Question

1. x2/3 + 3x1/3 and y = 10. What are the values of X?

A) -2, 5

B) -5, 2

C) -125, 8

D) -8, 125

E) None of the above

2. When a number is decreased by 20% of itself, the result is 144. What is the number?

  

  36

  72

  180

  900

3. A car rental agency charges $175 per week plus $0.20 per mile to rent a car. How many miles can you travel in one week for $295? ?

  234 miles

  575 miles

  600 miles

  1295 miles

?

1755 miles ?

4. The length of a rectangular room is 6 feet longer than twice the width. If the room's perimeter is 156 feet, what are the room's dimensions? ?

Width = 24 ft; length = 54 ft

Width = 29 ft; length = 64 ft

Width = 36 ft; length = 42 ft

Width = 48 ft; length = 108 ft

Width = 52 ft; length = 48 ft

5. Find the result of

-19

6-25i

6 + 5i

31

None of the above

6. Fine the answer for | 2(x+1) + 4 | =10

  {-6, 0}

  {-6, 4}

  {-6, 8}

  {-8, 0}

  {-8, 2}

7. A landscaping company sells 40-pound bags of top soil. The actual weight x of a bag, however, may differ from the advertised weight by as much as 0.75 pound. Write an inequality involving absolute value that expresses the relationship between the actual weight x of a bag and 40 pounds. Solve the inequality, and express the answer in interval form. ?

|40 - x|? 0.75; [39.25, 40.75]

|40 + x| ? 0.75; [39.25, 40.75]

|x + 0.75| ? 40; [39.25, ?)

|x|- 40 ? 0.75 ; (-?, 40.75]

None of the above

8. Write an equation that passes through (1, -6) with x-intercept = -1.

  y + 6 = - 3(x - 1) or y = - 3(x - 1)

y + 6 = - 3(x - 1) or y = - 3(x + 1)?

  y - 6 = - 3(x + 1) or y = - 3(x + 1)

  y - 6 = - 3(x - 1) or y = - 3(x - 1)

  y - 1 = - 3x or y - 6 = - 3(x + 1)

9. Suppose a life insurance policy costs $20 for the first unit of coverage and then $5 for each additional unit of coverage. Let C(x) be the cost of insurance of x units of coverage. What will 10 units of coverage cost?

  

  $45

  $55

  $65

  $75

10. An investment is worth $2282 in 2006. By 2010 it has grown to $2986. Let y be the value of the investment in year x, where x =0 represents 2006. Write a linear equation that models the value of the investment in the year x.

  

  

  

  

  

11. What is the equation for the line that passes through (4, 3) and perpendicular to the line whose equation is y = 8x + 7.

(x – 3)

(x + 3)

(x – 4)

y (x + 4)

12.   The linear function f(x) = -9.8x + 24 models the percentage of people, f(x), who eats at fast food restaurants each week x years after 2009. What is the slope and what does it mean?

m = 9.8; the percentage of people eating at fast food restaurants each week has decreased at a rate of 9.8% per year after 2009.

m = -9.8; the percentage of people eating at fast food restaurants each week has increased at a rate of -9.8% per year after 2009.

m = 24; the percentage of people eating at fast food restaurants each week has increased at a rate of 24% per year after 2009.

m = 24; the percentage of people eating at fast food restaurants each week has decreased at a rate of 24% per year after 2009.

m = -9.8; the percentage of people eating at fast food restaurants each week has decreased at a rate of -9.8% per year after 2009.

13. The function f(t) = models the U.S population in

millions, ages 65 and older, where t represents year after 1990. The function g(t) = models the total yearly cost of Medicare in billions of dollars, where t represents years after 1990. What does the function represents. Find

Cost per person in thousands of dollars. $0.16 thousand

Cost per person in thousands of dollars. $0.03 thousand

Cost per person in thousands of dollars. $8.64 thousand

Cost per person in thousands of dollars. $34.67 thousand

Cost per person in thousands of dollars. $30.8 thousand

14.   Find the inverse function of f(x) =

   

  

  

  

  

15.   Find the center and the radius of the circle

  (4, -3), r = 8

  (-3, 4), r = 8

  (-4, 3), r = 64

  (-3, -4), r = 64

  (-4, -3), r = 64

Answer 1

1) Since in the problem given that y = 10 but none of the options from A to D contains 10, therefore the correct option is E.

2) Let x be the number.

By given condition we have, x - x*20% = 144

i.e., x - (x*20/100) = 144

i.e., x - (1*x/5) = 144

i.e., x*(1-1/5) = 144

i.e., x*(4/5) = 144

i.e., x = 144*5/4

i.e., x = 180

Therefore, the number is 180.

3) Let x miles i can travel in one week for $295.

Then, by given conditions we have, 175+0.20*x = 295

i.e., 0.20*x = 295-175

i.e., 0.20*x = 120

i.e., x = 120/0.20

i.e., x = 600

Therefore, 600 miles i can travel in one week for $295.

4) Let the width of the rectangular room be x feet.

Then, the length of the rectangular room is = (2*x+6) feet.

By given conditions we have, 2*[x+(2*x+6)] = 156

i.e., x+2x+6 = 156/2

i.e., 3x = 78-6

i.e., x = 72/3

i.e., x = 24

Therefore, length and width of the rectangular room are 24 feet and 54 feet.

5) Question is incomplete.

6) Given, |2(x+1)+4| = 10

i.e., |2x+6| = 10

Then, either 2x+6 = 10 or -(2x+6) = 10

Now, 2x+6 = 10 gives 2x = 10-6 ,i.e., x = 4/2 ,i.e., x = 2

And, -(2x+6) = 10 gives 2x+6 = -10 ,i.e., 2x = -10-6 ,i.e., x = -16/2 ,i.e., x = -8

Therefore, x = {-8,2}.

7) Given the actual weight and advertised weight are x pound and 40 pound respectively.

Then, the difference of weight is =

In other words, the difference is |40-x| pound.

By the given condition, |40-x| = 0.75

Then, either 40-x = 0.75 or x-40 = 0.75

Now, 40-x = 0.75 gives x = 40-0.75 ,i.e., x = 39.25

And, x-40 = 0.75 gives x = 40+0.75 ,i.e., x = 40.75

Therefore, the solution is [39.25,40.75]

8) The equation that passes through (1, -6) with x-intercept = -1 is y + 6 = - 3(x - 1) or y = - 3(x + 1)?.

9) 10 units of coverage will cost = $[20+(10-1)*5] = $[20+9*5] = $[20+45] = $65.

10) Let the linear equation be y = mx+c

When x = 0, then y = $2282.

Thus we get, 2282 = m*0+c ,i.e., c = 2282

When x = 4, then y = $2986.

Thus we get, 2986 = m*4+c ,i.e., 2986 = 4m+2282 ,i.e., 4m = 2986-2282 ,i.e., m = 704/4 ,i.e., m = 176

Therefore, the linear equation is y = 176x+2282.

11) The equation of the line perpendicular to the line y = 8x + 7 is y = -(1/8)x+c.

Since, it passess through the point (4, 3).

Then, 3 = -(1/8)*4+c

i.e., c-(1/2) = 3

i.e., c = 3+(1/2)

i.e., c = 7/2

Therefore, the required line is y = -(1/8)x+7/2 ,i.e., 8y+x = 28.