Coordinate system Questions and Answers

Determine what type of transformation is represented. A. reflection B. translation C. rotation D. none of these

Explain in words how each of the following functions are related to y = √x and then sketch all five graphs on the same set of axes including the parent function. Be sure to identify which graph is which either by labeling or using different colours (a) y = √x-3 + 4 (b) y = -√x-2 + 1 (c) y = √-x+4 - 3 (d) y = 2√x - 5

Directions - Write an equation in Slope-Intercept Form (y = mx + b) for the line with the given slope (m) and y-intercept (b). m = 4,b=-3

Solve the following system by graphing. x+y-6=0 x-y=0 What is the solution of the system? (3,3) (-3,3) (3,-3)

Solve the following system of equations. 3x+2y-5=0 x=y+10 Make sure there are NO SPACES in your answer. Include a comma in your answer.

For the following system, use the second equation to make a sub x + 5y - 10 = 0 x= 2y-8 What is the resulting equation in simplest form? -3y-18-0 3y-18-0 7-18-0

A grid shows the positions of a subway stop and your house. The subway stop is located at (7, -7) and your house is located at (-3, 3). What is the distance, to the nearest unit, between your house and the subway stop? 11 14 19 24

An architect is designing a garden for a client on a planning sheet. The client requests the relocation of a water fountain by the rule (x,y) → (x+ 9, y-8). Later, the client decides that they would prefer the water fountain's location moved from this new position 5 units left and 3 units down. Find the composition as a single transformation. A. (x,y) → (x+4, y-11) B. (x,y) → (x+6, y-13) C. (x, y) → (x + 14, y − 5) D. (x, y) → (x-3, y-5)

Which set of ordered pairs has point symmetry with respect to the origin (0, 0)? (-12, 5), (12,5) (-12, 5), (-12,-5) (-12, 5).(-5, 12) (-12, 5), (12,-5)

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Find the regression equation.

One line passes through the points (-8,1) and (4,4). Another line passes through points (-9, -7) and (9.-3). Are the lines parallel, perpendicular, or neither? Choose 1 answer: Parallel Perpendicular Neither

The vertices of ΔJKL have coordinates J(5, 1), K(-2, -3), and L(-4,1). Under which transformation is the image ΔJ'K'L' not congruent to ΔJKL? (A) a translation of two units to the right and two units down (B) a counterclockwise rotation of 180 degrees around the origin (C) a reflection over the x-axis (D) a dilation with a scale factor of 2 and centered at the origin

What's the slope and y-intercept of the graph of 7x+y=8? A) Slope-7, y-intercept = 8 B) Slope 7, y-intercept = 8 C) Slope = -8, y-intercept = 7 D) Slope = -7, y-intercept = -8

If a translation maps point (3, 2) to (4, 5); or T: (3, 2) (4, 5), indicate the image for (2, 4). (3.7) (2, -1) (5, 3)

The longer base of an isosceles trapezoid joins points (-3, -2) and (7, -2). One endpoint of the shorter base is (-1, 4). What are the coordinates of the other endpoint? (0, -3) (5,4) (4, 5)

A boat heads directly north across a river, 68 m wide at a rate of 3 m/s. The current is flowing downstream (due west) at 1.9 m/s. A. What is the resultant velocity and direction of the boat? Write your angle as a bearing. B. How long does it take the boat to cross the river? (Hint: How long does it take to covert the vertical distance of 68m across the river?) C. How far downstream is the boar when it reaches the other side of the river?

An equation for the line L is: y = 11 + 10/7 (x-4) The angle I makes with the x-axis is:

If P (3,2), find the image of P under the following rotation. 180° counterclockwise about the origin

The y-intercept of the parent quartic function, f(3) = 4, is translated 3 units to the right and 1 unit down. Which equation represents this transformation? A g(t) = (x-3)^4 - 1 B. g(t) = (x+3)^4 - 1 C. g(s) = (x-1)^4 +3 D. g(x) = (x+1)^4 +3

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0? 4x-y-6=0 4x+y+6=0 4x+y-6=0

The vertices of a rectangle are R(-5, -5), S(-1,-5), T(-1, 1) and U(-5, 1). After R' is the point (3, 0). Find the translation and coordinates of U'. translation, [A] (8,-5); (3,-4) [B] (5,-8); (0,-7) [C] (-5, 8); (-10, 9) [D] (8,5); (3, 6)

The revolving restaurant on top of a hotel in San Francisco, California takes 45 minutes to complete a full counterclockwise rotation. A table that is 30 ft from the center of the restaurant starts at position (30, 0). What are the coordinates of the table after 9 minutes? Round to the nearest tenth. (9.3, 28.5) (11.3, 17.3) (28.5.9.3) (23, 19.3)

The point (7,-4) is on the terminal arm of angle θ in standard position. a) Draw a sketch of angle θ. Be sure to label the side lengths and θ. b)Determine the exact values of sin θ, cos θ, and tan θ. c) State the value of θ, to the nearest degree.

The polar coordinates of a point are (9,3π/2). Find the rectangular coordinates of this point. The rectangular coordinates are (Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed. Use integers or fractions for any numbers in the expression.)

The vertex form of the equation of a horizontal parabola is given by z= 1/4p(y-k)2+h, where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use GeoGebr to create a horizontal parabola and write the vertex form of its equation. Open GeoGebra , and complete each step below. Part A Mark the focus of the parabola you are going to create at R(-5, 2). Draw a vertical line that is 8 units to the right of the focus. This line will be the directrix of your parabola. What is the equation of the line?

Suppose a point has polar coordinates (6, 2π/3) with the angle measured in radians. Find two additional polar representations of the point. Write each coordinate in simplest form with the angle in [-2π, 2π].

Rectangle HIJK is dilated to produce rectangle H'T'J'K'. If the perimeter of HIJK is a and the perimeter of H'I'J'K' is b, what is the scale factor of the dilation?

Fairview is hosting a city-wide arts festival at which vendors can pay to have a small booth or a large booth. The fee for a small booth is $27, whereas the fee for a large booth is $81. The city hopes to receive at least $1,500 in fees. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. x = the number of small booths y = the number of large booths (27+ x)(81+ y) ≥ 1,500 27x 81y 2 1,500 27 + x +81 + y ≥ 1,500 27x+81y 2 1,500

If you flip the reciprocal parent function, F(x) = 1/x, across the y-axis, what is the equation of the new function? A. G(x) = -¹/-x B. G(x) = 1/x-1 C. G(x) = 1/x - 1 D. G(x) = x

If you apply the transformations below to the quadratic parent function, F(x) = x², what is the equation of the new function? Shift six units right. Shift four units down. A. G(x) = (x-6)²-4 B. G(x) = (x-4)² +6 C. G(x) = (x-4)²-6 D. G(x) = (x+6)² - 4

Choose the best definition of SAS Similarity. When two triangles have corresponding angles that are congruent and the included corresponding sides with identical ratios. None of the other answers are correct Sides that are in the same position in different plane figures. When two triangles have corresponding angles that are congruent, the triangles are similar. the result of a transformation.

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) None of the other answers are correct (-1.6, 5) (3.5, 2) (2.5, 2)

A scientist concerned about dehydration of soccer players on hot days measured the fluld consumption of twenty-six soccer players. The mean fluid consumption per day was 2,780 milliliters with a standard deviation of 567 milliters. What is the probability that a player consumed between 1,646 and 3,347 milliliters? Use the 68-95-99.7 normal distribution curve. 97.35% 81.5% 83.85% 81.3%

Solve the following system of equations. 2x² + 4y² = 132 5x² – 5y² = −45 Solution(s):

What is the area of a rectangle with vertices located at (-1, 1), (-1,-4), (5, -4), and (5, 1)? 20 square units 12 square units 15 square units 30 square units

Graph, label, and connect the following points: S(3, 2), D(6, 8), I(2, 8), and E(15, 2) to form polygon SIDE. a. Name the type of polygon. b. Find the length of the height. c. Find the area of the figure named SIDE. d. Calculate the lengths of segments SI and DE. e. Calculate the perimeter of SIDE. f. Find the slopes of SI and DE.

Which of the following most accurately describes the translation of the graph: y=(x-7)² + 16, from the origin (0, 0)? Select one: 7 units down, 16 units right 7 units up, 16 units right 16 units up, 7 units left 16 units up, 7 units right

Points (4, 5) and (10, 5) are vertices of a rectangle. The length of the rectangle is twice the width. The other vertices are located at (4,) and (10,). What could these ordered pairs be?

What is the image point of (9, 0) after a translation left 2 units and up 5 units?

The point H is plotted on the coordinate grid below. Plot the point H', the reflection of H over the x-axis. on the graph to plot a point.

Your candy factory makes Sticker Bars and N&N's. For each case of Stickers, you make $40 profit. For each case of N&N's, you make $55 profit. It takes 2 machine-hours to make Stickers and 5 man-hours to produce one case of candy. It takes 6 machine-hours to make N&N's and 4 man-hours to produce one case of candy. The total number of hours cannot exceed 150 machine-hours and 155 man-hours. Find the number of each type of candy that can be produced in order to maximize profit. Then determine the profit.

The number of hamburgers, and number of sodas, y, that Shaquile can purchase with $12 is represented by the inequality 4x + 2y ≤ 12 Which coordinate pair(s) (x, y) represent a possible number of hamburgers and sodas that Shaquile can purchase? Select all that apply.

f(x)=2x³+2x²-8x-8 If there is more than one answer, separate them with commas. Click on "None" if applicable.

The parent cosine function is shifted 5 units left, then vertically stretched by a factor of 4 and shifted up 2 units. Which statement is true about the graph of the transformed function? A. The midline is y = 2. B. The midline is y = 4. C. The midline is y = 8. D. The midline is y = 5.

Graph the solution to the following system of inequalities. 2x+5y>-20 -2x+7y<-21 Then give the coordinates of one point in the solution set.

Which of the following equations display= Select all that apply: r = 2sin θ+5θ T = -sinθ T = 5sin²θ+3cos²θ + 5sinθ+θ r = -sin²θ + 4θ+5 T = = -4cos²θ-sinθ + 2θ symmetry based on the test for θ = symmetry? Select all that apply.

Graph the linear equation by finding and plotting its intercepts. 9x - 4y = 36

ΔABC is reflected across the x-axis and then translated 4 units up to create ΔA'B'C. What are the coordinates of the vertices of ΔA'B'C? A. A'(-3, 3), B'(-1, 1), C'(-2, 3) B. A'(3, -3), B'(1, -1), C'(2, -3) C. A'(3, -5), B'(1, -7), C'(3, -5) D. A'(-3, 3), B'(-1, 1), C'(-2, -3)

Select the different types of transformations you can have with a function: Select one or more: a. Reflection about y axis b. Reflection about origin c. Reflection about x axis d. Horizontal Shifts e. Bolding f. Restriction g. Reflection about line y=x h. Shading i. Stretching j, Vertical Shifts k. Compression

Plot the point (0.5, -2.5) in a rectangular coordinate system. Indicate in which quadrant the point lies. Plot the point (0.5, -2.5) on the graph to the right.