Math Certify T

Three times the width of a rectangle plus five is the same as seven more than four times the width. If W is used to represent the width of the rectangle, which of the following expresses this relationship?

3w+5= 7+ 4w ~3W + 5 = 4W + 7. can also be 3w + 5 = 7 + 4w because of the commutative property

If 3y + 4x = 12, then what is the value of y in terms of x?

3y + 4x= 12 3y= -4x+ 12 y= 12-4x/3

Which counting technique method should be used to determine how many possibilities exist in forming a committee of six members in a high school that has 38 faculty members available to serve on this committee?

Combinations ~ Matrices are used to solve linear equations and are not a counting technique. ~ Permutations are used when a subset is formed from a set and order matters.

Amber's dog Mac eats approximately $85 of dog food in 2 weeks. How much will Amber spend on dog food in a year?

$2210 52/2=26, 85*26=2210

John is 12 years old. His Dad paid him $15 to mow the lawn 3 times last month. If he mows the lawn 5 times this month, using the properties of proportions how much can he expect?

$25

The phrase "add the two like terms and keep the sign of the largest" is a step in the algorithm of calculating ____________.

- ax + bx

Competency 003 Number Theory

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Competency 4 - Mathematical Reasoning

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What is the greatest common factor (GCF) in the following numbers? 6300 and 360

.180

Which of the following is not a prime number?

1 ~ The number one is neither a composite number nor a prime number. ~ A prime number is a natural number greater than one that has only two factors: itself and one.

The letters a, b, and c represent whole numbers greater than zero with a < b < c. Which of the following numbers is greatest?

C --- A ~ The quotient (result of division) of the largest number c by the smallest number a will yield the greatest value among the whole numbers a, b and c. The mathematical expression reads that b is greater than a and c is greater than b. Therefore c/a represents the largest number.

Given two even integers, a and b, determine what could be the least common multiple (LCM)?

ab ---- 2 ~ Of the choices given, ab⁄2 is the LCM. Since both numbers are even, both have factors of 2. So, the product can be reduced by 2. If the numbers have only one factor of 2 in either of them such as in 6 and 16, then 96 is the product and a multiple. However if 96 is reduced by 2, then 48 is the LCM.

Given the pattern shown above continues in the last two layers, use inductive reasoning to predict the pattern in the bottom layer of the triangle. 1, 1+1, 1+2+1, 1+3+3+1, 1+4+6+4+1, ........

1+6+15+20+15+6+1 ~1 + (1+4) + (4+6) + (6+4) + (4+1) + 1 ~1 + (1+5) + (5+10) + (10+10) + (10+5) + (5+1) + 1

What is the value of A/B+C if A /B = 5 and B/C = 2 ?

10/2=5 2/1=2 1+2=3

Write the equation of the line in standard form for a line through (3, 2) and parallel to 3x - 2y = 9.

3x-2y=5 -2y=9-3x y= 3/2x + 9/2 ~The slope of 3x - 2y = 9 is 3⁄2. Substituting m = 3⁄2 , x = 3, and y = 2 in the point-slope equation, the answer is y = 3⁄2 x - 5⁄2 . After writing this in standard form, the answer becomes: 3x - 2y = 5. ~Parallel lines have same slope. ~Negative reciprocal of the slope which would be for a perpendicular line application.

A shirt costs $49.99 plus 8.25% sales tax. What is the total cost of the shirt?

54.11 49.99* .0825=4.12. : 4.12 + 49.99=54.11.

Which of the following solves 5a⁄2 + 3b =7 for a.

5a⁄2 + 3b =7 5a +6b = 14 5a= 14- 6b a= 14- 6b/ 5

Sea-tac Airport in Seattle, WA, has a flight leaving for Dallas, TX every 2 hours and a flight leaving for Washington, D.C. every 45 minutes. At 5:00 A.M., on Monday, a flight to Dallas and a flight to Washington, D.C. leave at the same time. What is the next time that flights to Dallas and Washington, D.C. will leave at the same time?

6 hours @ 11:00 same day ~360 =LCD 120,240,360 5:45,6:30, 7:15, 8:00,8:45, 9:30, 10:15, 11:00

A parked oil barge off the Atlantic Coast is leaking oil. The oil is spreading over the water's surface in the shape of a circle. At any time t, in minutes after the start of the leak, the radius of the oil slick is r(t) = 4t feet. Let A(r) = p r 2. Which method below could also be used to find A(r) for t = {1, 3, 9, 27, 81}? (t). 1,,,,,,,, 3, ,,,,,,,9 r (t) 4, , ,12, , ,, 26 A(r). 50, 452, 4071

Geometric sequence with a ratio of 9

In reducing a fraction, which of the following ideas of number theory is used?

Greatest common divisor ~ The Fibonacci sequence is a sequence of numbers and has nothing to do with reducing a fraction. ~ The fundamental theorem of arithmetic deals with the fact that every composite number can be expressed as a unique product of its prime numbers.

Vickie is having her kindergarten class match each star with one moon by drawing one line from a star to a different moon. What type of matching relationship is this task?

Inverse functions Compared to x and y values being paired on coordinate plain.

Word problem: Troy and Walter are neighbors. They both have mowed their grass today. Troy mows his grass every 3 days. Walter mows his grass every 5 days. How many days will it be before they both mow their grass on the same day?

Least Common Multiple

In a proportion of 3/6 = 5/x , the linear equation of y=2x can be used to solve the proportion just as cross multiplication can be used to solve the problem. Can a linear equation of y = 2x + 1 be used to solve a proportion?

No ~Proportions are related by a factor and not by adding or subtracting a value to this.

Is the graph of a circle a function? Describe why or why not.

No. It does not pass the vertical line test. ~ Vertical line test determines if graph is a function ~ The horizontal line test is used to determine if a function has an inverse function. ~ The horizontal line test is used to determine if a function has an inverse function. are multiple vertical lines that can be drawn over the graph that will touch the graph in more than one place (two places to be exact), so the graph is not a function.

Divide 100 loaves between 10 men. Three of the men should receive double portions. How many portions does each of the ten men receive? This suggests that the ancient Egyptians had developed techniques for which of the following?

Solving algebraic equations in one variable ~ Analyzing the facts posed by the word problem one can conclude that one quantity (pick a variable to represent it) needs to be found (the single portion of loaf) to solve the problem.

Workers at a local factory make $8, $10, or $12.50 per hour. Each receives a $50 weekly gas allowance. Let h = hours and r= rate. Which expression can be used to represent the gross weekly pay of each individual?

hr + 50

Mary helps her mom wash dishes on nights that she does not have too much homework. Mary helped her mom wash dishes 3 times last week and earned $4.50. If Mary helps her mom wash dishes every night of the week, she earns $10.50 a week. Determine the slope of the linear equation that best models this scenario.

m = 1.5 ~3x=$4.50 7x= $10.50

Determine the choice that does not relate to the following: 10x + 5 A. expression B. Several employees in a small orchard make the same wages. This can be used to calculate the wages per day an employee makes given the hours he/she works each day. C. evaluated D. solve for the value of x

sole for the value of x ~A variable in an expression can never be solved for. It is independent. Any value may be substituted in for x.

The diagram shows the first two steps in modeling a computation involving numbers A and B using base-ten blocks. Which type of computation is being modeled with the blocks?

subtraction with regrouping

Which of the follow is NOT a proper way to denote multiplication? A. xy B. x9 C. 9x D. (a)(b)

x9 Should be written 9x

A math tutor decides there is a demand for her services. She offers tutoring sessions 3 times a week in 2-hour blocks. She pays $30 per hour for the rent of a room which covers utilities. The packets she provides for each student for the week with study material and examples cost her $5. Write her cost equation for each week and identify the marginal cost and fixed cost.

y = 5x + 180, marginal cost $5, and fixed cost $180. 3*2=6 hours, 6 hours*$30= $180+ 5x packet

. John is 12 years old. His Dad paid him $15 to mow the lawn 3 times last month. If he mows the lawn 5 times this month, using the properties of proportions how much can he expect? This particular problem could have been solved by developing a linear equation instead of using proportions. Determine the linear equation that can be used to solve this problem.

y = 5x+0 ~3x=15 5x=25

Which of the following solves 3x/4 - 8 = 2x/3 + 6?

~3(168)/4-8 504/4-8 126-8=118 2(168)/3+6 336/3+6 112+6=118

Given that a, b, and c are whole numbers, if a/b = 4 b/c =2 what is the value of what is the value of a/(b+c)?

~8/4=2 2/1=2 1+2=3