INTRODUCTION From natural gas‚ crude oils‚ and other fossil materials such as coal‚ few intermediates are produced that are not hydrocarbon compounds. The important intermediates discussed here are hydrogen‚ sulfur‚ carbon black‚ and synthesis gas. Synthesis gas consists of a nonhydrocarbon mixture (H2‚CO) obtain- able from more than one source. It is included in this chapter and is fur- ther noted in Chapter 5 in relation to methane as a major feedstock for this mixture. This chapter discusses
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Working with algebra you must understand why the properties of real numbers are so important. I will demonstrate my solutions to three problems and I will include my mathematical work. Also I will use five vocabulary words that help me find solutions to the problems. Properties of real numbers are useful for simplifying algebraic expression because a lot of thing we do in life are equations. We use a lot of mathematical terms in the real world. Lastly I will show every step I took to simplify and
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COMPETENCY 2 1). Simplify the expression by combining like terms. 5x - y - 2x + 3y a) 3x + 2y b) 2x –y c) x - y d) None of these 2. Use the distributive property to evaluate the expression. 3( x – 3 – 2y) a) 3x - 9 + 2y b) x –y c) 3x - 9 -6y d) None of these 3. Perform the indicated operation: a) b) c) d)
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CHAPTER 4: VARIABLES AND ARITHMETIC OPERATION 1. Name three numeric data types that can contain a decimal point. 2. Write a Dim statement for each of the following variables using the variable type and variable name that would be best for each value. a. Population of the Philippines b. Your weekly baon c. The smallest data type you can use for your age. d. A constant for the first initial of your first name e. The minimum allowance in a month f. The name of the city in which you live g. The answer
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Simplifying Expressions 2a(a-5)+4(a-5) The given expression. a*2 Multiply a and 2. 2a^2 2*a*2 = 2a^2. 2a^2*a-5 The distributive property removes the parenthesis. 2a × -5 = -10a Multiply 2a by -5=-10a. -10a 2a^2-10a + 4(a-5) Use the distributive property to remove the parentheses. 4*a= 4a 4*-5= -20 Multiply 4 by a-5. 4 × a = 4a 4*-5=-20 Multiply 4 by a‚ and 4 by -5 4a-20 2a^2-10a + 4a -20 Add the coefficients; combine like
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Class -8 Factorization MLP 1. Factorise the following expressions: (i) 7x – 42 (ii) 6p − 12q (iii) 7a2 + 14a (iv) −16z + 20z3 (v) 20 l2 m + 30 a l m (vi) 5x2y − 15xy2 (vii) 10a2 − 15b2 + 20c2 (viii) −4a2 + 4ab − 4 ca (ix) x2 y z + xy2 z + xyz2 (x) ax2 y + bxy2 + c xyz 2. Factorize: (i) x2 + x y + 8x + 8y (ii) 15xy − 6x + 5y – 2 (iii) ax + b x − ay – by (iv)15pq + 15 + 9q + 25p (v) z − 7 + 7xy – xyz 3. Add: 7xy + 5yz – 3 z x ‚ 4yz + 9zx – 4 y
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MATH 1003 Calculus and Linear Algebra (Lecture 1) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 1003 1 / 18 Outline 1 About MATH 1003 2 Mathematics of Finance 3 Simple Interest Albert Ku (HKUST) MATH 1003 2 / 18 About MATH 1003 About MATH 1003 Lecturer: Albert Ku (Office: Rm 3492. E-mail: maybku@ust.hk) Teaching assistant: Dy Chun Yin‚ Li Xing‚ Lau Hing Sang and Wong Kwok Pang Office hours at Learning Commons: Fri 10:00-noon Textbook:
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Animal Kingdom The animal kingdom is a taxonomic kingdom composed of multicellular‚ eukaryotic organisms. Mostly‚ their body structures become fixed as they develop‚ yet still some organisms in this kingdom have the ability to undergo metamorphosis. The majority of these organisms are motile‚ which means they can move on their own and with spontaneity. All animals are heterotrophic‚ which implies that they depend on other organisms for food. Animals live in places that provide their necessities
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Direct Variation Try the following: 1. If m varies directly as y and m is 6 when y is 36‚ find the Choose: constant of variation. 1/6 6 1/36 36 Explanation 2. "a varies directly as b". If a = 3 when b = 24‚ find b when a = 10. Choose: 1.25 8 36 80 Explanation 3. There are about 200 calories in 50 grams of Swiss cheese. Choose: Willie ate 70 grams of this cheese. About how many 210 calories were in the cheese that he ate if the number of 240 calories
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Why is it important to follow the order of operations? What are some possible outcomes when the order of operations is ignored? If you invented a new notation where the order of operations was made clear‚ what would you do to make it clear? In mathematics ‚ the order of operation also known as precedence rule is a rule used to clarify which procedures should be performed first in a given mathematical expression. When there is more than one operation involved in a mathematical problem‚ it must
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