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1. Sketch the line through A and B. A (โ4, 2 ), B ( 1 , โ2) Submission Data line: (-4,2),(1,-2) Find its slope m. (If an answer is undefined, enter UNDEFINED.) m = -4/5 -4/ 2. For each pair of lines below, determine if the two lines are parallel, perpendicular, or neither. Pair 1: y = 9x + 6 , y = x/9 + 6 parallel perpendicular neither Pair 2: 5x + 2y + 8 = 0 , 5x + 2y + 2 = 0 parallel perpendicular neither Pair 3: 2x + 5y + 2 = 0 , 5x - 2y - 8 = 0 parallel perpendicular neither 3. Which of the following is the equation for the vertical line through the point (3, 9)? x = 9 y = 9 y = 3 x = 3 4. Find the slope-intercept form of the line that satisfies the given conditions. Through A ( 5 , 0 ) and B (โ9, 2 ) Practice Another Version Practice Another Version Practice Another Version
5. IMPORTANT: For all parts of this question, provide exact expressions, not decimal approximations. Let L denote the line passing through the point (6, 3) and the center of the circle (x - 5)^2 + (y - 8)^2 = 64. Find the slope of L. Decimal approximations will be marked incorrect. Write an equation for L in terms of the variables x and y. Decimal approximations will be marked incorrect. 6. Write an equation in the variables x and y for the line that passes through the point (16, 20) and that is perpendicular to the line 8x + 7y = 170. Provide precise expressions, not decimal approximations. 7. Write an equation in the variables x and y for the line that passes through the point (12, 10) and that is parallel to the line -3x + 6y = 27. Provide precise expressions, not decimal approximations. 8. Write a complete equation (using the variables x and y) for the line passing through the point (3, 9) and having x-intercept 8. IMPORTANT: Provide an exact EQUATION with no decimal approximations. 9. Find the slope-intercept form of the line that satisfies the given conditions. x -intercept 7 , y -intercept 1 Practice Another Version Practice Another Version Practice Another Version Practice Another Version Practice Another Version
(b) y = (c) y =
(d) y = 12. The growth of a fetus more than 12 weeks old can be approximated by the formula L = 1.53 t โ 6.7, where L is the length (in centimeters) and t is the age (in weeks). Prenatal length can be determined by ultrasound. Approximate the age of a fetus whose length is 30 centimeters. (Round your answer to the nearest week.) 24 24 wk 13. A college student receives an interest-free loan of $9,800 from a relative. The student will repay $200 per month until the loan is paid off. (a) Express the amount P (in dollars) remaining to be paid in terms of time t (in months). (Give your answer in slope-intercept form.) (b) After how many months will the student owe $5000? 24 24 months (c) Sketch, on a tP -plane, a graph that shows the relationship between P and t for the duration of the loan. Practice Another Version Practice Another Version
A company purchases a piece of equipment for $25,000. After 5 years, the equipment loses 25% of its value. Assuming the value is a linear function of time, determine the time (in years) it will take for the machine to be worth 50% of its original value. A decimal answer must be rounded to at least two decimal places. Time in years: WatchIt 16. Nine years ago a house was worth $230,000. Now the house is worth $265,000. Assume a linear relationship between time (measured in years) and value (measured in dollars). (a) Find a formula for the value, V ( t ), at time t. ( t = 0 refers to now.) V ( t ) = (b) What will be the value of the house four years from now? Give an exact answer or round your answer to the nearest dollar. $ 17. If x < 0 and y > 0, determine the sign of the real number. (a) xy positive negative (b) x^2 y positive negative (c) x y
- x positive negative (d) y โ x Practice Another Version Practice Another Version
positive negative 18. Rewrite the expression without using the absolute value symbol, and simplify the result. | 5 + x | if x < โ 19. The population dynamics of many fish are characterized by extremely high fertility rates among adults and very low survival rates among the young. A mature specimen of a particular fish may lay as many as 2.5 million eggs, but only 0.00055% of the offspring survive to the age of 3 years. Use scientific form to approximate the number of offspring that live to age 3. (Round your answer to the nearest whole number.) 14 14 offspring Practice Another Version Practice Another Version
