Coordinate system Questions and Answers

Known a cube ABCD.EFGH with the side length 3p. A point P,Q, and R on FB,FG,and AD so that BP=GQ=DR=p. Let beta is a slice through P,Q, and R. Find the ratio of the area that result of the proyeksion beta on ABCD with area ABCD A. 14/18 3. 9/18 C. 13/18 D. 11/18

Solve graphically (using the Cartesian Plane): f(x) = |x|-2>-x² +4.

What is the midpoint of a line segment with endpoints at (-1, 4) and (5,8)? Select one: O (4,12) O (6,12) O (2.6) O (3,6)

A soccer team has 10 players and needs to choose 2 captains. How many ways can the captains be selected? Select one: O 45 O 20 O 90 O 180

Which lines are perpendicular to each other? Select two lines. Choose all that apply: 3x + 2y = 1 3y=-2x +9 3x+y=6 x+3y= −1 x-3y = 5

The vertices of triangle ABC are A (-4,-2), B (3,0) and C (0,4). Which type of triangle is it? Select one: O isosceles Oright O obtuse O acute

What is the most specific name of the quadrilateral ABCD created by connecting A (-1,3), B(1,-1), C (-1,-2); and D(-3,2)? O square O rhombus O rectangle O parallelogram

What is the equation of the line that is perpendicular to x + 2y = 4 and passes through (1, 1) y=2x-1 y=-1/2 x +2/3 y=-1/2 x +3/2 y = 2x

A line passes through A (-2, -1) and B (2,5). What is an equation a line that is perpendicular to AB? Select all that apply. Choose all that apply: y = 3/2x+2 2x+3y=7 3y=-2x + 11 y=-x+8 y=x+4

Write the following numbers in the polar form e^iθ,0 ≤ θ < 2pi (a)1/9 r=____ θ=_______ (b) 6+ 6i r=____ θ=_______ c) - 9 + 9i r=____ θ=_______ Write your answer for r using either exact value or decimal accurate to at least one deciaml place. Write your answer for θ in radian and accurate to at least one decimal place.

6. For the pair of polynomials given, select all the points of intersection of their graphs. g(x) = (x+3)(x-7) h(x) = x - 7 a. (-8,-13) b. (-7,0) c. (-2,-9) d. (-5, -10) e. (7,0)

Find the coordinates of a point on a circle with radius 30 corresponding to an angle of 220° (x, y) = Round your answers to three decimal places.

Convert the polar coordinate (6,2pi/3)to Cartesian coordinates. Enter exact values. x= y=

Convert the Cartesian coordinate (3,1) to polar coordinates, r>0 and 0 <θ< 2pi r = Enter exact value. θ=

Find an angle with 0° <θ< 360° that has the same: Sine as 20:θ=_________degrees Cosine as 20:θ=_________degrees

Which of the following has a slant asymptote when graphed? Oy=2x³ +3/(x-1) Oy=2x/(x-1) Oy= 2x²/(x-1) Oy=3/(x-1)

Find the point at which the line intersects the given plane. x = 2 - 2t, y = 3t, z = 1+ t; x+2y-z = 7 (x, y, z)=

Determine on which line(s) the invariant point lies if the graph of y = f(x) is transformed into: a) y = -f(x) b) y = f(-x) c) y = √f(x)

Sketch the region bounded by the surfaces z = √√x² + y2 and x² + y2 = 1 for 1 ≤ z ≤ 7. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. (Write an equation for the inner trace at z = 7 using x and y.) (Write an equation for the outer trace at z = 7 using x and y.). (Write an equation for the inner trace at y = 0 using x and z.) (Write an equation for the outer trace at y = 0 using x and z.) (Write an equation for the inner trace at x = 0 using y and z.). (Write an equation for the outer trace at x = 0 using y and z.) (Write an equation for where the two surfaces meet using z.)

graph the given functions on the coordinate plane. f(x) = (3)^x

1. Given a line 2x - 3y = 6 in the plane, (i) find the slope-intercept equation of the line that passes through the point (2,-4) and is parallel to the given line; use exact values for all the numbers in your answer. (ii) find the slope-intercept equation of the line that passes through the point (-6, 3) and is perpendicular to the given line.