Algebra Questions

Evaluate the following expression 3 14 7 3 3 14 7 3 Simplify your answer

Evaluate the following expression 875 335 695 285 875 335 695 285 Simplify your answer

Evaluate the following expression 7 15 5 7 15 5 Simplify your answer

Find the value of the expression 64 24 64 24 Simplify your answer

Evaluate the expression 20 47 20 47 Simplify your answer

Find the value of the following expression 35 147 35 147 Simplify your answer

wer to a subtraction problem is called the sum difference product

The additive inverse of 9 is 5 Type an integer or a fraction

Determine the additive inverse of the real number 5 72 The additive inverse of 5 72 is Type an integer or a decimal

What is the additive inverse of 3 The additive inverse of 3 is

Use absolute value to find the following sum 6 9 6 9 Simplify your answer

Express the data pictured in the graph as ordered pairs letting the first coordinate represent the year and the second coordinate the amount What is the ordered pair for the first bar on the graph billion Sales in billions 40 32 30 20 13 10 22 2000 2001 2002

The points 7 1 and 6 8 are the endpoints of the diameter of a circle Find the length of the radius of the circle The length of the radius is Round to the nearest hundredth as needed www

Find the midpoint of the segment with the given endpoints 5 5 2 8 2 3 and The midpoint is Type an ordered pair Simplify your answer Type an integer or a fraction

Question 5 Construct three different quadratic forms over R that has a matrix representation with eigenvalues 2 1 Answer

Find the distance between the points Give an exact answer and an approximation to three decimal places 5 4 and 8 7 The exact distance is Simplify your answer Type an exact answer using radicals as neede

Find the coordinates of the point shown on the graph What are the coordinates of the point Type an ordered pair 5

Find the angle in degrees rounded to one decimal 0 7 19

Find the exact value of the expression cos tan cos tan 4 1 1 3 4 3 COS 7 25 Simplify your answer including any radicals expression COS 1 1 7 25

1 2 Use the auxilliary equation to find three solutions of the following difference equation yk 37yk 2 7yk 1 15yk 0 for all k Find a basis for the solution space of the equation in Question 1 2 Justify your answer by referring to the appropriate theorems

Use the Laws of Logarithms to rewrite the expression below in a form with no logarithm of a product quotient or power log4 x x 9

year Initial cost P Annual M O year Refurbishment cost Trade in value S of P Life years A 15 000 6 000 0 20 4 B 20 000 9 000 2 000 every 4 years 40 12 5 Company X has two options A and B for the manufacture of switches The estimated cash flows for each option are given below Use an annual worth comparison to determine which option is preferable at an interest rate of 20 per year First cost Annual cort ar A 30 5 B 10 12

Solve the equation 2 4 8x 6 1 using two different methods Which method do you prefer Explain

1 25 points Let A B 0 b 1 1 2 a Use the Cramer s rule to find the solution to Ax b b Use the Gaussian elimination to find the solution to Ax b c Give the LU decomposition of A d Use the inverse of A to find the solution to Ax b e Let B 2 3 Give the eigenvalue decomposition of B diagonalization

Equations When a new charter school opened in 1990 there were 820 students enrolled Using function notation write a formula representing the number N of students attending this charter school t years after 1990 assuming that the student population N t a Decreases 30 students per year b Increases 17 per year c Increases 8 3 per year d Decreases 8 6 per year e Remains constant does not change g Increases 46 students per year N t N t N t N t N t

7 cm 16 cm 6 cm

3 Neville and Luna go to a used book sale where every book is the same price Neville buys 5 books and Luna buys 4 books They run into their friend Hermione who really loves to read and discover that she has bought 19 books Hermione received a 10 discount but she still spent 5 more than Neville and Luna combined How much does one book cost

Houghton Mifflin Harcourt Publishing Company A relation is a set of ordered pairs x y where x is the input value and y is the output value The domain is all possible inputs of a relation and the range is all possible outputs of a relation For example the given relation represents the number of whole wheat cracker boxes sold and the money earned 1 4 2 8 3 12 4 16 Domain 1 2 3 4 Reflect Range 2 12 16 For the following relation the input x is the ages of boys and the output y is their corresponding height in inches 1 41 8 45 9 49 10 52 10 53 11 55 12 59 B Fill the values in the table Plot the points on the graph Complete the mapping diagram E State the dornain of the relation State the range of the relation Height in 60 50 40 30 20 10 0 8 9 10 11 12 X 10 Age yr ID 2 4 6 Age yr Height in 41 45 49 52 53 55 59 45 419 52 Fr 8 10 12 nhrr 19 appears twice in the x column of the table How many times is it written in

36 Consider the following graph State the equation of the function in the forms y asin b x c d and YA 0 t y acos b x c d t 3 2 X

Find the least common denominator LCD of the rational numbers the LCD Septyn Step 1 Find the least common denominator of the fractions 50 2 5 14 2 7 Type your answer in factored form 9 50 Step 2 Rewrite each fraction with the least common denominator 9 7 50 7 Do not sikeplify 9 50 LCD 2 5 5 7 Write the common factors then write the remaining fac 350 and Write each denominator as the product of prime factors 1 14 9 Multiply the numerator and denominator of 50 by 7

Determine if the given number belongs to the set Whole 1 78778777 Natural Integers Rational Irrational Real

Replace the with the correct symbol 63 7 63 9

Replace the question mark by or whichever is correct 3 3 N 4 3 4

Determine if the given number belongs to the set Natural 5 6 5 6 Natural Yes Whole Whole Integers Integers Rational Rational Irrational Irrational Real Real

Replace the with the correct symbol 6 11 5 7

Determine if the given number belongs to the set 50 25 Natural Yes No Whole Integers Rational Irrati

Determine if the given number belongs to the set 6 Natural Yes Whole Integers Rational Irrational

Replace the with the correct symbol 3 4 11

Replace the with the correct symbol 1 13 0 08

Determine whether the statement is true or false 3 2 1 5 Is the statement true or false O True O False

Determine whether the statement is true or false 7 7 Is the statement true or false O False O True

Fill in the blank below The symbols and are called absolute values

Replace the question mark by or whichever is correct 3 8 0 4 0 4

In the following problem replace the question mark with or whichever is correct 6 30 25 6 5 5 30 25

The point on the real number line whose coordinate is 0 is called the scale

For males in a certain town the systolic blood pressure is normally distributed with a mean of 135 and a standard deviation of 5 Using the empirical rule determine the interval of systolic blood pressures that represent the middle 99 7 of males

List all elements of the set Select all that apply A 5 3 53 3 C 0 E 8 737717 that are also elements of the set of integers 8 0 6 2 7377377 B 6 D 2 73773777 F No elements in the set are in the set of integers

List the numbers in the given set that are whole numbers 13 5 5 7 0 12 1 42 x 6 Select all that apply A 0 C 5 E T G 7 6 00 B 5 D 13 2 F 1 42 H There are no whole num

Use the number 33 a List all the prime numbers that must be checked for divisibility b Determine whether the number is prime or composite a Choose the correct answer below OA 2 3 5 7 8 OB 2 3 5 OC 2 3 D 2 3 5 6

List all elements of the set Select all that apply A 0 C 10 E 9 9 0 10 5 73773777 that are also elements of the set of natural numbers 3 B 5 73773777 D 8 3 F No elements in the set are in the set of natural numbers