Coordinate system Questions and Answers

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)

You need 330 mL of a 90% alcohol solution. On hand, you have a 70% alcohol mixture. How much of the 70% alcohol mixture and pure alcohol will you need to obtain the desired solution? You will need and mL of the 70% solution mL of pure alcohol.

Graph g(x) = -x/2-5. Use the graphing tool to graph the function. .....

A horse eats about 2 lbs of food for every 100 lbs of body weight. This can be represented by the function f(x) = 2x for x hundred lbs. Graph the function, and use the graph to find the amount of food a 1000 lb horse would eat.

Graph f(x)=-10x. Use the graphing tool to graph the function.

2 Write the equation of the line passing through the point (3, – 6) with slope 3 The equation of the line is 0

Fill in each blank so that the resulting statement is true. The graph of the exponential function f with base b approaches, but does not touch, the -axis. This axis, whose equation is is a asymptote.

You are going to make and sell bread. A loaf of Irish soda bread is made with 2 c flour and c sugar. Kugelhopf cake is made with 4 c flour and 1 c sugar. You will make a profit of $1.50 on each loaf of Irish soda bread and a profit of $4 on each Kugelhopf cake. You have 16 c flour and 3 c sugar. How many of each kind of bread should you make to maximize the profit? b. What is the maximum profit?

Given below are the coordinates of two points on a coordinate plane: (3, 1) and (6, 3) What are the coordinates of the third point for the points to be collinear? O (4,4) O (4, 6) O (9,5) O (5,9)

Suzy has a transparent ballpoint pen in which she can see its ink level. After two weeks of use, she notices that she has 18 cm of ink left in the pen. After four weeks, she has 15 cm of ink left in the pen. After eight weeks, she has 9 cm of ink left in the pen. Suzy presumes she is using the same amount of ink each week. a) If Suzy's presumption is correct, how much ink was in the pen when she started using it? b) Write an equation that models the length of ink in Suzy's pen each week. c) If she continues this pattern of use, for how many total weeks will Suzy be able to use her pen? Justify your answer.

A chameleon is resting quietly on a lanai screen, waiting for an insect to come by. Assume the origin of a Cartesian coordinate system at the lower left-hand corner of the screen and the horizontal direction to the right as the +x-direction. If its coordinates are (7.000 m, 4.500 m), find the following. (a) How far is it from the corner of the screen (in m)? (b) What is its location in polar coordinates? (Give the radial coordinate in meters such that r≥0, and the angle in radians counterclockwise from the +x-axis such that 0 < φ ≤ 2π. Do not include units in your answer.) (r, φ) =

Which lines are parallel and which are perpendicular? 1.) Line QR: Q (5, 5) & R (8,-4) 2.) Line ST: S (0, -1) & T (2,3) 3.) Line UV: U (6,-4) & V (7,-2) 4.) Line WX: W (4, 3) & X (7,4) Parallel lines are Perpendicular lines are

The coordinates of AABC are A(-11,7), B(-5, -3), C(-2,3). After a dilation, the coordinates are A'(22,-14), B'(10,6), C'(4, -6). Find the scale factor. -2 3/2 3 5/2

Consider the following system of two equations and two unknowns. [x+y = 2 [3x + y = 0 a) Solve the system using substitution. b) Solve the system using linear combination (a.k.a. the elimination method). c) Solve the system by graphing. (A sketch on regular paper is ok, but be sure to label any key points.) d) Check your work by confirming that your solutions for parts a, b, and care the same! (Be sure to write a note on your paper that you completed this step.)

Describe and correct the error a student made in finding the midpoint of CD with C(-4,5) and D(- 1,-4). (-4-1-1), 5-1-4) 996 X The student did not add the x- and y-coordinates when calculating the midpoint. O The student used incorrect coordinates when calculating the midpoint. O The student swapped the x- and y-values when calculating the midpoint. O The student did not divide the numerator and denominator by 2 when calculating the midpoint.

Write an equation and sketch the graph for the described linear relation. a) Kenji started with $50 in his bank account, then deposited $10 per week. Let x = # of weeks and y = account balance. b) A tree is 10 inches tall when it is planted. It grows at a constant rate of 1.5 inches Let x = # of months from when the tree was planted and y = the height of the tree. per month. c) A snowball weighed 60 pounds when it started to melt. It melted at a constant rate of 4 pounds per hour. Let x = # of hours the snow had been melting and y = weight of the snowball.

Starting at noon, Brody observed the amount of snow on his lawn during a blizzard. He wrote an equation to represent s, how many inches of snow were on the lawn: s = 0.015x + 2.5, where x represents the number of minutes past noon. What could the number 0.015 represent in the equation? The amount of snow on the lawn at noon. The amount of snow on the lawn when the blizzard ended. The amount of snow on the lawn at 1 p.m. How much more snow is added to the lawn every minute.

If the function y = e-3x is vertically compressed by a factor of 4, reflected across the y-axis, and then shifted down 5 units, what is the resulting function? Write your answer in the form y= ceax + b. Provide your answer below: y=

The graph of y = f(x) is shown 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.

Which of the following is true when a plane intersects a cone to form a parabola? The plane slices through a double cone and is perpendicular to the base of the cone. The plane slices through a single cone and is parallel to the base of the cone. The plane slices through a single cone and is at an angle parallel to the slanted edge of the cone. The plane slices through a double cone and is neither parallel nor perpendicular to the base of the cone.

Work with a partner. Consider the absolute value equation |x + 2 = 3. a. On a real number line, locate the point for which x + 2 = 0. -10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10 b. Locate the points that are 3 units from the point you found in part (a). What do you notice about those points? c. How can you use a number line to solve an absolute value equation?

The points represent the vertices of a polygon. Use a matrix to find the coordinates of the image after the given transformation. Graph the preimage and the image. A(2, 3), B(-1,-4), and C(2, -2); a translation 1 unit left and 4 units down.

Here are graphs of x = 4 and x + y = 12. Complete the graphs (by shading regions and adjusting line types as needed) to show all the allowable numbers of widgets and zurls that the factory can produce in one day.

The diagonals of a parallelogram ABCD intersect at E(-5, -1.5).Two vertices are located at A(-10, -1) and B(-1, 3.5). Find the coordinates of the other two vertices C and D. Use decimals in your answer. The coordinates for vertices C = The coordinates for vertices D =

A right triangle has vertices X(0, 0), Y(0, 2a), Z(2b, 0). What is the circumcenter of the triangle? Make a conjecture about the diameter of a circle that is circumscribed about a right triangle.

1. A movie theater charges $10 for an adult ticket and $9 for a child ticket. The goal is to make $1,200 on adult tickets each week. Did the theater make its goal this week? How much more or less than the goal did the theater make?

The value of y varies directly as the square of and y = 27 when z = 9. Find the equation represents this relationship. Report the proportionality constant as a reduced fraction when necessary.

The longest sides of two similar triangles are 28 ft and 21 ft. What is the scale factor? 2/1 18/13 4/3 28/21

Find the coordinates of the point(s) on the curve y = √x + 4 that are closest to the point (5, 0). a) O (0, 2) and b) ○ (1, √5) √38 90 (1/1, V28) c) O 2 d) O 9 √34 2² 2 e) ○ (9, √13) 9 5

3. Find all the points on the graph of f(x) = 3x - 52x³ +300x² - 672x +900. For which the tangent line is horizontal. A) (2,388) only B) (2,0), (4,0) and (7,0) c) (2,388), (4,452) and (7,263) D) (4,452) and (7,263) only E) (4,0) and (7,0) only

Select the correct answer from each drop-down menu. Polygon ABCDE has the vertices 4(2, 8). 84. 12), 410, 12), (8, 8), and 86, 6), Polygon MNOPQ has the vertices M-2, 8). M-4, 12), Q-10, 12) P(-8, 8), and Q-6, 6). A transformation or sequence of transformations that can be performed on polygon 48CDE to show that it is congruent to polygon MNOPQ is a If polygon MNOPQ is translated 3 units right and 5 units down, it will coincide with a congruent polygon, MMXX with its vertices at

Graph the solution of the system of linear inequalities. y + 4x ≥0 5x-3y ≤ 15

Graph the linear equation. x = 4y

Graph the equation y = -x² + 14x - 48 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Find an equation of the line with the slope m = 1/8 that passes through the point (-7,0). Write the equation in the form Ax + By = C. Choose the correct answer below. A. 8x+y=7 B. x+8y= -7 C. 7x+y = -8 D. 7x+y=8

Consider the following relation. x = 3|y|-5 Find four points contained in the inverse. Express your values as an integer or simplified fraction.

The points (4, -6) and (9, -6) represent the location of two towns on a coordinate grid, where one unit is equal to one mile. What is the distance, in miles, between the two towns? Enter your answer in the box. miles

Let m1 and m2 represent the slopes of two lines. Determine if the lines are parallel, perpendicular, or neither m1 = 6/4, m2=2/3.

Sketch the hyperbolas below and write the coordinates of the vertices and co-vertices and the equations of the asymptotes. In your sketch, clearly show the x- and y-axes, central box, asymptotes, branches, vertices, and co-vertices. 1 a. 25 Coordinates of vertices: Coordinates of co-vertices: Equations of asymptotes: Sketch:

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve list of ordered pairs.) x = t³ - 3t, y = t² - 5 horizontal tangent vertical tangent (x, y) = (x, y) = X X 4

Find the area under the standard normal curve: (Keep 4 dec- imal places in your answers.) a. between z = 0 and z = 2.29 b. between z = 0 and z = -2.49 c. between z = 0.93 and z= 1.91 d. between z = -0.65 and z = -2.39 e. between z = -2.27 and z = 1.65

In a triangle, which point of intersection, or concurrency, is the intersection of the perpendicular bisectors? Centroid Medians Incenter Circumcenter

Use synthetic division to find f(-2). f(x) = 2x4-x³-16x² + 34x - 32.

Find the equation of the line parallel to the graph of -3x + 3y = - 2 that contains the point (-4,-4). Write the answer in slope-intercept form. Preview syntax error: this is not an equation 4

Triangle ABC is taken to triangle A' B'C' by a dilation. Which of these scale factors for the dilation would result in an image that was larger than the original figure? A. B. 3/w D. 25 C. 1

- A city planner designs a park that is a quadrilateral with vertices at I(-3, 1), K(1, 3), L(5, -1), and M(-1, -3). There is an entrance to the park at the midpoint of each side of the park. A straight path connects each entrance to the entrance on the opposite side. Assuming each unit of the coordinate plane represents 10 meters, what is the total length of the paths to the nearest meter?

Communicate Mathematical Ideas A video game designer places an anthill at the origin of a coordinate plane. A red ant leaves the anthill and moves along a straight line to (1, 1), while a black ant leaves the anthill and moves along a straight line to (-1,-1). Next, the red ant moves to (2, 2), while the black ant moves to (-2,-2). Then the red ant moves to (3, 3), while the black ant moves to (-3,-3), and so on. Explain why the red ant and the black ant are always the same distance from the anthill.

On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(-3, 1), B(2, 3), and C(4, -1). A bank employee drives from Branch A to Branch B and then drives halfway to Branch C before getting stuck in traffic. What is the minimum total distance the employee may have driven before getting stuck in traffic? Round to the nearest tenth of a mile.

In a recent survey, 80% of the community favored building a health center in their neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the health center? 1.55 0.55 2.40 0.98

Which pair of variables can't be represented on a scatter plot? Circle the answer. Write a sentence about why it can't be represented. The heights and age of the KC Chiefs players. The names and runs batted in (RBI) statistics of the NY Yankees players. The free throws made (FTM) and free throws attempted (FTA) of the SA Spurs players.