Algebra Questions

1 Find the slopes and the equations in slope intercept form of each line Slope 3 2 Equation Slope intercept form 1 Slope 3 2 1 Equation y A Slope 1 Ay Equation Slope Point form 2 3 XY

5 Find the equation of a line that passes through 5 2 and 1 3 in a point slope form b slope int form c general form

9 passes through the point 4 3 and is parallel to the line y 9 x 5

Make a scatter plot of the points in the table type of function from those below that would best represent the data X 5 3 2 5 6 8 10 Y1 65 23 12 15 32 78 140 The data is best represented by a quadratic function The data is best represented by an exponential function The data is best represented by a linear fung

Find the equation of a line in General Form 8 passes through the points 5 0 and 1 3

5 Graph the following lines A A line goes through the point 2 5 and has a slope of 4 3 b y 2 4 3 2 1 x 4 AX O 1 2 y x 3

Are the following lines Parallel Perpendicular or Neither Explain Line A passes through point 4 1 and 1 5 and line B passes through points 1 1 and 5 1 Line A passes through point 2 5 and 4 1 and line passes through points 7 0 and 1 4

Graph Using x and y intercepts 2x 3y 6 0 y 2x 4 2 3 AN

m m une m 3 Find the slopes of the lines that go through the points A 2 4 and B 5 1 parallel ml m parallel perpendicular ml perpendicular

You want to have 100 000 in an account after 30 years for your retirement Your investment counselor suggests that you make regular quarterly deposits into an annuity that pays 5 interest compounded quarterly Find the amount that must be deposited quarterly rounded to the nearest cent P 11 r nxt 11 288 90 68 39 40 95

Suppose 13 000 is deposited into a savings au interest compounded semi annually Find the balance in the account after 20 years Round to the nearest cent Use one of these formulas to solve the problem Future Value Present Value nt P 1 ht A 267 858 50 23 582 24 252 372 05 7 166 41 P A nt 1 2 ht

Listen In order to start a small business a student takes out a simple interest loan for 3 000 00 for 6 months at a rate of 7 50 How much interest must the student pay For simple interest A P 1 r t I P r t O 112 50 1 350 O 75 00 1 125 00

Listen I wish to have 12 000 in my account in 5 years to much money should I deposit now into my account earning 2 interest compounded quarterly Use one of the formulas below to solve the problem Future Value A P 1 1 xt Present Value P A 1 z nxt 13 258 75 10 860 75

Listen A manufacturer has total revenue given by the function R x 5 80x and has total cost given by C x 1 80x 76 where x is the number of units produced and sold How many units must be produced to break even 578 304 10 19

Find m2T n 10 T 10 S

Use the information given below to write an equation in the form y mx b for the average cost y of a math text book x years after 1990 Then use the equation to predict the average cost in 2016 Cost in Dollars 50 40 90 80 60 70 0 46 Average cost of a Math Textbook 4 70 4 5 6 Years after 1990 7

How much fencing is required to enclose a circular garden whose radius is 70 m round to the nearest meter 440 m 110 m 140 m 15 386 m

A 12 foot pole is supported by a wire that extends from the top of the pole to a point that is 16 feet from the base of the pole Use the Pythagorean Theorem to find the length of the wire 12 ft 24 feet 28 feet 14 feet 20 feet 16 ft

ht each kilogram of a person s weight 20 milligrams of a drug is to be given WE dosage should be given to a person who weighs 200 pounds Use 1 pound 0 45 kg Multiply by 10 for each step to the right X10 km hm dam m dm cm mm Divide by 10 for each step to the left 444 44 mg 4 000 mg 1 800 mg 8888 89 ma 10

Find m B D 10 C m B

Given x 0 simplify Vx27 completely

4 Graph the image of trapezoid EFGH after a dilation with a scale factor of 5 centered at the origin 10 8 6 4 2 104 8 6 4 2 F 24 4 6 8 E G 2 H 4 6 8 10 Vic Ver en esp

Write the coordinates of the vertices after a dilation with a scale factor of centered at the origin 10 d 6C 4 2 8 6 4 2 P 4 9 8 2 B 4 A6 8 AO 10 7

Find the indicated term of the geometric sequence 3 6 12 24 the 11th term The 11th term of the geometric sequence is

Write a formula for the general term the nth term of the arithmetic sequence a a2 a3 a4 Then use the formula for a to find ago the 20th sequence 5 0 5 10 OA 5n 100 OB 5n 100 O c 5n 10 90 OD 5n 10 110

Expand x 1 x 1 Simplify your answer

Find the nth or general term for the geometric sequence 4 4 4 Which represents the nth OA 4 1 1 OB 4 1 O c 40 1 OD 4 n 1

Evaluate 8 31 51 O A 56 O B 1D 5040 O c 8 O D 1

Simplify the sum State any restrictions on the variable y 1 y 2 y 9 y 9 Select the correct choice below and fill in the answer box es to complete your choice OA y 1 y 2 for y y 9 y 9 Simplify your answers Use a comma to separate answers as needed OB y 1 y 2 y 9 y 9 Simplify your answer for all values of y

Find the Least Common Multiply LCM of 3 4 and z z Do not add spaces in your answer LCM

Find the sum if it exists 24 12 6 Select the correct choice below and fill in any answer boxes in your choice OA The sum is Type an integer or a simplified fraction B The sum does not exist

2 3 X 6 x 5 Select the correct choice below and fill in any answer boxes within your choice Simplify your answer Use integers or fractions for any numbers in the expression Use a comma to separate answers as ne 2 3 OA x 6 x 5 OB 2 3 x 6 x 5 X www no numbers must be excluded

Add and simplify your answer Do not add spaces in your answer 3x 2 5x 7

Find the nth or general term for the geometric sequence 4 4 4 4 Which represents the nth term OA 4 1 1 OB 4 n 1 OC 4 1 OD 4 1

Find the indicated term of the geometric sequence 2 4 8 16 the 9th term The 9th term of the geometric sequence is

Write a formula for the general term the nth term of the arithmetic sequence a a2 a3 a4 Then use the formula for an to find azo the 20th term of the sequence 5 0 5 10 OA 5n 10 90 OB 5n 100 C 5n 10 110 D 5n 100

Evaluate 8 31 51 O A 1 5040 OB 1 C 8 OD 56

Find the sum of the first 32 terms of the arithmetic series 4 13 22 31 32

Write a formula for the general term the nth term of the arithmetic sequence a a2 a3 a4 Then use the formula for an 5 0 5 10 OA 5n 10 110 B 5n 100 O C 5n 10 90 O D 5n 100 to find a20 the 2

Evaluate 8 3 5 OA 56 OB 8 O C 1 5040 O D 1

rigonometric Patios find an Find mZD D 47 E

Find the first term and the common difference 3 1 1 3 a d

Find the nth or general term for the geometric sequence 5 6 6 6 Which represents the nth term OA 6 1 1 OB 6 1 OC 6 1 OD 6 n 1

Find the sum of the first 53 terms of the arithmetic series 36 38 40 42 S53

Find m2V X 12 3 W mzv 12

Find mLX W 33

Find mZV V mZV Submit 3 26 W 3 13 X

2 Determine if each of the following is a group a monoid that is not a group a semigroup that is not a monoid or not a semigroup Explain your answer for each one Z addition on the set of positive integers It farms bernise a group It satisfies closure associativity identity element and every element has an inverse ii Q subtraction on the set of rational numbers This is not a semigroup because the set of rational numbers under subtration isn t closed under subtraction iii C32 addition on a 32 hour clock It satisfies Closure associativity identity element and every element has an in verse It forms a group iv C15 0 multiplication on a 15 hour clock with 0 removed This doesn t form a group or monoid Not element has an inverse every v 0 0 1 0 1 U the set is P 0 1 and the operation is union a semigroup but not a monoid This is on the power set of 0 1 forms a sem igroup The set is closed under the union operation which is associative It doesn t have an identity element so it s not a mencid vi 0 1 2 where x y y for example 0 2 2

1 3 Multiply Rational Expressions Simplify each expression 35m 65n 10 28n 4n 1 A 10n n 1 3 n 3 n 1 3 C 21n 53n 8 6n 13n 8 A 2 5n 3 C70 B Sn B D 3n 50n 80 n 1 n 9 3 An n 8 20n 10n 42n 6 9 5n 9 n 2 2 4 his reserved 2 7r 70 5r 39r 54 35r 42 10r A 4 C r 1 r 8 7 6 r 3 B v 3 A 7 C v 9 v 4 6v 35v 5 63y 9v 5v 45 r 10 r 9 10r D r 5 2 3 v 9 D 7 v 6 B

9 9 6b 3b 5b 13b 6 3b 9 5b 22b 8 A B b 3 1 b b 4 7 b 8 b 3 b 9 C 18 D 186 10 10 3a 6 21a 66a 48 A C 2 5 a 8 10 a 1 9 14a 16 5a 40 3a a 8 B D a 1 27a