Exam 2

Solve for the indicated variable.

"r":√(w/k) = √(r^2) Simplifying further:√(w/k) = r So, the correct answer is r = √(w/k).

Solve the problem. Aliyah earned an $6,000 bonus from her sales job for exceeding her sales goals. After paying taxes at a 30% rate, she invested the remaining money in two stocks. One stock returned the equivalent of 10% simple interest after 1 yr, and the other returned 4% at the end of 1 yr. If her investments returned $240.00 (excluding commissions) how much did she invest in each stock

$3,000 at 4% and $1,200 at 10%

Solve the problem. 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?

$4,200.00

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?

$416

Solve the problem. If $13,000 is borrowed at 5.8% simple interest for 10 years, how much interest will be paid for the loan?

$7,540.00

Solve the absolute value inequality. Write the solution in interval notation. |2b - 23| > -15

(-∞, ∞)

Solve the inequality. Write the solution set in interval notation. 45y−16≥y+2545y−16≥y+25

(−∞,−176](−∞,−176]

Simplify and write the result in standard form, a + bi. 6−−18√−36−−18−3

-2 + i2-√2

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

-35 - 35i

Solve the problem The daily profit in dollars made by an automobile manufacturer is P(x) = -40xsq + 2,240x - 17,000 where x is the number of cars produced per shift. Find the maximum possible daily profit.

. $14,360

Solve the problem. A rectangular garden covers 46 yd^2 . The length is 3 yd longer than the width. Find the length and width. Round to the nearest tenth of a yard.

. length = 8.4; width = 5.4 yd

Write an absolute value inequality equivalent to the expression. "All real numbers whose distance from 0 is more than 82."

. |x| > 82

Solve the problem. A consultant traveled 255 miles to attend a meeting, traveling 45 mph hours for the first part of the trip, then increasing to a speed of 60 mph for the second part. If the entire trip took 5 hours, how far did the consultant travel at the faster speed?

120 mi

Solve the problem. The length of a rectangle is 4 yd more than twice the width x. The area is 390 yd^2 . Find the dimensions of the given shape.

13 yd. by 30 yd.

Solve the problem. The length of a rectangle is 4 yd more than twice the width x. The area is 390 yd . Find the dimensions of the given shape.

13 yd. by 30 yd.

Simplify the expression.

2

Solve the problem. It takes Terrell 69 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 49 minutes. How long would it take them working together? Round to the nearest tenth of a minute.

28.7 minutes

Simplify the expression. −25√9√−259

5353 i

Evaluate b2−4ac−−−−−−−√b2−4ac for the given values of a, b, and c, and simplify. a = 4, b = -2, and c = 7

6i3-√3

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

78

Solve the problem. One number is 33 more than another number. The quotient of the larger number and smaller number is 5 and the remainder is 1. Find the numbers.

8 and 41

Solve the problem. 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. Two campers hiking in Colorado boil water for tea. If the water boils at 196°F, approximate the altitude of the campers. Give the result to the nearest hundred feet.

8,700 ft

Solve the problem. Rita earns scores of 75, 82, 69, 82, and 67 on her five chapter tests for a certain class and a grade of 68 on the class project. The overall average for the course is computed as follows: the average of the five chapter tests makes up 55% of the course grade; the project accounts for 10% of the grade; and the final exam accounts for 35%. What scores can Rita earn on the final exam to earn a "B" in the course if the cut-off for a "B" is an overall score greater than or equal to 80, but less than 90? Assume that 100 is the highest score that can be earned on the final exam and that only whole-number scores are given.

92 through 100 inclusive

Write an absolute value inequality equivalent to the expression. "All real numbers whose distance from 0 is more than 82."

> 82

Solve the equation. −14x−16=−16(x+1)−112x−14x−16=−16(x+1)−112x

All real numbers

Solve the problem. Sparky has scores of 71, 60, and 69 on his first three Sociology tests. If he needs to keep an average of 70 to stay eligible for lacrosse, what scores on the fourth exam will accomplish this?

He must score 80 or higher

Solve for the indicated variable. T = cMN^2 for N^ 2

N^2 = T/CM (d)

Solve the problem. The length of the longer leg of a right triangle is 14 ft longer than the length of the shorter leg x. The hypotenuse is 6 ft longer than twice the length of the shorter leg. Find the dimensions of the triangle

Short leg = 10, long leg = 24, hypotenuse = 26

Solve the problem. The length of the longer leg of a right triangle is 14 ft longer than the length of the shorter leg x. The hypotenuse is 6 ft longer than twice the length of the shorter leg. Find the dimensions of the triangle.

Short leg = 10, long leg = 24, hypotenuse = 26

Solve the problem. How many gallons of gasoline that is 5% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 3% ethanol?

The correct answer is: 3,000

Determine whether the equation is a conditional equation, an identity, or a contradiction. y - 12 + 3y = 2y + 4

The correct answer is: Conditional

Solve the equation by using the square root property.

The correct answer is: {±5}

Solve the inequality. Write the solution set in interval notation. 20 > 3x and 11 + 2x ≥ 2

[−92,203)[−92,203)

A patio is configured from a rectangle with two right triangles of equal size attached at the two ends. The length of the rectangle is 38 ft. The base of the right triangle is 4 ft less than the height of the triangle. If the total area of the patio is 1,232 ft2, determine the base and height of the triangular portions.

base = 18 ft; height = 22 ft

Solve the problem. If $13,000 is borrowed at 5.8% simple interest for 10 years, how much interest will be paid for the loan?

d. $7,540.00

Solve for the indicated variable. m = h2kt2x for t > 0

t = mkx√hkxmkxhkx

Make an appropriate substitution and solve the equation. (3x + 7)^2 + 2(3x + 7) - 15 = 0

x = - 3 ??

Solve for the indicated variable -8x - 9y = 7 for y

y = −89x−79−89x−79

Solve the inequality. Write the solution set in interval notation. 98−5y<5498−5y<54 and 47y+1<91447y+1<914

{ }

Solve the equation by using the quadratic formula. t (t - 2) = -2

{1 ± i }

Solve the equation. 5v−4−8v+1=34v2−3v−45v−4−8v+1=34v2−3v−4

{1}

Solve the equation by using the quadratic formula. 0.49x2 = 0.28x - 0.04

{27}{27}

Solve the equation by using the quadratic formula. (3w - 2)(w - 1) = -3

{56−35√6i,56+35√6i}{56−356i,56+356i}

Solve the equation. - = -1

{7}

Solve the problem. Determine the set of values of x for which the radical expression would produce a real number.

{x | x ≤ 15}

Solve the equation

{±,± 6i}

Solve the equation. -5(w2 - 7)(w2 + 4)

{±7-√7 , ±2i}

Solve the equation. 4z4 + 68z2 + 225 = 0

{−52√2i,−32√2i,32√2i,52√2i,}{−522i,−322i,322i,522i,}