Coordinate system Questions and Answers

Match the following items In the figure below several reflections are illustrated Note one line if symmetry is m and one is I Pay close attention to the line of reflection being indicated by R and Rm 1 Rm T 2 Rm Z 3 Rm X 4 R Y 5 R A 6 R C m S B F E T Y E

What is the 5th term in the expansion of Drag a value into each box to correctly express the term Apply the convention of a leading numerical coefficient and variables listed in alphabetical order 64 4x y 1 y 315 7 8064 1008 X 5 11 28 X x15 x 18

The Harrington family belongs to a yacht club On Saturdays they take their sailboat out in the bay They usually spend about 3 hours sailing around This past Saturday they ended up at a point that was a 51 angle from the dock and 445 yards away How far east from the dock were they at this point boatdock O 280 04 yards O 549 53 yards O 345 83 yards O 330 26 yards boat N 4 W E S

Mellissa plotted the graph of a function The function contains the points 2 4 and 3 6 The domain of the function is all whole numbers y 6 5 4 3 2 1 e 54365 3 6 2 4 2 3 4 5 6 Mr Wilson reviewed her work and said that the graph is incorrect Explain why this graph is incorrect Draw a correct graph

Vector u has initial point at 8 6 and terminal point at 6 12 Which are the magnitude and direction of u Ollull 15 232 0 23 199 Ollull 15 232 0 156 801 Ollull 13 416 0 63 435 Ollull 13 416 0 116 565

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A hotel currently has enough room to accommodate at most 200 guests per night They plan to expand their capacity by 12 guests every year In order to make a profit the hotel must have at least 40 guests staying in the hotel The hotel manager expects that threshold to increase by 10 every year The manager modeled this situation with a system of inequalities where x is time from today in years and y is the number of guests He graphed the system to show the solution region when the hotel is making a profit Number of Guests 560 480 400 320 240 160 80 0 What system of inequalities did the manager create 4 8 12 16 Years X 28 20 24

3 The table shows population x and licensed driver y statistics from a recent year Work the problems on a separate piece of paper take a picture and upload State Arkansas Illinois Kansas Licensed Drivers Population Number of Drivers millions milliont 2 8 2 0 Massachusetts Pennsylvania Texas 12 8 2 8 6 4 12 4 23 5 8 1 2 0 4 7 8 5 14 9 a Make a scatter plot by hand b Draw a trend line c The population of Michigan was approximately 10 million that year About how many licensed drivers lived in Michigan in that year Describe how you found your answer orrelation between population and number of licensed drivers strong or weak Explain your response

The minute hand on a clock rotates in clockwise direction If the clock was laid on a coordinate plane with its center at the origin and the minute hand currently had an endpoint of 4 6 what will the coordinates of the endpoint be in 15 minutes A 6 4 B 6 4 C 6 4 OD 4 6 OB

A directed line segment begins at F 10 4 ends at H 8 4 and is divided in the ratio 6 to 2 by G What are the coordinates of G 3 3 5 O None of the other answers are correct O 1 6 5 O 3 5 2 O 2 5 2

Question 13 of 15 Which of the following systems of linear inequalities is represented by the solution graphed below OA x22 and y x OB x 2 and y2 x C v 2 and s

Follow the guided instructions below to create the line of reflection that would map the pink figure onto the blue figure Click and drag to draw lines connecting all corresponding points from the figure to its reflected image 10 9 8 7 6 5 4 3 2 1 10 9 y 8 7 6 5 4 3 2 1 L 2 02 4 10 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 x

The graph shows the population of black toads in a forest reserve since their introduction It also includes functions drawn by different researchers to estimate the change in population of the toads Which function best models the researchers data Black Toads thousands 16 14 12 10 0 A B OC On function A function B function C function D 2 Black Toad Population D B A 4 6 Years Since Introduction 8 X 10

The dash lined figure is a dilation image of ABC with center of dilation P not shown Is the dilation an enlargement or a reduction What is the scale factor n of the dilation a Ob C Od A do 8 4 A op y reduction n 1 2 reduction n 2 reduction n 1 4 enlargement n 2 B X

5 Use the Method of Elimination to find the equation of the line in y mx b form that passes through each set of points Set up a system first like we did Exercises 3 and 4 from the lesson Then solve the system for the slope m and the y intercept b a 3 10 and 5 18 b 2 5 and 6 7 6 Lilly and Rosie are sisters The sum of their ages is 19 and the positive difference of their ages is 9 Set up a system of equations involving Lilly s age L and Rosie s age R assuming that Lilly is the older child Solve the system to find their ages 7 Shana bought sodas and popcorn for the movies Sodas cost 3 each and popcorn costs 4 per bag Shana bought 7 things from the concession all either sodas or bags of popcorn Shana spent a total of 26 Write a system of equations involving the number of sodas s and the bags of popcorn b Solve the system to see how many of each Shana bought

Select the correct answer Each week Marcia travels to the office where she works the supermarket and a local fitness center The three locations represent the vertices of a triangle Marcia wants to move to an apartment that is equidistant from these three places Where should her new apartment be located OA the center of the inscribed circle of the triangle the center of the circumscribed circle of the triangle the point of intersection of the angle bisectors for the triangle the point of intersection of the perpendicular bisectors and the angle bisectors for the triangle B OC D Reset Next

me graph Wh in blue Draw the graph of y f 3x shown in red by determining how a stretch or compression will transform the location of the indicated blue points Drag the movable red points to the desired coordinates Hint Drag the red dot to where you think it should be It will fall into the correct place if you are right You may click on a point to verify its coordinates Provide your answer below 74 6 5 4 3 2 1 A

Look at the black arrow to the left. This is called a vector or a directed line segment. How many spaces is the black vector moving right? How many spaces is the black vector moving down?

Luke purchased a warehouse on a plot of land for his business. The figure represents a plan of the land showing the location of the warehouse and parking area. The coordinates represent points on a rectangular grid with units in feet. In the future, Luke has plans to construct a circular storage bin centered at coordinates (50,40) on the plan. Which of the listed measurements could be the diameter of a bin that will fit on the plot and be at least 2 feet away from the warehouse? Select all that apply.

One transmitting station is located 170 miles north of another transmitting station. Each station simultaneously sends out a radio signal. The signal from the north station is received 800 milliseconds after the signal from the south station. If the radio signal travels 0.18 miles per millisecond, find the equation of the hyperbola on which the ship is presently located.

Determine the slope and intercepts of the graph below. Vertical Intercept Horizontal Intercept

Consider the function: f(x) = x² + 8x - 20 The direction of the graph is like which of the following: The y-intercept is at y = The x-intercepts are at x = The vertex is at the point

1. On November 27th 2021, low tide in a harbour occurs at midnight with a depth of 3 meters. High tide occurs at 12:00 pm that day, with a depth of 11 meters. a) Graph the depth in the harbour for the first 48 hours.

The graph of x =- 4t and y = 3t^2 is a a. Circle b. Ellipse c. Parallel Lines d. Half Parabola e. Parabola

1. Follow the steps below to help you prove or disprove that the point (1, V15) lies on the circle that is centered at the origin and contains the point (0, 4). To earn full credit, you must show your work. Step 1: Plot a point at the origin and at (0, 4). Use these to help you draw the circle centered at the origin that contains (0, 4). Step 2: Determine the radius. Step 3: Use the radius and the coordinates of the center to write the equation of the circle. Step 4: Substitute the x- and y-coordinates of the point (1, V15) in the equation of the circle to check whether they satisfy the equation.

There are three types of solutions to any system of two equations. What are the types? What do those solutions look like graphically?

For each of the following equations, identify which conic section the equation represents (circle, ellipse, hyperbola or parabola), state the orientation (vertical or horizontal), and the coordinates of the center (for circles, ellipses, and hyperbolas) or the vertex (for parabolas).

List the intercepts of the equation y = 3x³ - 81. List the intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.

Graph the funtion. f(x) = 3√x-2 Plot five points on the graph of the function, as follows. • Plot the first point using the x-value that satisfies √√x-2 = 0. • Plot two points to the left and two points to the right of the first point. Then click on the graph-a-function button.

Determine if each of the following functions is a growth exponential or a decay exponential. a.y=4-2.2x b. y=3e-7x c. y = 20.1x d.y=0.32x

Write the first five terms of the sequence. f(0) = 3: f(n) = f(n-1). 2 f(0) = ƒ(1) = f(2)= f(3) = f(4) = 0.00

Give the coordinates of the point obtained from each reflection. (a) Reflect the point (0, 4) across the y-axis: (b) Reflect the point (0, 4) across the X-axis:

The second section of the walk continues from point B along Bell Avenue to the finish line at point C, as shown on the map. a. Each unit on the map represents 1 kilometer. What is the distance in kilometers from point B to point C? b. What is the total length of the race (from point A to point B and from point B to point C) in kilometers? c. A water station is located at the midpoint M of BC. Another water station is located at the midpoint N of MC. A race coordinator says that the map coordinates of point N are (6, 8). Is the race coordinator correct? Support your answer.

Which set of transformations is needed to graph f(x) = -0.1cos(x) - 4 from the parent cosine function? (1) reflection across the y-axis, vertical compression by a factor of 0.1, vertical translation 4 units up (2) reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down (3) vertical stretching by a factor of 0.1, vertical translation 4 units down, reflection across the y-axis (4) vertical stretching by a factor of 0.1, vertical translation 4 units up, reflection across the x-axis

The vertices of a square are H(0,2), I(2,0), J(0-2), and K(-2,0). Which statements are true of the image of HIJK after the given composition of transformations? Select all that apply. Step 1: x,y) → (-y,x) Step 2: (x,y) → (3x, 3y) a)H"(-2,0) b) HIJK = H'I'J'K' c)H'I'J'K'~H"T")"K" d)J"(6,0) e)y= x is a line of symmetry for the HIJK and H"1"J"K".

Solve the triangle with α= 55°, γ = 69°, and c = 25.91. β= degress a= b= Round all answers to 2 places after the decimal point. Give angles in degrees (but do not type "degrees" in the answer box). As in the text, side a is opposite from angle α, side b is opposite from angle β , and side c is opposite from angle γ. If no such triangle exists, then enter DNE in each answer box. If multiple triangles exist, then enter the values of the missing sides and angles for each triangle, separated by commas.

A company discovers that to produce x = 660 new electronic parts, it will cost y = $51,080. To produce 850 new electronic parts, it will cost $63,050. Compute the slope of the costs and choose the most accurate statement from the following: Costs are decreasing at a rate of $63 per item. Costs are increasing at a rate of $64 per item. Costs are decreasing at a rate of $57 per item. Costs are increasing at a rate of $57 per item. Costs are increasing at a rate of $63 per item. Costs are decreasing at a rate of $64 per item.

A Red Cross helicopter takes off from headquarters and flies 115 km in the direction 220° from North. It drops off some relief supplies, then flies 75 km at 325° from North to pick up three medics. .if the helicopter then heads directly back to headquarters, find the distance and direction (rounded to one decimal place it should fly. a)Distance _____km b)Direction _____degrees from North

Determine which of the following are true statements. Check all that apply. A. (6, - 6) is a solution to 8x + 2y ≤ 32 B. (7, - 7) is a solution to – 10x - 3y ≥ - 49 C. (9, - 10) is a solution to - 4x + 6y < - 94 D. (5, - 2) is a solution to -5x + 7y > - 37

Find the midpoint of the line segment joining the points corresponding to the complex numbers in the complex plane. (8 + i, 2 + 3i) (x, y) =

A hole is cut through the center of a sphere of radius 1.1. The height of the remaining spherical ring is 1.54. Find the volume of the ring. 1). 8.78453 2). 14.1372 3). 4.84905 4). 5.27667 5). 1.91232 6). 2.48271 7). 1.53111 8). 4.44518 9). 6.70882 10).2.85454

Systems of Linear Equations Mini-Lesson Review Which of the following are True about Systems of Linear Equations? Check all that apply. ▢ Two linear equations that relate the same two variables are called a system of equations. ▢ lf a Linear System of Equations has no solution, the two lines are parallel and will never intersect ▢ If a Linear System of Equations have infinitely many solutions, the two lines are parallel and will never intersect ▢ If a Linear System of Equations has one unique solution, the lines intersect at exactly one point. ▢ The solution to a system of equations is always exactly one point. ▢ The SOLUTION to a system of equations is the POINT at which the graphs intersect.

A company recently found out that the new mechanical equipment it needs currently costs $42,000. In 10 years it will be out of date and thus can then be scrapped for $6,000. Create a line that shows the depreciation relationship of the cost (C) over time (t) in years. Graph the line. What is the slop of the line? What are the x and y intercepts of your line and what do they represent? How much would it be worth if it they decided to get rid of if early, after 7 years?

For the point (1,3π/4) in polar coordinates, (a) plot the point, (b) give two other pairs of polar coordinates for the point, and (c) give the rectangular coordinates of the point. (a) Choose the graph that represents the point (1,3π/4).

Graph the linear equation. f(x) = -(2/3)x Use the graphing tool to graph the equation.

Match the solution region of each system of linear inequalities with one of the four regions shown in the figure. 9. x+2y ≤ 8 x-2y ≥ 0 10. x+2y ≥ 8 x-2y ≤ 0 11. x+2y ≥ 8 x-2y ≥ 0 12. x+2y ≤ 8 x-2y ≤ 0 Drag each of the regions given above and shown in the figure into the appropriate system of linear inequalities below to complete questions.9 through 12.

The parametric equations x = t +2 and y = t² + 3t represent a plane curve. Which of the following rectangular equations represents the plane curve? y=x² - 4x + 7 y=x²-x-2 y=x² + 3x y=x² +7x+10

Given point Q=(-6√3,-6) in rectangular coordinates, what are the corresponding polar coordinates? 6, 5π/6 12, 5π/6 6, 7π/6 12, 7π/6

Graph the solution set of the following system of inequalities. y≥x²-9 x-y≥-3

The equation of line r is y = -x+4/9 Parallel to line r is line s, which passes through the point (1, 7). What is the equation of line s? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.