Answers SS26 Math 3 S2 M3960OXModeling with Systems

Unit Test Answers

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Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. If the prices are the same at both concession stands, what is the price of a hot dog?

$0.40

$2.50

$3.75

$4.00

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Solve for in the equation .

x = 3 plus-or-minus StartRoot 23 EndRoot

x = 3 plus-or-minus StartRoot 51 EndRoot

x = 3 plus-or-minus StartRoot 41 EndRoot

x = 3 plus-or-minus StartRoot 5 EndRoot

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

y = negative 6 (x minus 1) squared + 8

y = negative 6 (x + one-fourth) squared + thirteen-eighths

y = negative 6 (x minus one-fourth) squared + nineteen-eighths

y = negative 6 (x minus one-half) squared + seven-halves

The table below shows the data for a car stopping on a wet road. What is the approximate stopping distance for a car traveling 35 mph? Car Stopping Distancesv(mph)d(ft)1517.92031.850198.7

41.7 ft

49.7 ft

97.4 ft

115.3 ft

Which quadratic inequality does the graph below represent?

mc012-2.jpg

mc012-3.jpg

mc012-4.jpg

mc012-5.jpg

When graphed, which parabola opens downward?

y = –3x2

y = (x – 3)2

y = one-third x squared

y = x2 – 3

Which equation represents a graph with a vertex at (1, –6)?

y = 3x2 + 6x – 3

y = 3x2 – 6x – 3

y = 3x2 – 8x – 1

y = 3x2 – 3x – 6

Which expression is equivalent to (4 + 6i)2?

–20 + 48i

8 + 12i

16 – 36i

20 + 48i

Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?

mc007-1.jpg

mc007-2.jpg

mc007-3.jpg

mc007-4.jpg

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction 2 StartRoot 15 EndRoot Over 11 EndFraction

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot Over 11 EndFraction

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot i Over 11 EndFraction

Which pair of complex numbers has a real-number product?

(1 + 3i)(6i)

(1 + 3i)(2 – 3i)

(1 + 3i)(1 – 3i)

(1 + 3i)(3i)

Gabriella is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by where x and y are measured in inches. Where should she place the bulb to ensure a perfect beam of light?

6.5 in. to the left of the vertex

6.5 in. above the vertex

6.5 in. to the right of the vertex

6.5 in. below the vertex

An egg is dropped from a height of 90 ft. If acceleration due to gravity is –16 ft/s2 and initial velocity is 0 ft/s, approximately how long will it take for the egg to reach the ground?h(t) = at2 + vt + h0

1.9 s

2.4 s

9.7 s

40.7 s

Tim throws a stick straight up in the air from the ground. The function h = –16t2 + 48t models the height, h, in feet, of the stick above the ground after t seconds. Which inequality can be used to find the interval of time in which the stick reaches a height of more than 8 feet?

–16t2 + 48t > 8

–16t2 + 48t < 8

–16t2 + 48t ³ 8

–16t2 + 48t £ 8

Which equation is an example of the commutative property of multiplication?

(4 + 2i) = (2i + 4)

(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)

(4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)(1)

(4 + 2i) = (4 + 2i + 0)

If the discriminant of a quadratic equation is 4, which statement describes the roots?

There are two complex roots.

There are two real roots.

There is one real root.

There is one complex root.

For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?

m greater-than negative StartFraction 25 Over 8 EndFraction

m less-than negative StartFraction 25 Over 8 EndFraction

m less-than StartFraction 25 Over 8 EndFraction

m greater-than StartFraction 25 Over 8 EndFraction

What is one solution of the following system?

(–6, 0)

(–2, 4)

(0, –6)

(4, –2)

Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. Which ordered pair generated by this model should be discarded because the values are unreasonable?

(–4, 1)

mc006-1.jpg

mc006-2.jpg

(6, 0)

For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?

During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?

the height of the bird and the ball when the ball and the bird are the same distance from the player

the height of the bird and the ball when the player hits the ball

the time when the height of the ball and the bird are the same

the time when the ball and the bird hit the ground

Rene is designing a satellite that is the shape of a parabola that opens upward with a diameter of 8 in. and a depth of 2 in. The feed antenna focuses the incoming radio waves. At what point should the feed antenna be placed?

(–8, 0)

(–2, 0)

(0, 2)

(0, 8)

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

Option

Samara is adjusting a satellite because she finds it is not focusing the incoming radio waves perfectly. The shape of her satellite can be modeled by where x and y are modeled in inches. She realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite?

(–3, –6)

(–3, –4)

(3, 6)

(6, 3)

What are the values of x in the equation x2 – 6x + 9 = 25?

x = –2 or x = 8

x = –1 or x = –11

x = 1 or x = 11

x = 2 or x = –8

A store owner puts in an order for product X and product Y for a total of 4,000 units. It costs $0.10 per item to ship of product X and $0.04 per item to ship product Y. If the total shipping cost is $352, which system of equations can be used to determine how much of product X and product Y the store owner bought?

StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2nd Row 10 x + 4 y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row 10 x + 4 y = 4,000 2nd Row x + y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2ndRow 0.1 x + 0.04 y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row 0.1 x + 0.04 y = 4,000 2nd Row x + y = 352 EndLayout

During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation y = –0.01x2 + 0.32x + 4. The path of pumpkin B is modeled by the equation y = –0.01x2 + 0.18x + 5. If x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?

the height at which the pumpkins reach their greatest horizontal distance from the launch site

the horizontal distance of the pumpkins from the launch site when they reach the ground

the starting height of the pumpkins when they are at the launch site

the horizontal distance of the pumpkins from the launch site when their heights are the same

When graphed, which parabola opens downward?

y = –3x2

y = (x – 3)2

Option

y = x2 – 3

If the discriminant of a quadratic equation is 4, which statement describes the roots?

There are two complex roots.

There are two real roots.

There is one real root.

There is one complex root.

Which system is equivalent to

StartLayout Enlarged left-brace 1st row 5 minus x = 9 x squared 2nd row y = 5 minus x EndLayout

StartLayout Enlarged left-brace 1st row y = 9 y squared minus 90 y + 225 2nd row x = y minus 5 EndLayout

StartLayout Enlarged left-brace 1st row 5 + x = 9 x squared 2nd row y = 5 + x EndLayout

StartLayout Enlarged left-brace 1st row y = 3 x 2nd row x + 3 x = 5 EndLayout

Dimitri is solving the equation x2 – 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

100

What is the sum of 12 – 5i and –3 + 4i?

–16 + 63i

9 – i

9 – 9i

15 – 9i

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