2 log5 3x 4 b. lnx 2 ln2x 3 2 ln x Answers: a. x. Time A jogger leaves a point on a fitness trail running at a rate of 4 miles per hour. Where t 0 represents 1990.
U u v uv v uv 1. w w w w w w 7. 1 (a) f 0 (b) f 2 (c) f 2 (d) f 2. No, because there are only 12 months, but the temperature ranges from 15 F to 58 F. 4. 4x2 x3 8 2x 4 xx 2 2 100. Y 3x 4. y 2x 1 37. y 12 x 3. y 2x 1 5. Solution 3x3 15x2 18x. Use the Zero-Factor Property to solve equations.
16t 2 36. x 2x 6x 6x 9 4. x5 5x 4 3x3 8x 2 11x 12. x 2 400. x 4 6x3 5x 2 18x 6. x 4 16x3 96x 2 256x 256. 6x 5 6x 5 5 6x 1 True. Equation of a Line In Exercises 79–86, use a determinant to find the equation of the line through the points. Is xy a monomial. 2 2 y 2 2y 2y2 y2 2. x 3 2 2 x 9 x 5x 6. x 1 2 x x 30 x5. Use the properties of logarithms to condense ln x 4 ln y. ln. You can use the point-slope form of the equation of a line to write the equation of a line when you are given its slope and a point on the line. 0 16t2 32t 192 t. 32 ± 322 416192 216.
The triangles are shown in Figure 3. In Exercises 51–58, find the specified term in the expansion of the binomial. Keep in mathematical shape by doing these exercises before the problems of this section. This means that the LCM must contain all the different factors in the polynomials and each of these factors must be repeated the maximum number of times it occurs in any one of the polynomials. The width of a rectangle is 8 feet less than its length. Study Tip There are other ways to solve the decimal equation in Example 10. 53. f x Horizontal asymptote: y 0 x 54. f x 34 1 Horizontal asymptote: y 1. Solution To determine the percent of air pollutants in the stack emissions that can be removed for $420, 000, substitute 420, 000 for C in the model. Check to see if x1, y1 satisfies each inequality in the system. Is x a monomial. Take logarithm of each side. In the second job, you tutor for $7. Commutative Property Multiply.
X 2 55x 750 square meters. Infinitely many solutions 5. 38 feet See Section 9. Some, however, are slightly elliptical, which tends to make pedaling easier. 2 Composite and Inverse Functions. Isolate the variable x. Y 25x 5000 See Additional Answers. N 8 10 2n2 n 8 10n 4,, 3n 12 6n2 6n2 n 4 6n2 n 4 8s 3 36., s 22 s 3 s2 2s 35.
16 u 3 u 1 16u 19 u 3 35. 26. f x. gx x 1 (a) f gx. The set of integers is also a subset of the set of real numbers. 9x2 47x 10 Answers: a. Solution One way to solve this problem is to use the formula that relates distance, rate, and time. Find an expression for the area of the parking lot. 23 rises two units for each unit of horizontal change from left to right, and so this line has a slope of m 2. y. m=2. This produces the following result. Hint: The total area under a 20 by 20 foot canopy is 20 20 400 square feet. ) How much does the person weigh? Equations An equation is a statement that two algebraic expressions are equal. In general, to factor a trinomial ax 2 bx c by grouping, choose factors of the product ac that add up to b and use these factors to rewrite the middle term.
26. log5 2x log5 36. Nutrition A dietitian is asked to design a special dietary supplement using two different foods. 5. x 2, y 3. x − y = −3 x 6. 2 Factor out the greatest common monomial factor from polynomials. Perform all additions and subtractions from left to right. Next, use the points (2, 1) and (4, 4), as shown in Figure 4.