Question: Solve the equation. /
Solve the equation.
> Evaluate the expression. Assume x ≠0.
> Determine whether the statement is true or false. Modify each false statement to make it a true statement. 49 is a factor of 7.
> 2. The numbers that form a sequence are called its _________. 4. The amount by which each pair of successive terms differ in an arithmetic sequence is called the common _________. 6. The constant found by dividing any term in a geometric sequence by the
> Evaluate the expression.
> Convert each mixed number to an improper fraction.
> Evaluate the expression. Assume x ≠ 0. ( a) -5-2 (b) (-5)-2
> Determine whether the statement is true or false. Modify each false statement to make it a true statement. 48 is a multiple of 8.
> P = i2r; determine r when p = 62,500 and i = 5(electronics).
> Determine the volume of the block shown in Fig. 6.2, excluding the hole. The formula for the volume of a rectangular solid is V = lwh. The formula for the volume of a cylinder is V = πr2 h.
> Determine whether the number is rational or irrational.
> Volume of an Ice-Cream Cone An ice-cream cone is filled with ice cream to the top of the cone. Determine the volume, in cubic inches, of ice cream in the cone if the cone’s radius is 1.5 in. and the height is 7 in. (See the figure.) The
> Savings Account Christine borrowed $5200 from a bank at a simple interest rate of 2.5% (or 0.025) for one year. (a) Determine how much interest Christine paid at the end of 1 year. (b) Determine the total amount Christine will repay the bank at the end o
> Solve for the variable indicated. A = P(1 + rt) for t
> Solve for the variable indicated. C= 5/9(F – 32) for F
> Solve for the variable indicated.
> Solve for the variable indicated. y = mx + b for x
> Solve for the variable indicated. V = 1/3πr2 h for h
> Solve for the variable indicated. C= 2 πr for r
> Solve for the variable indicated. P= a + b + S 1 + S2 for S1
> Solve for the variable indicated. V = lwh for w
> Reduce each fraction to lowest terms.
> Solve the equation for y 10x - 3y = 0
> Solve the equation for y -9x + 4y = 11
> Solve the equation for y 4x - 2y = 10
> Determine A when P = 100, r = 6% (or 0.06) n = 1, and t = 3 (banking).
> P = nRT/V; determine V when P = 12, n = 10, R = 60, and T = 8 (chemistry).
> c =√a2 + b2; determine c when a = 5 and b = 12 (geometry).
> X= ;determine x when a = 2,b = -5, and c = -12 (mathematics).
> Determine z when x = 66, m = 60, s = 15, and n = 25 (statistics).
> C = 5/9 (F – 32); determine C when F = 77 (temperature conversion)
> V = 1/3 πr2. h; determine h when V = 47.10 and r = 3 (geometry).
> Evaluate the expression. Assume x ≠ 0. (a) 5-1 (b) 2-4
> Determine h when A = 36, b1 = 4, and b2 = 8 (geometry).
> M = a + b + c/3 ; determine a when m = 85, b = 77, and c = 92 (statistics).
> S = 4lw + 2wh; determine l when S = 336, w = 8, and h = 9 (geometry).
> A = π(R2 - r2 ); determine A when R = 5 and r = 4 (geometry).
> Evaluate the expression for the given value(s) of the variable(s). 4x - 7, x = 5
> Evaluate the expression for the given value(s) of the variable(s). -x3, x = -4
> Evaluate the expression for the given value(s) of the variable(s). -x2 , x = -1
> Evaluate the expression for the given value(s) of the variable(s). x2 , x = 8
> Does (x + y)2 = x2 + y2 ? Complete the table and state your conclusion.
> Height of a Diver A diver jumps from a platform diving board that is 32 feet above water. The height, h, of the diver above water, in feet, t seconds after jumping from the platform, can be determined by the equation h = -16t 2 + 20t + 32. Determine the
> Determine whether the statement is true or false. Modify each false statement to make it a true statement. 36 u 9
> Cost of a Tour The cost, c, in dollars, for Crescent City Tours to provide a tour for x people can be determined by the equation c = 220 + 2.75x. Determine the cost for Crescent City Tours to provide a tour for 75 people.
> Solve the equation. 41t - 32 + 8 = 412t – 62
> Solve the equation. 6x + 8 - 22x = 28 + 14x - 10 + 12x
> Solve the equation.
> Solve the equation. 61t + 22 - 14 = 6t - 2
> Solve the equation. 31x + 22 + 21x - 12 = 5x - 7
> Solve the equation. 6t - 7 = 8t + 9
> Solve the equation. 5x + 0.050 = -0.732
> Solve the equation.
> Determine whether the number is rational or irrational. 3.14159
> Solve the equation. 25 = 4x + 5
> Solve the equation. y - 4 = 13
> 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
