Heights & Distances Questions and Answers

Which side is the hypotenuse of triangle DEF F 5 in 13 in D 12 in E

Darcie is baking a cake and has mixed 360 mini chocolate chips into the batter Darcie pours the batter is poured into a rectangular pan that measures 9 inches by 6 inches After poured the batter measures exactly 1 inches in height What is the density of chocolate chips in the batter Round your answer to two decimal places as necessary Show your work here

you are dealt 4 cards from a shuffled deck of 52 cards find the probabil e probability is ound to six decimal places as needed

2000 ft 75 71 Mountain height B 11 11 11 11 18 w a it B A plane is flying 2000 feet above sea level toward a mountain as shown The pilot observes the top of the mountain to be a 16 above the horizontal then immediately flies the plane at an angle of B 19 above horizontal The airspeed of the plane is 100 mph After 5 minutes the plane is directly above the top of the mountain How high is the plane above the top of the mountain when it passes over What is the height of the mountain Round to the nearest 10 feet Height of plane above mountain feet h feet

raione evlinder 7 Identify name center and opening direction the following quadric surface y 4y 22 3

Simplify 512

2 Two buildings are apart The taller building is and casts a shadow of Determine the height of the smaller building

1 A lighthouse casts a shadow of and a sailor standing at a distance of from the base of the lighthouse If th sailor is is determine the height of the lighthouse to the nearest foot

ove similarity statements ETX plete the proof that APQT APRS P 1 2 3 4 Q R Statement QT RS LP LP LPTQ LS APQT APRS T S Reason Given Reflexive Property of Congrue Corresponding Angles Theore

1 Use the following graph for the problems on this page and the next page 6 4 8 6 2 0 2 a Sketch a graph off on top of the graph of f x above

To estimate the height of a building two students find the angle of elevation from a point at ground level down the street from the building to the top of the building is 32 From a point that is 100 feet closer to the building the angle of elevation at ground level to the top of the building is 49 If we assume that the street is level use this information to estimate the height of the building The height of the building is foot

115 ft 190 ft A building that is 115 feet tall casts a shadow that is 190 feet long Determine the angle at which the rays of the sun hit the ground to the nearest degree

12 Consider the equation x 6x 9 0 Part A Which of these describes the solution s to the equation A one real solution B two real solutions one complex solution D two complex solutions Part B What are the solution s to the equation A x 3 x 3 3 2 3 x 3 x 3 3i 2

1 The base of a triangle is 5 in and its perimeter is 15 in A similar larger triangle has perimeter of 60 in Determine the length of the base of the larger triangle Show your work a 20 inches b 1 25 inches 80 inches d 180 inches C

Is AABC ADEF Explain A B AAS No C HL E ASA LL F are the triangles are not SAS Yes congru

Dalton deposited 7 000 in an account earning 10 interest compounded annually To the nearest cent how much interest will he earn in 4 years

A man on a cliff spots a ship at an angle of depression of 32 The distance from the bottom of the cliff to the ship is 179 m How tall is the cliff Round to two decimal places as needed

A ranger in a fire tower spots a fire at an angle of depression of 20 The tower is 56 ft tall How far is the fire from the base of the tower Round to two decimal places as needed fire tower ranger angle of depression line of sight fire

Which angle refers to the same angle as LBPF A G P F B

Q3 3pts AABC acute MNPQ a square Prove that ABC 2 MNPQ A Hint Consider h AA QP PN NM MC x i Show that QAQP A ABC Express x in terms a Bonus 2p B MA N of a ha and use TAM GM in the denominator areas Does the inequality in 193 remain valid if MNPC is a rectangle Justify

a Model for Gases object The word kinetic refers to motion The energy an has because of its motion is called kinetic energy Scientists explain some of the properties of matter in terms of the kinetic energy of the particles that make up the substance The model scientists use called the kinetic theory describes all matter as tiny particles that are in constant motion Gases in Kinetic Theory The particles in a gas are small hard spheres with insignificant volume They are all in motion and colliding at room temperature K There are no attractive forces between particles so all collisions are perfectly elastic meaning there is no loss of kinetic energy in the collision The motion of the particles is rapid constant and random and particles move in straight lines until they collide with other particles or the container walls 3 SEP Develop a Model In the cube of gas particles draw in extra particles so that there are twice as many particles Show how those particles interact les of the

In circle V m UXW 63 Solve for x if mUW 5x 32 If necessary round your answer to the nearest tenth Answer x X v W U Submit Answer

Use the dropdown menus to complete the statements below Parallel lines have Select Perpendicular lines have Select slopes slopes

Now you will attempt to copy your original triangle using one of its angles Draw a line segment DE of any length anywhere on the coordinate plane but not on top of AABC Choose one of the angles on AABC From point D create an angle of the same size as the angle you chose Then draw a ra from D through the angle You should now have an angle that is congruent to the angle you chose on AABC Create a point anywhere outside the mouth or opening of the angle you created The point will initially be named F by the tool but you should rename it point G Now draw a ray from E through G such that it intersects the first ray Your creation should be a closed shape resembling a triangle Label the point of intersection of the two rays F and draw ADEF by creating a polygon through points D E and F Click on point G and move it around By moving point G you can change ZDEFand ZEFD while keeping LFDE fixed Take a screenshot of your results for one position of G save it and insert the image in the space below BIUX X 15px EEEEE Font sizes

Find sin 0 where 0 is the angle shown Give an exact value not a decimal approximation 0 8 15 sin 0

Find cos8 where 8 is the angle shown Give an exact value not a decimal approximation 0 5 3

A skier is traveling down a mountain at a constant speed of 20 meters per second The angle of incline of the slope is decreasing at a rate of 0 5 degrees per second At what rate is the skier s altitude changing when the angle of incline is 35 degrees

8 A toy store is having a sale All items are half price Rick buys 5 toy cars and 2 dinosaurs Let c represent the regular price of a toy car and let d represent the regular price of a dinosaur Which expression does NOT represent the total cost of his purchases after the discount A B A B 0 5 5c 0 5 2d 5c 2d 2 A B 9 A clothing store has marked down the original price of a hat h by 8 The original price of a pair of pants p was reduced by 17 George bought 2 hats and 2 pairs of pants Which expression below could NOT be used to determine the total cost of his purchase before tax 2h 2p 8 17 2h 2 8 2p 2 17 C D 2 6h 4q 2 6h 2 4q 5c 2d 5c 2d 2 C 2 h 8 2 p 17 2 h 8 p 17 D 10 Mark and Jenny each have h hexagons and q quadrilaterals Which expression below could NOT represent the number of sides they have on their combined shapes C D 6h 4q 6h 4q 2 6h 2 4g

Find the tangent of ZF 68 F 32 H Simplify your answer and write it as a proper fraction improper fraction or whole num tan F

11 Given the figure to the right which of the following statements are NOT true a 21 and 25 are corresponding angles b 22 and 27 are alternate interior angles c 24 and 27 are a linear pair d 25 and 28 are vertical angles 1 3 2 4 5 7 6 8 m

10 26 25 1 Is the triangle above a right triangle 2 If the triangle above IS a right triangle show the math that you used If the triangle above IS NOT a right triangle change one side leng

Determine the scale factor Pre Image Image 1 1 3 4 5 1 3 3 9 12 15 3

21 Write the equation for the absolute value function graphed below 18 2 Type a response 2 2 4 8 6 6 y X

Problem 2 5 points A spherical tank with a radius of 15 feet is full of propane which has a density of 31 pounds per cubic foot Compute the work required to pump all the propane out of a 7 foot spout at the top of the tank Leave your answer in foot pounds rounded to the nearest whole number no dec imals

The curve C is the graph of y f Determine x interval s on which the curve is concave upward C is concave upward on t2 1 2t 2 1 0 dt B Find the antiderivative for the function f t that has constant term rer Graph of y f t The blue line in the graph above defines a linear function y f t A Suppose that 3 is a point that may vary on the t axis Find the accumulated area function A a f t dt that calculates the net area of the shaded region on the interval 0 2 Hint What is the area of a triangle A z x 2 4 2x

30 Given PQRS is a kite with perimeter 32 inches find the length of SR A 4 inches B 12 inches C 16 inches D 24 inches O A OB C S 2x 6x R

The vertices of quadrilateral ABCD have coordinates A 1 2 B 2 5 C 5 7 and D 4 4 Prove that ABCD is a parallelogram Justify mathematically and explain

3 5 POINTS Find the missing bearings for the following traverse 5 75 39 13 1 4 1515142 575 42 34 E 1 486 39 311 444 65 153

1 10 Pts Find a unit vector in the direction of steepest ascent increase and a unit vector that is tangent to the level curve of the function f x y x y at the point P 2 1

As Amaya gazes at the edge of the Grand Canyon she decides to try to determine the height of the wall opposite from her Using an app on her phone she determines that the top of the wall is at a 38 angle above her while the bottom is at a 46 angle below her as shown in the diagram at right If the base of the wall is 253 feet from the point on the ground directly below Amaya determine the height of the wall opposite from her Freda

Find the volume of the box 3 ft 6 ft 5 ft The volume of the box is cubic feet

55 A 60 foot flagpole was placed in front of a post office perpendicular to the ground After many years the flagpole began to lean The distance from the top of the flagpole to the ground is now 50 feet Which expression shows how to determine the angle the flagpole makes with the ground

3 32 cm 41 cm 63 cm True False 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 5 and type your answer type your answer 9 x 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 7 and 14 type your answer x type your answer 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 8 and 13 type your answer x type your answer 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 10 and 12 type your answer x type your answer 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 5 and 5 type your answer x type your answer paints

Question 9 1 point Given SV X Prove ASTX AVUT What is the reason for 3 Prove SAS Vertical Angles AA Statements 1 2 3 AGHI STX 4UTV AKJL Reasons 1 Given 2 3

If a bone contains 91 of its original carbon 14 how old is the bone Carbon 14 has a half life of 5730 years The bone is years old Round the final answer to the nearest year as needed Round all intermediate values to six decimal places as needed

Given the two lines are parallel below and the Z2 55 which statement is false 27 21 28 55 55 125 5 6 7 8 3 1 4 2

4 point Find than answer for x Type your answer 1 point Given m n find the value for x 8x 4 6x 12 7x 30 6x 10 m

Francisco asks the students in his school what pets they have. He studies the events shown. • Event S: The student has a cat. • Event T: The student has a dog Francisco finds that the two events are independent. Select all the equations that must be true for events S and T. P(SUT) = P(S) · P (T) P(ST) = P(S) P(T|S) = P(T) P(S|T) = P(T) P(T|S) = P(S) P (S∩T) = P (S) · P (T)

A uniform ladder of mass 30kg and length 5 m rests against a smooth vertical wall with its lower end on rough horizontal ground. The ladder is inclined at 60° to the floor. The coefficient of friction between the ladder and the ground is 0.4. Find how far a man of mass 80 kg can climb up the ladder without it slipping.

Find the normal curvature Kn of the curve a(t) = (acost, asint, bt) on a cylindrical surface of radius r=a, where a, b are constants.