Domanda del libro di testo
Evaluate each exponential expression in Exercises 1–22.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 18
State the name of the property illustrated: (3 • 7) + (4 • 7) = (4 • 7) + (3 •7)
Guida verificata passo dopo passo1
Observe the given expression: \( (3 \cdot 7) + (4 \cdot 7) = (4 \cdot 7) + (3 \cdot 7) \). Notice that the two products are being added together on both sides.
Identify that the terms on the left side are \(3 \cdot 7\) and \(4 \cdot 7\), and on the right side, the same terms appear but in reversed order: \(4 \cdot 7\) and \(3 \cdot 7\).
Recall the Commutative Property of Addition, which states that changing the order of addends does not change the sum. In symbolic form, this is \(a + b = b + a\).
Since the expression shows the sum of two products with their order switched but the sum remains the same, this illustrates the Commutative Property of Addition.
Therefore, the property illustrated by the equation is the Commutative Property of Addition.
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Commutative Property of Addition
The commutative property of addition states that changing the order of addends does not change the sum. For example, a + b = b + a. In the given expression, the sums on both sides have the same terms added in different orders, illustrating this property.
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5:36
Change of Base Property
Distributive Property
The distributive property connects multiplication and addition, stating that a(b + c) = ab + ac. Although the given expression resembles terms from distribution, it primarily shows rearrangement of terms rather than distribution itself.
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04:15Multiply Polynomials Using the Distributive Property
Multiplication of Real Numbers
Multiplication of real numbers is commutative, meaning a × b = b × a. This allows factors to be reordered without changing the product, which is essential in understanding why (3 • 7) and (7 • 3) are equivalent in the expression.
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03:31Introduction to Complex Numbers
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A football was kicked vertically upward from a height of 4 feet with an initial speed of 60 feet per second. The formula h=4+60t-16t2 describes the ball's height above the ground, h, in feet, t seconds after it was kicked. Use this formula to solve Exercises 19–20. What was the ball's height 2 seconds after it was kicked?
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