5 0 A B 5 D 10

The town plaza in a certain town is a parallelogram The town s planning committee has decided to build a fountain at the center of the plaza This sketch shows the corner points when placed on a coordinate grid 2 3 1 5 2 1 3 2 1 3 2 215 5 0 5 5 1

A rectangular board is shown I cut the end of at 32 degree and 28 degree angles and formed ADEF What is the measurement of D D 32 28 E FL

Question 12 el has a maximum height of 2

Find the Equation with a Point and Slope 5 6 6 6

Let triangle ABC be a right triangle with angle ACB 90 Prove that the median CD from vertex C to side AB lies on the Euler line of triangle ABC

In circle R with m QRS 36 and QR 11 units find the length of arc QS Round to the nearest hundredth S R Q

In the diagram the measure of angle ACB is 25 degrees What is the measure of angle AOB 25 0 B

Sketch the graph of the function by plotting points f x 3 log x 1 103 1 102 10 10 4 y 6r X 2 1 10 1 2 4 9 4 y 6r 20 f x 3 log x 000000 40 60 80 X 100 O y 6 4 2 2 4 y 6r 20 40 60

4 Identify the following in the circle C shown below H D A G C K F E J B

SPIRAL 4 Use the circle on the coordinate plane to answer the following a The coordinates of the center b The coordinates of the endpoints of a diameter List 2 points and c What is the radius of the circle d What is the length of the chord shown in the diagram y

6 5 4 3 2 5 4 3 2 4 2 3 4 5 6 3 4 5 1 2 3 q The graph above is a transformation of the function f x Write an equation for the function graphed above 6

Prove AC Step 1 211 ADBC Statement ABCD is a square Type of Statement 4 A Reason Given E

Consider the composite area shown below all dimensions in mm Determine the coordinates of the centroid relative to the x y axes shown 9 0 10 0 21 y 12 0 12 0 x number rtol 0 01 atol 1e 05 number rtol 0 01 atol 16 05 8 0 11 0 mm mm

Write an equation for the function graph 9 7

Price per Unit P A O the area OBQ2 the area P1AB the area OAB zero B O the area OP1B Q Q MR In the figure above producer surplus for the perfectly competitive market is Quantity S D

The point P 5 4 lies on the curve y 4 4 x a If Q is the point x 4 4 x use your calculator to find the slope mpo of the secant line PQ correct to six decimal places for the following values of x 1 4 9 mpQ ii 4 99 MpQ 4 999 mpo iv 4 9999 mpQ v 5 1 MpQ vi 5 01 mpQ vii 5 001 mpQ viii 5 0001 mpo b Using the results of part a guess the value of the slope m of the tangent line to the curve at P 5 4 m c Using the slope from part b find an equation of the tangent line to the curve at P 5 4

The area of a circle may be found by using the formula Area xr where r radius Note The diameter is a straight line passing from side to side through the center of a circle The radius is half of the diameter The radius in this example is half of 14 or 14 2 Find the area of the geometric figure d 14 in The exact area of the geometric figure is Type a decimal in terms of The symbol your value of r by 3 14 just include the symbol for pi after it This anwer would be 49 sq in can be found at the bottom of the screen Do not multipy To find an approximate area use 3 14 for it The approximate area of the geometric figure is sq in Type a decimal and round to three decimal places The approximate area is when you will multiply your value of r by 3 14 Both answers are considered correct They are just expressed in different forms

5 The width of a rectangular dance floor is w feet The length of the floor is 6 feet longer than its width Which of the following expresses the perimeter in feet of the dance floor in terms of w A 2w 6 B 4w 12 C w 6 D w 6w SIK

At what meter mark will Ario be when Miguel starts the race Round to the nearest tenth x mm x x X m n Start End 0123 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Miguel and his brother Ario are both standing 3 meters from one side of a 25 meter pool when they decide to Miguel offers Ario a head start Miguel says he will start when the ratio of Ario s completed meters to Ario s remaining meters is 1 4 4 4 meters 7 4 meters 17 6 meters 20 6 meters

Find the area of the right triangle in square centimeters First convert all measurements to centimeters 2 54 centimeters Use the conversion factors and 12 inches 1 foot Note that the figure is not drawn to scale 1 inch The area of the right triangle in 32 inches 2 feet

8 The president of Kramerica Industries that manufactures rubber bladders for oils tankers thinks that the function P b 26 14b 20 represents the company s profit where b is the number of bladders produced in thousands and P b represents the company s profit in hundreds of thousands of dollars a Determine the number of bladders the company must produce to breakeven 4 b Determine the maximum profit the company can earn 3

From Lesson 8 05 Figures in a Coordinate Plane W 3 3 5 4 2 1 Z 3 2 5 4 15 2 1 1 2 5 E X 2 3 2 4 5 Y 4 4 What is the perimeter of kite WXYZ x 2 53 2units 2 53 5units 2 53 10units 2 53 14units

What is the equation of the line that is parallel to the line y 1 4 x 3 and passes through the point 4 32 y x 33 y x 36 y 4x 16

Which equations represent the line that is perpendicular to the line 5x 2y 6 and passes through the point 5 4 Select THREE options y x 2 2x 5y 10 2x 5y 10 y 4 x 5

4 Lisa is just five face to face Spell Offs away from making it to the state spelling bee She has a 90 chance of beating Ralph a 95 chance in her second match 80 84 and 86 chance on the rest Bart claims she has a better chance of flipping a coin Which has the higher chance of happening Lisa winning all of his matches or flipping a coin

5 Homer is getting scared of something horrific happening to him and dying so he goes to get life insurance He decides that he ll most likely die from a lightning strike 1 in 130 000 plane crash 1 in 7000 car accident 1 in 98 or firework accident 1 in 650 000 What s his overall probability of dying from one of these Hint Is there any overlap to subtract

Question 8 12 5 points Given the parent function f x x how would the function g x 3x 2 compare to f x O g x is the same as f x vertically compressed by a factor of to the x axis and translated down 2 units O g x is the same as f x vertically stretched O by a factor of 3 from the x axis and translated right 2 units O g x is the same as f x horizontally stretched by a factor of 3 to the x axis and translated right 2 units g x is the same as f x horizontally compressed by a factor of to the y axis and translated down 2 units

to the best of your ability Please 1 What is an equation of the line that passes through the point 4 6 and has a slope of 3 1 y 3x 6 2 y 3x 6 3 y 3x 10 4 y 3x 14 2 What is an equation of the line that passes through the point 3 1 and has a slope of 2 1 y 2x 5 2 y 2x 1 3 y 2x 4 4 y 2x 7 3 Which equation represents the line that passes through the point 1 5 and has a slope of 2 1 y 2x 7 2 y 2x 11 3 y 2x 9 4 y 2x 3 4 What is an equation of the line that passes through the point 2 8 and has a slope of 3 1 y 3x 2 2 y 3x 22 3 y 3x 2 4 y 3x 22 5 What is the equation of the line that passes through the point 3 7 and has a slope of 3 4 4 x 3 2 y x 3 3 1 y

Question 5 20 points Use your TI 83 84 Calculator to graph each side and then use the Intersect command to find a solution to rounded to one decimal place of the following equation 2 3 x TI 84 Plus Silver Edition TEXAS INSTRUMENTS In the blank below just put the numeric answer for x e g If x 4 395218 just put 4 4 in the blank

Is parallelogram QRST a rhombus T yes S no Q R

3 Line k not graphed is the image of k y 2x 3 graphed above After a dilation about 0 0 by a scale factor of what is the y intercept of k A 2 B 3 C 6 D 7 y

Which angles are supplementary angles M K L I JKH and GHF ZJKH and JKM G H F ZLKM and GHF ZIHF and GHK

DF and GI are parallel lines D G H E J Which angles are vertical angles ZIHE and FEH I ZIHE and ZDEC ZIHE and DEH ZIHE and GHJ

Question 6 Multiple Choice Worth 1 points 02 03 MC S 4 E B

tion 14 Multiple Choice Worth 1 p MC ale DEF if m D 4x mZE

Question 7 Multiple Choice Worth 1 points 02 04 MC Triangles ABD and CBD are shown A D AB BC B C If m ZADB 110 what is the relationship between AB and BC

Finding Angle Measures Lines and 2 are parallel lines Determine the measures of 41 throu 412 m47 49 m41 49 O Part O

Which of the following is the correct name for a figure with vertices at 1 4 5 2 3 2 and 5 2 O A rectangle O B rhombus O C square O D trapezoid

The town plaza in a certain town is shown below The town s planning committee has decided to build a fountain where the diagonals intersect This sketch shows the corner points when placed on a coordinate grid I the town plaza is in the shape of a parallelogram which coordinates show where the fountain will be located O A 2 1 2 1 OB O C O D 1 2 2 3 3 1 12 D 2 0 A 0 4 B 6 1 C 4 3

Use the graph of the parabola to fill in the table 10 8 6 10 HLO a Does the parabola open upward or downward upward b Find the equation of the axis of symmetry equation of axis of symmetry downward c Find the coordinates of the vertex vertex 2 0 d Find the intercept s For both the x and y intercept s make sure to do the following 8 0 0 X

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