Alg2 lesson 9-2
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The document describes performing operations on like terms with LCD. It shows adding a term and subtracting a term with a common denominator, then simplifying the expression.
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Alg2 lesson 9-2
This document provides examples for operations using the least common denominator (LCD), including adding and subtracting fractions with different denominators, simplifying expressions with fractions, and dividing fractions. Examples 2-3a through 2-5a demonstrate finding the LCD and performing the specified operations on fractions and fractional expressions.
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1) Decimals represent numbers using place value with decimal points. To write decimals in expanded form, they are broken into place value terms using positive and negative exponents.
2) Fractions can be converted to decimals using division or by writing the fraction as a ratio of two numbers and setting up a proportion to solve for the decimal.
3) Scientific notation is used to write very large or small numbers in a standard form, such as 3.603 x 107. Operations can be done on decimals by lining up the decimal points or moving them with multiplication/division.
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Alg2 lesson 9-2
This document provides examples for operations using the least common denominator (LCD), including adding and subtracting fractions with different denominators, simplifying expressions with fractions, and dividing fractions. Examples 2-3a through 2-5a demonstrate finding the LCD and performing the specified operations on fractions and fractional expressions.
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This document provides a summary of Class 6 of the Programming with Data course. It introduces lists and common list procedures like cons, car, and cdr. It also discusses practice procedures like identity, pick-one, and middle. The class covers the history of Scheme and Lisp and how cons pairs are used to represent lists. Students are charged to read ahead and be prepared for an upcoming quiz covering material from the first five classes.
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Ratios, proportions, and percents can be used to compare quantities and solve problems. A ratio compares two quantities, like the number of squares to circles. Equal ratios form a proportion, which can be used to solve for unknown values. Percents represent a number out of 100. Common percent calculations include finding a percent of a number and converting between fractions, decimals, and percents. The percent proportion states that the percent equals the part divided by the whole quantity.
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1) Decimals represent numbers using place value with decimal points. To write decimals in expanded form, they are broken into place value terms using positive and negative exponents.
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The document contains instructions for finding trigonometric function values given specific angle measurements or terminal side locations. It includes:
1) Finding the six trig functions of an angle with a terminal side at (8, -15)
2) Finding the six trig functions of an angle with a terminal side at (-3, 4)
3) Finding the reference angle of 330°
4) Finding the reference angle of an angle in Quadrant III
5) Finding the value of sin(135°)
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1) Finding the six trig functions of an angle with a terminal side at (8, -15)
2) Finding the six trig functions of an angle with a terminal side at (-3, 4)
3) Finding the reference angle of 330°
4) Finding the reference angle of an angle in Quadrant III
5) Finding the value of sin(135°)
6) Finding the remaining five trig functions of an angle in Quadrant III with a terminal side of (-4, -3)
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1) This document contains examples of evaluating logarithmic expressions and solving logarithmic equations.
2) Logarithmic expressions are broken down using properties such as loga(bc) = loga(b) + loga(c) and their values are calculated.
3) Logarithmic equations are set up and solved by isolating the logarithmic term and using inverse logarithm properties.
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The document discusses various aspects of whole number operations including:
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This document discusses solving an ambiguous triangle where it is not a right triangle and the measures of angles and sides are not fully known. It determines that trigonometric functions and the Law of Sines cannot be used. It identifies that the Law of Cosines is the appropriate theorem to use to begin solving since it requires only knowing the measures of three sides.
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The document discusses solving for unknown sides and angles of triangles using trigonometric functions like the law of sines. Several multi-step example problems are worked through that involve determining if a triangle is possible based on given information, finding missing side lengths, and calculating angles. Diagrams are included to illustrate each step of the example problems.
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The document contains instructions for finding trigonometric function values given specific angle measurements or terminal side locations. It includes:
1) Finding the six trig functions of an angle with a terminal side at (8, -15)
2) Finding the six trig functions of an angle with a terminal side at (-3, 4)
3) Finding the reference angle of 330°
4) Finding the reference angle of an angle in Quadrant III
5) Finding the value of sin(135°)
6) Finding the remaining five trig functions of an angle in Quadrant III with a terminal side of (-4, -3)
Alg2 lesson 13-3
The document contains instructions for finding trigonometric function values given specific angle measurements or terminal side locations. It includes:
1) Finding the six trig functions of an angle with a terminal side at (8, -15)
2) Finding the six trig functions of an angle with a terminal side at (-3, 4)
3) Finding the reference angle of 330°
4) Finding the reference angle of an angle in Quadrant III
5) Finding the value of sin(135°)
6) Finding the remaining five trig functions of an angle in Quadrant III with a terminal side of (-4, -3)
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The document describes how to draw angles in standard position on a unit circle and convert between degrees and radians. It provides examples of drawing angles such as 210°, -45°, and 540° in standard position and rewriting angles such as 30°, 45°, and an unspecified angle in radians and degrees. It also gives examples of finding coterminal angles for 210° with one positive and one negative measure.
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This document discusses trigonometric functions and their ratios, including sine, cosine, tangent, cosecant, secant, and cotangent. It provides examples of using trigonometric functions to solve values in right triangles, including finding missing side lengths and angle measures. Special right triangles with ratios of 1/2, 1/√3, and 1/√2 are also covered.
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The document provides information about arithmetic and geometric series. It defines arithmetic and geometric series, provides examples of finding sums of arithmetic series using formulas, and defines the key terms (first term, common ratio, number of terms, last term) used in the formula to calculate the sum of a geometric series.
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The document discusses geometric sequences, which are patterns of numbers where each term is found by multiplying the previous term by a constant called the common ratio. It provides examples of geometric sequences with different common ratios and shows how to write equations to find the nth term in a sequence. It also explains how to find specific terms in a geometric sequence and calculates the geometric means between two nonconsecutive terms.
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The document discusses arithmetic sequences, which are patterns of numbers where each term is found by adding a constant value to the previous term. It provides examples of arithmetic sequences with different common differences and shows how to write equations to determine the nth term. It also explains how to find terms within an arithmetic sequence and determine arithmetic means between two non-consecutive terms.
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The document discusses exponential growth and decay models, including that exponential decay models how much of a substance is left over time. It provides an example of calculating the decay rate (k) of Sodium-22 given its half-life of 2.6 years, and uses this rate to determine that a meteorite containing only 10% as much Sodium-22 as when it reached Earth must have arrived about 9 years ago.
Alg2 lesson 10-4 and 10-5
A common logarithm has a base of 10. The log key on a calculator will find common logs. Solving log equations involves changing bases using log properties. Natural exponential functions involve the constant e, which is approximately 2.71828. The inverse of an exponential function is the natural log function.
Alg2 lesson 10-3
1) This document contains examples of evaluating logarithmic expressions and solving logarithmic equations.
2) Logarithmic expressions are broken down using properties such as loga(bc) = loga(b) + loga(c) and their values are calculated.
3) Logarithmic equations are set up and solved by isolating the logarithmic term and using inverse logarithm properties.
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This document provides an introduction to converting between exponential and logarithmic forms. It includes examples of writing expressions in exponential form given the logarithmic form, and vice versa. It also gives examples of evaluating logarithmic expressions and solving simple logarithmic equations.
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