Algebra II Semester 2 Practice Final _9 Pages

ID: AID: A20. Use the Change of Base Formula to evaluatelog 462. Then convert log 462 to a logarithm in base2. Round to the nearest thousandth.a. 2.977; log 27.874b. 4.127; log 27.874c. 1.792; log 231d. 2.977; log 23121. Is the relationship between the variables in the tablea direct variation, an inverse variation, or neither?If it is a direct or inverse variation, write a functionto model it.x 0 1 2 3y 0 9923a. direct variation; y = 9xb. inverse variation; y = 9 xc. neither22. Expand the logarithmic expression.log 83d 2a. 3log 8d 2b. log 83 ⋅ 2 log 8dc. log 83 − 2 log 8dd. log 83 + 2 log 8d23. Let f(x) = 4x + 6 and g(x) = 2x + 7. Find(f û g)(5).a. 74b. 26c. 59d. 1724. Rationalize the denominator of the expression.3437a.3287b.31967c.37 28d. none of these25. In how many different orders can you line up 6cards on a shelf?a. 6b. 720c. 120d. 126. Write an equation for the translation of y = −7xthat has the asymptotes x = –2 and y = –7.a. y =−7x − 2 − 7b. y =−7x + 2 − 7c. y =−7x − 7 − 2d. y =−7x + 7 − 227. The values (5.1, 10) and (x, 3) are from an inversevariation. Find the missing value and round to thenearest hundredth.a. 17.00b. 1.53c. 51.00d. 153.0028. Solve 27x 3 + 343 = 0. Find all complex roots.a.7 21 ± 21 3,3 18b. no solutionc. − 7 3 , 7 3d. − 7 21 ± 21i 3,3 1830. Use synthetic division to find P(–4) forP(x) = x 4 + 8x 3 + 2x 2 + 5x − 9.a. –253b. –4c. –73d. 76531. Expand the logarithmic expression.log 48k 4a. log 48 − 4 log 4kb. log 48 + 4 log 4kc. log 48 ⋅ 4 log 4kd. 8log 4k 432. Divide using synthetic division.(x 4 − 12x 3 + 20x 2 + 36x − 45) ÷ (x − 3)a. x 3 − 9x 2 − 7x + 15b. x 3 − 7x 2 + 15x − 9c. x 3 + 6x 2 + 34x + 6d. x 3 − 12x 2 + 6x + 633. Use natural logarithms to solve the equation. Roundto the nearest thousandth.2e 4x + 11 = 22a. 0.426b. –2.151c. 0.300d. 0.70134. Solve the equation.x + 9 − 8 =−4a. –5b. 16c. 25d. 735. Use natural logarithms to solve the equation. Roundto the nearest thousandth.8e 4x + 11 = 30a. 0.216b. 0.409c. 0.092d. –2.42036. Multiply or divide. State any restrictions on thevariables.x 2x − 4 ⋅ x 2 + x − 20x 2 + 4xa.b.c.d.x 2 + 5xx + 4 , x ≠ 4, − 4x 2 + 5x, x ≠ 4, 0, − 4x + 4x + 5, x ≠ 4, 0, − 4x + 4x + 5x + 4 , x ≠ 4, − 437. Write the equation in logarithmic form.4 2 = 16a. log 16 = 2b. log 16 = 2 ⋅ 4c. log 416 = 2d. log 216 = 429. Zach wrote the formula w(w – 1)(2w + 3) for thevolume of a rectangular prism he is designing, withwidth w, which is always has a positive valuegreater than 1. Find the product and then classifythis polynomial by degree and by number of terms.a. 6w 2 ; quadratic monomialb. 2w 5 + w 4 − 3w 3 ; quintic trinomialc. 2w 4 + w 3 − 3w 2 ; quartic trinomiald. 2w 3 + w 2 − 3w; cubic trinomial34