Mixed practice: All Math — set 1

Answer: B / 7 Divide by 6: 2x − 1 = 7, so x = 4 and x + 3 = 7. The requested expression is not just x.

Linear target / Standard Review: Example 1.01.

Answer: 120 The paid fraction is 0.85 of the original price p. Solve 0.85p = 102 to obtain p = 120.

Reverse percentages / Standard Review: Example 4.02.

Answer: B / (x − 2)² − 9 The vertex is (2, −9) and the curve passes through (0, −5). In a(x − 2)² − 9, substitution gives 4a − 9 = −5, so a = 1.

Quadratic graphs / Standard Review: Example 1.07.

Answer: A / 4 Add the equations to get 8x = 32, so x = 4. Both original equations then give y = 7/2.

Linear systems / Standard Review: Example 3.01.

Answer: 36 Perimeter scales like length, so the smaller-to-larger length factor is 21/35 = 3/5. The area is 100(3/5)² = 36.

Similarity / Standard Review: Example 1.14.

Answer: D / W(t) = 1200(0.8)^t For positive bases, (0.64)^t/2 = ($\sqrt{\text{0.64}}$)^t = (0.8)^t. The one-hour retention factor is 0.8.

Equivalent exponential models / Standard Review: Example 1.09.

Answer: −3 The prediction is 1.5(10) + 8 = 23. Observed minus predicted is 20 − 23 = −3. The point lies below the fitted line.

Residuals / Standard Review: Example 2.09.

Answer: D / 2 No solution occurs when the coefficient is zero and the right side is nonzero. Thus a − 2 = 0 and a = 2, producing 0 = 5.

Parameter exceptions / Standard Review: Example 2.12.

Answer: C / 120 The other leg is $\sqrt{{\text{26}}^{\text{2}}\text{−}{\text{10}}^{\text{2}}}$ = $\sqrt{\text{576}}$ = 24. The perpendicular legs give area $\frac{\text{1}}{\text{2}}$(10)(24) = 120.

Right triangles and area / Standard Review: Example 6.03.

Answer: 7 Simplify to x + 5 = 12 with x ≠ 5. Thus x = 7, which is allowed. The original value is (49 − 25)/2 = 12.

Rational equations / Standard Review: Example 1.05.

Answer: A / 51% The interval is 44% through 50%. Therefore 51% is outside, while 44%, 47%, and 50% are within it.

Margin of error / Standard Review: Example 5.08.

Answer: C / 7 The slope is (15 − 7)/(5 − 1) = 2. Using (1, 7) gives b = 5, so m + b = 7.

Lines / Standard Review: Example 1.02.

Answer: D / 1 Absolute value is zero only when its input is zero, so x − 4 = 0 and x = 4. There are not two distinct solutions in this boundary case.

Absolute-value solution count / Standard Review: Example 3.08.

Answer: 120 The circumference is 24π, so the arc is one-third of a circle. The angle is (1/3)(360°) = 120°.

Arcs and angles / Standard Review: Example 6.09.

Answer: B / The volunteers may not represent the wider student population. Random assignment supports a causal comparison within a well-conducted study. It does not make volunteers a random sample of all students, so broad generalization needs additional justification.

Statistical claims / Standard Review: Example 4.15.