Coordinate system Questions and Answers

A point on the unit circle in the third quadrant has an x-value of -1/4, and makes an angle of a with the positive x-axis. (a) Draw the unit circle and plot the point. Indicate a.

A sequence of transformations is described below: A dilation with a scale factor of 3 A translation left 4 units and down 1 unit Select the statement that describes the resulting image. A. The angle measures are preserved, but the image is a reduction B. The angle measures are preserved, but the image is an enlargement C. The angle measures are not preserved, and the image is a reduction D. The angle measures are not preserved, and the image is an enlargement

The midpoint of AB is M(-1,-4). If the coordinates of A are (-3,-7), what are the coordinates of B?

The temperature in an industrial pasteurization tank is f(x) = x2 - 9x + 119 degrees centigrade after x minutes (for 0 ≤ x ≤ 13). (a) Find f'(x) by using the definition of the derivative. f'(x) = (b) Use your answer to part (a) to find the instantaneous rate of change of the temperature after 2 minutes. Be sure to interpret the sign of your answer. The temperature is ---Select--- at a rate of degrees per minute after 2 minutes. (c) Use your answer to part (a) to find the instantaneous rate of change after 6 minutes. The temperature is ---Select--- at a rate of degrees per minute after 6 minutes.

A new lookout tower is going to be built so that it is the same distance from three ranger stations. If the stations are at A(-90, 28), B(0, -35), and C(125, 20) on a grid, determine the coordinates of the point where the new tower should be built.

An average school bus holds 45 people. Sketch a graph showing the relationship between the number of students who need bus transportation and the number of buses required. Be sure to label the axes.

The coordinates of the endpoints of RT are R(-6,-5) and T(4,0), and point S is on RT. The coordinates of S are (-2,-3). Which of the following represents the ratio RS: ST? 1:2 2:3 3:2 3:4

Find the slope m of the line passing through the given pair of points. (Give an exact answer. Do not round. If an answer is undefined, enter UNDEFINED.) (3,-3) and (-1, 3) m=

Find the equation of the line passing through (2, -1) and (-2, 1). y =

Your itinerary contains a grid map of Sydney, with each unit on the grid representing 0.125 kilometers. If the Sydney Opera House is located at (-9.-9) and the Queen Victoria Building is located at (-2, 10), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in kilometers? Round your answer to two decimal places, if necessary.

Find the slope of the line passing through the points given below or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (5,4) and (6,9) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The slope is . B. The slope is undefined. Indicate whether the line through the points rises, falls, is horizontal, or is vertical. Choose the correct answer below. A. The line falls from left to right. B. The line is horizontal. C. The line is vertical. D. The line rises from left to right.

Graph: y ≥ 4x + 1 y > - 2x - 2

What is the image of the point (6, 9) after a rotation of 270° counterclockwise about the origin?

Round to the nearest hundredth if necessary. If there is more than one x-intercept, separate them with commas.

Plot the intercepts to graph the equation. 5x-3y=-15

Hooke's law states that the force needed to stretch a spring is proportional to the amount the spring is stretched f 20.00 b stretches a certain spring 10.0 m, how much will the spring be stretched by a force of 9.00 lb? inches. A force of 9.00 lb will stretch the spring by (Simplify your answer. Type an integer or a decimal.)

Chase made a scale drawing of a neighborhood park. The scale of the drawing was 1 millimeter: 8 meters. The volleyball court is 16 meters long in real life. How long is the volleyball court in the drawing?

Graph the system of equations and write the solution as an ordered pair. Write "DNE" if the Solution does not exist, or use the infinity symbol if the system has infinitely many solutions.

Find the equation of the tangent line to the curve f(x) = 4 sec(x) - 8 at the point

Directions: Given each set of coordinate points, calculate the slope between the two points. Type your answer in simplified form in the cell provided. Incorrect answers will appear red and correct answers will reveal the mystery image!

Use the intercepts to draw the graph of y = 3x + 6. PLOT intercepts on the graph using the point tool. Then connect them to draw the line. NOTE!! You must plot the intercepts FIRST using the point tool. Then plot the line, using the line tool

A map in the coordinate plane shows the distance between two cities in miles. The x-axis runs east/west, and the y-axis runs north/south. The town of Elgin is located at (-3, 2). The town of McDade is 8 mi east and 4.5 mi south of Elgin. Plot and label the locations of both towns in the coordinate plane.

Below are the coordinates of the vertices of ΔVWX and its image after a reflection. ΔVWX: V(2, 1), W(3,5), X(4,2) ΔV'W'X': V'(-2, 1), W'(-3, 5), X'(-4,2) a. What do you notice when you compare corresponding x-coordinates and corresponding y-coordinates of the vertices of ΔVWX and ΔV'W'X'? b. What is the line of reflection?

Find the coordinates of the midpoint M of ST. Then find the distance between points S and T. Round the distance to the nearest tenth. S(-2, 4) and T(3, 9). The midpoint is M.). The distance between S and T is about

On a map of a hiking trail, Jennifer starts the trail at (0,0), then the trail takes her to the top of a mountain at (2,4). Afterwards, the trail leads her to the waterfall located at (5,0). The trail then takes her DIRECTLY back to where she started. If each unit represents one mile, what is the TOTAL distance that Jennifer traveled on her hike? Round to the nearest hundredth if necessary.

If the graph of the line y = mx + b is reflected over the y-axis, what will be the slope and intercepts of the new graph? (Your answers will depend on the parameters b and m. (a) The slope will be -m (b) The y-intercept will be y = (c) The x-intercept will be x =

Determine the viewing window used. Xmin= -15 Xmax = 15 Xscl= 3 Ymin = Ymax= Yscl=

In Exercises 3-6, describe the transformation of f represented by g. Then graph each function. 14. f(x) = x³, g(x) = -3x³ 16. f(x) = x¹, g(x)=x²-3 15. f(x) = x¹, g(x) = 3x² + 2 17. f(x) = x¹, g(x) = (x + 3)¹

On the real number line below, with coordinates as labeled, an object moves according to the following set of instructions: from point P the object moves right to Q, then left to R, then right to S, and finally left until it returns to its original position at P. What is the closest estimate of the total length, in coordinate units, of the movements this object makes?

The image point of A after a translation right 3 units and up 3 units is the point B(-4, 8). Determine the coordinates of the pre-image point A.

Write the following equation in the form y=mx+b. Then, using a calculator, graph the line in the window indicated. 1.6x +1.2y=5.0, [-4,4] by [-6,6] The equation in the form y = mx + b is y=

Write the slope-intercept form of the line that passes through with slope m = 1/4 Do not use a calculator.

Kara plots points L and M in the coordinate plane. The x-coordinate of point Lis the opposite of the x-coordinate of point M. The y-coordinate of point L is the opposite of the y-coordinate of point M. Which statements are true about the points? Choose all the correct answers. A The points are on opposite sides of the x-axis. B The points are in Quadrant I and Quadrant IV. C The points are the same distance from the y-axis. D The points are located on the same horizontal line. E The points are reflections of each other across the x-axis.

Find the equation of the line satisfying the given conditions, giving it in slope-intercept form, Through (0,-4), parallel to 3x+y=8 y=

Write the equation in the form y = mx + b. Then, using your calculator, graph the line in the window [-10,10] by [-10,10]. 4x + 3y = 12 Write 4x + 3y = 12 in the form y = mx + b. y =

Graph y=3x-6 by plotting points. Based on the graph, determine the intercept(s). Use the graphing tool to graph the equation.

Find the slope and y-intercept of the line. Graph the line. 2x+y=5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Slope = B. The slope is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is (Type an integer or a simplified fraction.) B. The line 2x+y=5 does not have a y-intercept. Use the graphing tool to graph the line.

Which of the coordinate pairs below are separated by a horizontal distance of less than 5 units? Select all that apply. A) (1.2, 5) and (-3.3, 5) B) (-3, 4) and (-4,4) C) (1.4,-5) and (-5, -5) D) (5.2, 1.4) and (1.5, 1.4)

Find the distance d (P₁, P₂) between the given points P, and Pa P₁ (6,3) P₂ (-3,4)

Consider a curved mirror y = f(x) passing through (8, 6) and having the property that all rays emerging from origin after getting reflected from the mirror become parallel to the x-axis. The equation(s) of the curve(s) is/are y² = 4 + 4x y²=36 (9-x) y²=3(x+y) - 6 y² = -x +44

Find the midpoint of the segment with the following endpoints. (10, 10) and (2,6)

Find the distance d (P1. P2) between the given points P₁ and P2 P₁=(-3,1) P₂ = (6,5) d (P₁, P₂) = (Simplify your answer. Type an exact answer, using radicals as needed.)

When finding the intersection of two lines from both Algebra I and Geometry, you first "set the linear equations equal" to each other. Find the intersection point of the two lines whose equations are shown below. Be sure to find both the x and y coordinates.

A ball is thrown straight up from 5 feet above the ground with a velocity of 30 feet per second. The height of the ball over time can be modeled by the function h(t) = -16t² + 30t+5. What is the maximum height of the ball? When you set the right-hand expression equal to 0, multiply the equation by -1, = 0. Complete the and divide by 16, the resulting equation is 12-15 5

The point (15,16) is on the graph of y=f(x). Find the corresponding point on the graph of y = g(x), where g(x)=f(-x).

a. Rewrite the equation 5x+y-1=0 in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. a. The slope-intercept form of the equation is y= -5x +1. b. The slope of the equation of the line is -5 and the y-intercept is c. Use the slope and y-intercept to graph the line.

Think about what you know about the coordinate plane. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can.

Find the x- and y-intercepts. 7x-4y=28 Write each intercept as an ordered pair. If there is more than one intercept, use the "and" button. Select "None" if applicable.

Graph the equation by plotting points. y=√√x

Consider the following system of linear inequalities. Which are the vertices of the solution region? 2x≤y+4 2≥y -2x-4≤y A) (0, 2), (0, -4), and (3, 2) B)(-3, 2), (0, -4), and (3, 2) C)(-3, 2), (-2, 0), and (-1,-2) D)(1, 2), (2, 0), and (3, 2)