Answers LPS CR - Algebra II - APerforming Operations with Complex Numbers

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What is the rectangular form of the parametric equations x = 6t and y =?

y = StartFraction x squared Over 4 EndFraction

y = StartFraction x squared Over 9 EndFraction

y = StartFraction x Over 144 EndFraction

y = StartFraction x Over 9 EndFraction

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Eliminate the parameter in the equations y = t + 2 and x = . How can the rectangular equation be described?

cubic

linear

quartic

quadratic

Which conic section is represented by the following equation?–5x2 + 9xy + 5y2 + 6x – 4y + 11 = 0

circle

ellipse

parabola

hyperbola

A soccer ball on the ground was kicked with an initial velocity of 35 ft/sec at an elevation angle of 40°. Create a set of parametric equations to model the path of the soccer ball. Approximately how far had the soccer ball traveled when it hit the ground?

19 feet

26 feet

38 feet

52 feet

Convert 9x2 + 4y2 – 54x – 8y – 59 = 0 into standard form.

StartFraction (x + 3) squared Over 4 EndFraction + StartFraction (y + 1) Over 9 EndFraction = 1

StartFraction (x minus 3) squared Over 4 EndFraction + StartFraction (y minus 1) Over 9 EndFraction = 1

StartFraction (x + 3) squared Over 16 EndFraction + StartFraction (y + 1) Over 36 EndFraction = 1

StartFraction (x minus 3) squared Over 16 EndFraction + StartFraction (y minus 1) Over 36 EndFraction = 1

The graph of a hyperbola is shown.

9 units

12 units

18 units

24 units

A coach throws a football from a height of 4 feet with an initial velocity of 59 feet per second at an elevation angle of 45°. Which parametric equations represent the path of the football?

x(t) = 59sin(45o)t and y(t) = –16t2 + 59cos(45o)t

x(t) = 59cos(45o)t and y(t) = –16t2 + 59sin(45o)t

x(t) = 59cos(45o)t and y(t) = –16t2 + 59sin(45o)t + 4

x(t) = 59sin(45o)t and y(t) = –16t2 + 59cos(45o)t + 4

The foci and the vertices of the hyperbola are labeled.

= 1

Which rectangular equation represents the parametric equations x = and y = 4t?

y = 4x2, for x ≥ 0

y = one-fourth x squared, for x greater-than-or-equal-to 0

y = 16x2, for x ≥ 0

y = StartFraction 1 Over 16 EndFraction x squared, for x greater-than-or-equal-to 0

Eliminate the parameter in the equations x = and y = t – 4. How can the rectangular equation be described?

cubic

linear

quartic

quadratic

What is the rectangular form of the parametric equations x = 4 cos t and y = 5 sin t, where 0 ≤ t ≤ 2π?

StartFraction x squared Over 25 EndFraction + StartFraction y squared Over 16 EndFraction = 1

StartFraction x squared Over 16 EndFraction + StartFraction y squared Over 25 EndFraction = 1

StartFraction x squared Over 5 EndFraction + StartFraction y squared Over 4 EndFraction = 1

StartFraction x squared Over 4 EndFraction + StartFraction y squared Over 5 EndFraction = 1

A player hits a baseball with an initial velocity of 117 ft/sec at an elevation angle of 50°. When struck, the baseball is 2 feet above the ground. What is the maximum height the baseball reaches?

31 feet

126 feet

211 feet

421 feet

Which graph represents 9x2 – 16y2 – 54x + 64y – 127 = 0?

On a coordinate plane, an Ellipse has center (3, 2) and goes through (7, 2), (3, negative 1), (negative 1, 2), and (3, 5).

On a coordinate plane, an Ellipse has center (3, 2) and goes through (6, 2), (3, negative 2), (0, 3), and (3, 6).

Option

On a coordinate plane, one part of a conic graph goes through (negative 1, 6), has a vertex at (0, 2), and goes through (negative 1, negative 1). The second part goes through (7, 6), has a vertex at (6, 2), and goes through (7, negative 1).

Which graph represents the parametric equations x = t2 + 2t and y = –t, where –4 ≤ t ≤ 1?

On a coordinate plane, a curve starts at (3, negative 1), curves up through (0, 0) to (negative 1, 1), and curves up through (0, 2) and (3, 3).

On a coordinate plane, a curve starts at (negative 1, 1) and curves down through (0, 0) and (8, negative 2).

On a coordinate plane, a curve starts at (3, 1), curves down through (0, 0) to (negative 1, negative 1), and then curves down through (0, negative 2) to (8, negative 4).

Option

An ellipse has a center at the origin, a vertex along the major axis at (20, 0), and a focus at (16, 0). The equation of the ellipse is in the form below.

Review the graph of circle A.

(x – 1)2 + (y – 1)2 = 5

(x + 1)2 + (y + 1)2 = 5

(x – 1)2 + (y – 1)2 = 25

(x + 1)2 + (y + 1)2 = 25

An animation features an airplane flying in a straight line across the screen from (0, 10) to (45, 160) in 5 seconds. Which parametric equations represent the onscreen path of the airplane?

x(t) = 30t and y(t) = 9t

x(t) = 9t and y(t) = 30t

x(t) = 30t and y(t) = 9t + 10

x(t) = 9t and y(t) = 30t + 10

Which is the equation of an asymptote of the hyperbola whose equation is = 1?

y = −3x − 5

y = −3x − 7

y = 3x − 5

y = 3x + 7

The graph of an ellipse is shown.

Option

A soccer ball on the ground is kicked with an initial velocity of 37 feet per second at an elevation angle of 70°. Which parametric equations represent the path of the soccer ball?

x(t) = 37cos(70o)t and y(t) = –16t2 + 37sin(70o)t

x(t) = 37sin(70o)t and y(t) = –16t2 + 37cos(70o)t

x(t) = 37cos(70o)t and y(t) = –16t2 + sin(70o)t + 37

x(t) = 37sin(70o)t and y(t) = –16t2 + cos(70o)t + 37

What is the diameter of a circle with the equation (x – 4)2 + (y + 6)2 = 64?

Question text not available

= 1

An animation shows a beetle crawling in a straight line from the point (0, 10) to the point (28, 84) in 2 seconds. Write a pair of parametric equations to model the path of the beetle. Which point represents the location of the beetle 5 seconds after starting?

(38, 94)

(70, 195)

(80, 185)

(184, 269)

Which image shows a plane slicing a double-napped cone to produce a hyperbola?

2 cones are stacked at their points. A horizontal plane goes through the center of a cone.

2 cones are stacked at their points. A plane goes diagonally through the center of a cone.

2 cones are stacked at their points. A plane goes diagonally along the sides of the cones.

2 cones are stacked at their points. A plane goes diagonally through both cones.

Question text not available

x = −4.6 and x = 4.6

x = −3.5 and x = 3.5

y = −4.6 and y = 4.6

y = −3.5 and y = 3.5

Which features describe the graph of =1? Select two options.a focus at (104, 0)a focus at (0,−96)a vertex at (−40, 0)a vertex at (0, 96)the center at (0, 0)

a focus at (104, 0)

a focus at (0,−96)

a vertex at (−40, 0)

a vertex at (0, 96)

the center at (0, 0)

Which graph represents the parametric equations x = 1 – t2 and y = 2t, where 0 ≤ t ≤ 5?

On a coordinate plane, a curve starts at (1, 0) and curves up through (0, 2) to (negative 24, 10).

On a coordinate plane, a curve starts at (1, 0) and curves down through (0, negative 2) to (negative 24, negative 10).

On a coordinate plane, a curve starts at (1, 0) and curves down through (2, negative 2) to (26, negative 10).

On a coordinate plane, a curve starts at (1, 0) and curves up through (2, 2) to (26, 10).

A bicycle path starts 5 miles due east of an intersection, and continues in a straight line to finish 8 miles due north of the same intersection. Let the intersection be represented by the point (0, 0). Suppose a cyclist rides the path from start to finish in 2 hours. Which parametric equations model the path of the rider?

x (t) = negative five-halves t + 5 and y (t) = 4 t

x (t) = negative five-halves t + 5 and y (t) = 4 t + 8

x(t) = 5t + 2 and y(t) = 8t

x(t) = 5t and y(t) = 8t + 2

Which equation represents a parabola with its vertex at (1, –5) and its focus at (1, 0)?

= (x – 1)2

20(y + 5) = (x – 1)2

–20(y + 5) = (x – 1)2

= (x – 1)2

The equation represents a hyperbola centered at the origin with a focus of (0,-10). What is the value of b?

One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5). The center is (−1, −3).What is the equation of the hyperbola?

= 1

What is the positive slope of the asymptote of = 1? The positive slope of the asymptote is .

Answer not available

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