(Solution) MAT101 Graded Exam 2 Polynomial and Other Equations

MAT101 Graded Exam 2

Solve the rational equation.

Solve for the indicated variable.

L = 1/3πq²s for s

Question 3
In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The boiling temperature of water T (in °F) can be approximated by the model T = -1.83a + 212, where a is the altitude in thousands of feet. Determine the temperature at which water boils at an altitude of 9,000 ft. Round to the nearest degree.

The Correct Answer is 196 °F

To determine the temperature at which water boils at an altitude of 9,000 feet, the given formula is:

T=−1.83a+212

where T is the temperature in °F and a is the altitude in thousands of feet. Since the altitude is 9,000 feet, we can set a=9 (because 9,000 feet is 9 thousand feet).

Now, substitute a=9 into the formula:T=−1.83(9)+212

T=−16.47+212

T=195.53

Question 4

The property tax on a $160,000.00 house is $2,400.00. At this rate, what is the property tax on a house that is $280,000.00?

Correct Answer 4,200

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Two cars are 261 miles apart and travel toward each other on the same road. They meet in 3 hours. One car travels 3 mph faster than the other. What is the average speed of each car?

Select one:

a.42 mph; 45 mph

b.41 mph; 44 mph

c.39 mph; 42 mph

d.40 mph; 43 mph

Question 6

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Solve the problem.

Suppose that a merchant buys a patio set from the wholesaler for $260. At what price should the merchant mark the patio set so that it may be offered at a discount of 25% but still give the merchant a 20% profit on his $260 investment?

Select one:

a.$325

b.$416

c.$312

d.$377

Question 7

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Perform the indicated operation. Write the answer in the form a + bi.

(6 + −9−−−√−9)(8 – −9−−−√−9)

Select one:

a.

57 – 2i9–√9

b.39

c.39 + 2i9–√9

d.57 + 2i9–√9

Question 8

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Perform the indicated operation. Write the answer in the form a + bi.

(-5 – 9i)(6 + 6i)

Select one:

a.-84 – 84i

b.24 – 84i

c.24

d.-30 – 54i

Question 9

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Perform the indicated operation. Write the answer in the form a + bi.

7i(-5 + 5i)

Select one:

a.35 – 35i

b.-30i

c.-35 – 35i

d.-70i

Question 10

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Solve the quadratic equation by completing the square and applying the square root property.

n² + 18n = -75

Select one:

a.{-9 – 249−−−√249, -9 + 249−−−√249} 

b.{−18−249√2,−18+249√2}{−18−2492,−18+2492}

c.{-9 – 6–√6, -9 + 6–√6}

d.{9 – 6–√6, 9 + 6–√6}

Question 11

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Solve the equation by using the quadratic formula.

y² = 4y – 9

Select one:

a.{-4 ± 2i 5–√5}

b.{- 2 ± i 5–√5}

c.{4 ± 2i 5–√5}

d.{2 ± i 5–√5}

Question 12

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Solve the equation by using the quadratic formula.

5y – 6 + 50y² = 0

Select one:

a.{35±2,791√5i}{35±2,7915i}

b.{13,25}{13,25}

c.{52,−103}{52,−103}

d.{−25,310}{−25,310}

Question 13

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Solve the problem.

A model rocket is launched from a raised platform at a speed of 176 feet per second. Its height in feet is given by
h(t) = -16t² + 176t + 20 (t = seconds after launch).
After how many seconds does the object reach its maximum height?

Select one:

a.2.75 seconds

b.7.5 seconds

c.20 seconds

d.5.5 seconds

Question 14

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Solve the problem.

The width of a rectangular box is 4 in. The height is one-fifth the length x. The volume is 180in2180in2. Find the length and the height of the box.

Select one:

a.length = 4 in.; height = 20 in.

b.length = 20 in.; height = 4 in.

c.length = 3 in.; height = 15 in.

d.length = 15 in.; height = 3 in.

Question 15

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Solve the equation by using substitution.

(t + 3)² – (t + 3) – 12 = 0

Select one:

a.{4, -3}

b.{1, -6}

c.{-7, 0}

d.{-1, 6}

Question 16

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Make an appropriate substitution and solve the equation.

(3x + 7)² + 2(3x + 7) – 15 = 0

Select one:

a.{−23,−43}{−23,−43}

b.{−4,−43}{−4,−43}

c.{−23,−103}{−23,−103}

d.{−4,−103}{−4,−103}

Question 17

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Solve the equation.

100x³ + 25x² + 4x + 1 = 0

Select one:

a.{−14}{−14}

b.{−14,±15i}{−14,±15i}

c.{−14,±15}{−14,±15}

d.{−4,±5}{−4,±5}

Question 18

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Solve the compound inequality. Graph the solution set, and write the solution set in interval notation.

−1≤2x+33<4−1≤2x+33<4

Select one:

a.(−3,92](−3,92]

b.(−∞,−3)(−∞,−3) U [92,∞)[92,∞)

c.(−∞,−3](−∞,−3] U (92,∞)(92,∞)

d.[−3,92)[−3,92)

Question 19

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Solve the inequality. Write the solution set in interval notation.

-2(4y – 7) + y ≥ 2y – (-8 + y)

Select one:

a.(34,∞)(34,∞)

b.(−∞,34)(−∞,34)

c.(−14,∞)(−14,∞)

d.(−∞,34](−∞,34]

Question 20

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Solve the problem.

The width of a rectangle is fixed at 30 cm, and the perimeter can be no greater than 170 cm. Find the maximum length of the rectangle.

Select one:

a.70 cm

b.55 cm

c.110 cm

d.140 cm

Related: (Solution) MAT101 Graded Exam #3 Graphing Polynomial Functions

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