Write an expression for the general or nth term, an, for the geometric sequence 3, 12, 48, 192, …..
> Combine like terms.
> Combine like terms.
> Combine like terms. 0.9(2.3x – 2) + 1.7(3.2x – 5)
> Combine like terms. 6(r – 3) – 2(r + 5) + 10
> Combine like terms. 2p - 4q - 3p + 4q - 15
> Combine like terms.
> Combine like terms. 4.7x - 6.1 + 8.2x
> Combine like terms. -0.2x + 1.7x - 4
> Reduce each fraction to lowest terms.
> (2). The symbol used to represent the set of real numbers is _________. (4). The equation 2 + 3 = 3 + 2 demonstrates the _________ property of addition. (6). The equation (2 + 3) + 4 = 2 + (3 + 4) demonstrates the __________ property of addition. (8). Th
> Combine like terms. -3x + 4x - 2 + 5
> Combine like terms. x - 4x + 3
> Combine like terms. -9x - 2x + 15
> Combine like terms. 8x - 5x
> Determine whether the given value is a solution to the equation. 2x2 - 4x = -6, x = -1
> Determine whether the given value is a solution to the equation. -2x2 + x + 5 = 20, x = 3
> Determine whether the given value is a solution to the equation. 7x - 1 = -29, x = -4
> Evaluate the expression for the given value(s) of the variable(s).
> Evaluate the expression for the given value(s) of the variable(s). -x2 + 3x - 10, x = -2
> Evaluate the expression for the given value(s) of the variable(s). 4x - 3, x = -1
> Evaluate the expression. Assume x ≠ 0. (a)-6x0b) (b)( -6x)0
> Determine whether the sequence is a Fibonacci type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence 0, π, π, 2π, 3π, 5π, …
> Determine whether the sequence is a Fibonacci type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence 2, 3, 6, 18, 108, 1944,……
> Draw a line of length 5 in. Determine and mark the point on the line that will create the golden ratio. Explain how you determined your answer.
> Find the ratio of the second to the first term of the Fibonacci sequence. Then find the ratio of the third to the second term of the sequence and determine whether this ratio was an increase or decrease from the first ratio. Continue this process for 10
> The eleventh Fibonacci number is 89. Examine the first six digits in the decimal expression of its reciprocal, 1/89. What do you find?
> Lucas Sequence (a) A sequence related to the Fibonacci sequence is the Lucas sequence. The Lucas sequence is formed in a manner similar to the Fibonacci sequence. The first two numbers of the Lucas sequence are 1 and 3. Write the first eight terms of the
> (a) Select any three consecutive terms of a Fibonacci sequence. Subtract the product of the terms on each side of the middle term from the square of the middle term. What is the difference? (b) Repeat part (a) with three different consecutive terms of th
> Twice any Fibonacci number minus the next Fibonacci number equals the second number preceding the original number. Select a number in the Fibonacci sequence and show that this pattern holds for the number selected.
> The greatest common factor of any two consecutive Fibonacci numbers is 1. Show that this statement is true for the first 15 Fibonacci numbers.
> The sum of any six consecutive Fibonacci numbers is always divisible by 4. Select any six consecutive Fibonacci numbers and show that for your selection this statement is true.
> Determine whether the statement is true or false. Modify each false statement to make it a true statement. 16 divides 2.
> Determine whether the sequence is a Fibonaccitype sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence
> Write the first five terms of the arithmetic sequence with the first term, a1, and common difference, d. a1 = -3, d = -4
> Determine r and a1 for the geometric sequence with a2 = 24 and a5 = 648.
> Sums of Interior Angles The sums of the interior angles of a triangle, a quadrilateral, a pentagon, and a hexagon are 180°, 360°, 540°, and 720°, respectively. Use this pattern to find a formula for the general term, an, where an represents the sum of th
> India’s Population Growth In 2014 India’s population was about 1.3 billion people. If India’s population is growing by about 1.2% per year, estimate India’s population in the year 2030. Round your answer to the nearest tenth of a billion people.
> A Bouncing Ball When dropped, a ball rebounds to four-fifths of its original height. How high will the ball rebound after the fourth bounce if it is dropped from a height of 30 ft?
> Samurai Sword Construction While making a traditional Japanese samurai sword, the master sword maker prepares the blade by heating a bar of iron until it is white hot. He then folds it over and pounds it smooth. Therefore, after each folding, the number
> Annual Pay Raises Rita is given a starting salary of $35,000 and promised a $1400 raise per year after each of the next 8 years. (a) Determine her salary during her eighth year of work. (b) Determine the total salary she received over the 8 years.
> A Bouncing Ball Each time a ball bounces, the height attained by the ball is 6 in. less than the previous height attained. If on the first bounce the ball reaches a height of 6 ft, find the height attained on the eleventh bounce.
> Determine the sum of the first 50 multiples of 3.
> Determine whether the number is rational or irrational. 0.212112111 …
> Determine the sum of the first 100 odd natural numbers
> Determine the sum of the first n terms of the geometric sequence for the values of a1 and r. n = 20, a1 = 4, r = 2
> Determine the sum of the first n terms of the geometric sequence for the values of a1 and r. n = 9, a1 = -3, r = 5
> Determine the sum of the first n terms of the geometric sequence for the values of a1 and r. n = 7, a1 = 1, r = 3
> Write an expression for the general or nth term, an, for the geometric sequence -3, 6, -12, 24, …..
> Write an expression for the general or nth term, an, for the geometric sequence
> Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r. Determine a7 when a1 = -3, r = -3.
> Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r.
> Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r. Determine a8 when a1 = 3, r = 4
> Reduce each fraction to lowest terms.
> Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r. a1 = -6, r = -2
> Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r.
> Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r. a1 = 2, r = 3
> Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given. -4, -11, -18, -25, ……. , -193; n = 28
> Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given. 5, 9, 13, 17, ……. , 101; n = 25
> Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given. 2, 4, 6, 8, ….. , 100; n = 50
> Write an expression for the general or nth term, an, of the arithmetic sequence. -7, -2, 3, 8, ……
> Write an expression for the general or nth term, an, of the arithmetic sequence. 3, 9, 15, 21, 27,…..
> Write an expression for the general or nth term, an, of the arithmetic sequence. 2,4,6,8,…
> Determine the indicated term for the arithmetic sequence with the first term, a1, and common difference, d.
> Evaluate the expression. Assume x ≠ 0. (a)(-6)0 (b)-(-6)0
> Determine the indicated term for the arithmetic sequence with the first term, a1, and common difference, d. Determine a12 when a1 = 7, d = -3.
> Determine the indicated term for the arithmetic sequence with the first term, a1, and common difference, d. Determine a10 when a1 = 9, d = -3.
> Determine whether the integers are closed under the given operation. Addition
> Determine whether the natural numbers are closed under the given operation. Division
> Describe three other activities that can be used to illustrate the associative property (see Exercises 69–74).
> Determine whether the activity can be used to illustrate the associative property. For the property to hold, doing the first two actions followed by the third would produce the same end result as doing the second and third actions followed by the first.
> Mowing the lawn, trimming the bushes, and removing dead limbs from trees
> Determine whether the activity can be used to illustrate the associative property. For the property to hold, doing the first two actions followed by the third would produce the same end result as doing the second and third actions followed by the first.
> Turning on a computer and sending an email on the computer
> Putting your wallet in your back pocket and putting your keys in your front pocket
> Use the sieve of Eratosthenes to find the prime numbers less than or equal to the given number. 150
> Use the distributive property to multiply. Then, if possible, simplify the resulting expression.
> Use the distributive property to multiply. Then, if possible, simplify the resulting expression.
> Use the distributive property to multiply. Then, if possible, simplify the resulting expression.
> Use the distributive property to multiply. Then, if possible, simplify the resulting expression. -4(3x – 5)
> Use the distributive property to multiply. Then, if possible, simplify the resulting expression. 8(3d – 5)
> Use the distributive property to multiply. Then, if possible, simplify the resulting expression. 8(b + 7)
> State the name of the property illustrated. g • (h + i) = (h + i) • g
> State the name of the property illustrated. (r + s) • t = (r • t) + (s • t)
> State the name of the property illustrated.
> State the name of the property illustrated. 4 • (11 • x) = (4 • 11) • x
> Determine whether the number is rational or irrational. π
> State the name of the property illustrated. c + d = d + c
> State the name of the property illustrated. 13 + 5 = 5 + 13
> Does a + (b • c) = (a + b) • (a + c)? Give an example to support your answer.
> Does the associative property hold for the integers under the operation of subtraction? Give an example to support your answer.
> Halfway between Two Numbers to find a rational number halfway between any two rational numbers given in fraction form, add the two numbers together and divide their sum by 2. Find a rational number halfway between the two fractions in each pair.
> Give an example to show that the associative property of multiplication may be true for the negative integers.
> Halfway between Two Numbers to find a rational number halfway between any two rational numbers given in fraction form, add the two numbers together and divide their sum by 2. Find a rational number halfway between the two fractions in each pair.
> Give an example to show that the commutative property of multiplication may be true for the negative integers.
> Income Tax Some states allow a husband and wife to file individual tax returns (on a single form) even though they have filed a joint federal tax return. It is usually to the taxpayers’ advantage to do so when both husband and wife work. The smallest am
> Dense Set of Numbers A set of numbers is said to be a dense set if between any two distinct members of the set there exists a third distinct member of the set. The set of integers is not Dense, since between any two consecutive integers there is not ano
> Write the first five terms of the arithmetic sequence with the first term, a1, and common difference, d. a1 = -11, d = 5
> Use proportions to solve the problem. 15 units of insulin from a vial marked U40
> Does the commutative property hold for the rational numbers under the operation of division? Give an example to support your answer.
> Use proportions to solve the problem. Speed Limit When Jacob crossed over from Niagara Falls, New York, to Niagara Falls, Canada, he saw a sign that said 50 miles per hour (mph) is equal to 80 kilometers per hour (kph). a) How many kilometers per hour ar
