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mat126 survey of mathematics - functions

by Angel
(VA)











































someone please help im lost


2. Adult tickets for a play cost $19 and child tickets cost $17. If there were 36 people at a performance and the theatre collected $646 from ticket sales, how many children attended the play? (Points : 1)
17 children
20 children
18 children
19 children

3. Find the coordinates of the x-intercept.
2x + y = -6 (Points : 1)
(-6, 0)
(0, -3)
(0, -6)
(-3, 0)

4. Find the vertex of the parabola.
y = -4x2 - 16x - 11

(Points : 1)
(5, 2)
(2, 5)
(-2, 5)
(5, -2)

5. Determine whether the system is consistent, inconsistent, or dependent.
3x - 3y = -9
9x - 9y = -27 (Points : 1)
Consistent
Dependent
Inconsistant

6. Find the domain and range of the relation, and state whether or not the relation is a function.
{(3, 9), (3, 10), (3, 11), (3, 12)} (Points : 1)
Domain = {9, 10, 11, 12}, Range = {3}
The relation is a function.
Domain = {9, 10, 11, 12}, Range = {3}
The relation is not a function.
Domain = {3}, Range = {9, 10, 11, 12}
The relation is not a function.
Domain = {3}, Range = {9, 10, 11, 12}
The relation is a function.

7. Determine whether or not the network is traversable.
(Points : 1)
No, it is not traversable.
Yes, it is traversable.

8. Determine whether or not the relation is a function.
{(1, 9), (2, 10), (3, 11), (4, 12)} (Points : 1)
No
Yes

9. Identify the quadrilateral.
(Points : 1)
Rhombus
Rectangle
Trapezoid
Parallelogram

10. The triangles in the figure below are similar. Use the proportional property of similar triangles to find the measure of x.
(Points : 1)
34.2 km
29.2 km
25.2 km
19.2 km

11. Find the slope of the line passing through the points (10, 0) and (0, 3). (Points : 1)
-10/3
10/3
3/10
-3/10

12. The amount of revenue a company makes per day by selling x items is given by the function f(x) = 14x - 0.2x2. How many items should be sold if the company wants to maximize their profit? (Points : 1)
30 items
35 items
70 items
40 items

13. Identify angles 2 and 7 as alternate interior, alternate exterior, corresponding, or vertical.
(Points : 1)
Alternate exterior
Vertical
Alternate interior
Corresponding








15. Find the measure of the supplement of 58°. (Points : 1)
32°
148°
302°
122°

16. Carla invested $23,000, part at 16% and part at 15%. If the total interest at the end of the year is $3,500, how much did she invest at 16%? (Points : 1)
$4,000
$18,000
$6,000
$5,000

17. Find the circumference of the circle. Use  = 3.14.
(Points : 1)
113.04 cm
18.84 cm
56.52 cm
37.68 cm









19. Determine whether the system is consistent, inconsistent, or dependent.
2x + 2y = 2
6x + 6y = 6 (Points : 1)
Inconsistant
Consistent
Dependent
Consistent and Dependent

20. Write the equation in the slope-intercept form.
4x - 10y = 11 (Points : 1)
y = 2/5x - 11
y = -2/5x + 11/10
y = -2/5x + 11
y = 2/5x - 11/10

Comments for mat126 survey of mathematics - functions

Click here to add your own comments

Feb 05, 2012
Potpourri of Functions
by: Staff


--------------------------------------------
Part IV



15. Find the measure of the supplement of 58°. (Points : 1)
32°
148°
302°
122°

Supplement = 180° - 58°

Supplement = 122°

>>>The final answer is: Supplement = 122°


16. Carla invested $23,000, part at 16% and part at 15%. If the total interest at the end of the year is $3,500, how much did she invest at 16%? (Points : 1)
$4,000
$18,000
$6,000
$5,000

x = dollar amount of money invested at 16%

y = dollar amount of money invested at 15%

Equation 1: x + y = $23,000

Equation 2: x*.16 + y*.15 = $3,500


Multiply equation1 by .16

.16x + .16y = .16 * 23000

.16x + .16y = 3680


Subtract equation 2 from this equation

.16x + .16y = 3680
-(.16x + .15y = 3500)
------------------------
.16x - .16x +.16y - .15y = 3680 - 3500

0 + .01y = 180

.01y = 180

.01y/.01 = 180/.01

y = 180/.01


y = $18,000

x = $23,000 - $18,000

x = $5,000


>>>The final answer is: x = $5,000; y = $18,000





= 3.14.π17. Find the circumference of the circle. Use
(Points : 1)
113.04 cm
18.84 cm
56.52 cm
37.68 cm

C = πd or C = 2πr

The diameter or radius is not given in the problem statement. There is not enough information to answer this question.






19. Determine whether the system is consistent, inconsistent, or dependent.
2x + 2y = 2
6x + 6y = 6 (Points : 1)
Inconsistent
Consistent
Dependent
Consistent and Dependent

>>>The final answer is: This system is CONSISTENT and DEPENDENT.


20. Write the equation in the slope-intercept form.
4x - 10y = 11 (Points : 1)
y = 2/5x - 11
y = -2/5x + 11/10
y = -2/5x + 11
y = 2/5x - 11/10
4x - 10y = 11

4x - 10y + 10y = 11 + 10y

4x + 0 = 11 + 10y

4x = 11 + 10y

11 + 10y = 4x
11 - 11 + 10y = 4x - 11

0 + 10y = 4x - 11

10y = 4x – 11

10y/10 = 4x/10 – 11/10

y = 4x/10 – 11/10

y = .4x – 1.1

>>>The final answer is: y = .4x – 1.1




Thanks for writing.

Staff
www.solving-math-problems.com

Feb 05, 2012
Potpourri of Functions
by: Staff


--------------------------------------------

Part III

6. Find the domain and range of the relation, and state whether or not the relation is a function.
{(3, 9), (3, 10), (3, 11), (3, 12)} (Points : 1)

Domain: {3}
Range: {9, 10, 11, 12}

This is not a function.

>>>The final answer is: Domain = {3}, Range = {9, 10, 11, 12}
The relation is not a function.


7. Determine whether or not the network is traversable.
(Points : 1)
No, it is not traversable.
Yes, it is traversable.

A traversable network is a network can be traced with a pencil without ever tracing a path more than once.

There is no network diagram. There is not enough information to answer the question.


8. Determine whether or not the relation is a function.
{(1, 9), (2, 10), (3, 11), (4, 12)} (Points : 1)
No
Yes

Yes, this relation is a function.


9. Identify the quadrilateral.
(Points : 1)
Rhombus
Rectangle
Trapezoid
Parallelogram

There are no diagrams, so I don’t have enough information to answer the question.




10. The triangles in the figure below are similar. Use the proportional property of similar triangles to find the measure of x.

(Points : 1)
34.2 km
29.2 km
25.2 km
19.2 km

There are no diagrams, so I don’t have enough information to answer the question.


11. Find the slope of the line passing through the points (10, 0) and (0, 3). (Points : 1)
-10/3
10/3
3/10
-3/10

Use the slope intercept form of a linear equation

m = slope
b = y-intercept

y = mx + b

note that the two points are listed in reverse order (10, 0) and (0, 3). They should be listed left to right as (0, 3) and (10, 0).

(0, 3)

x₁ = 0
y₁ = 3

(10, 0)

x₂ = 10
y₂ = 0


m = slope = rise/run

m = (y₂ - y₁)/(x₂ - x₁)

m = (0 - 3)/(10 - 0)

m = -3/10



y = mx + b

y = (-3/10)*x + b

calculate “b” by substituting the x and y values for either point

in this example, I have used x₁ = 0 and y₁ = 3

3 = (-3/10)*(0) + b

3 = 0 + b

3 = b

b = 3

y = (-3/10)*x + 3


>>>The final answer is: y = (-3/10)x + 3




12. The amount of revenue a company makes per day by selling x items is given by the function f(x) = 14x - 0.2x². How many items should be sold if the company wants to maximize their profit? (Points : 1)
30 items
35 items
70 items
40 items

f(x) = 14x - 0.2x²

d(f(x))/dx = 14 – 0.4x

14 – 0.4x = 0

14 – 0.4x + 0.4x = 0 + 0.4x

14 + 0 = 0 + 0.4x

14 = 0.4x

14/0.4 = 0.4x/0.4

35 = x

x = 35



>>>The final answer is: x = 35 items





13. Identify angles 2 and 7 as alternate interior, alternate exterior, corresponding, or vertical.
(Points : 1)
Alternate exterior
Vertical
Alternate interior
Corresponding



There are no network diagrams. There is not enough information to answer the question.


--------------------------------------------

Feb 05, 2012
Potpourri of Functions
by: Staff


--------------------------------------------

Part II






19. Determine whether the system is consistent, inconsistent, or dependent.
2x + 2y = 2
6x + 6y = 6 (Points : 1)
Inconsistent
Consistent
Dependent
Consistent and Dependent

20. Write the equation in the slope-intercept form.
4x - 10y = 11 (Points : 1)
y = 2/5x - 11
y = -2/5x + 11/10
y = -2/5x + 11
y = 2/5x - 11/10
Answer:


2. Adult tickets for a play cost $19 and child tickets cost $17. If there were 36 people at a performance and the theatre collected $646 from ticket sales, how many children attended the play? (Points : 1)
17 children
20 children
18 children
19 children

Equation 1: A + C = 36

Equation 2: 19A + 17C = 646


Multiply Equation 1 by 19

19*A + 19*C = 19*36

19A + 19C = 684

Subtract Equation 2 from this equation

19A + 19C = 684
-19A - 17C = -646
----------------------
0 + 2C = 38

Solve for C

2C = 38

2C/2 = 38/2

C = 19

>>>The final answer is: 19 children




3. Find the coordinates of the x-intercept.
2x + y = -6 (Points : 1)
(-6, 0)
(0, -3)
(0, -6)
(-3, 0)


Substitute y = 0 for y

2x + y = -6

2x + 0 = -6

2x = -6

2x/2 = -6/2

x = -3

>>>The final answer is: the x intercept = -3



4. Find the vertex of the parabola.
y = -4x² - 16x - 11

(Points : 1)
(5, 2)
(2, 5)
(-2, 5)
(5, -2)


Equation of a parabola:

y = ax² + bx + c

y = -4x² - 16x - 11



Vertex of a parabola:

x = -b/2a

y = a(-b/2a)² - 16(-b/2a) - 11

x = -(-16)/(2*-4)

x = -2


y = -4*(-2)² - 16*(-2) - 11

y = 5



>>>The final answer is: Vertex = (-2, 5)


5. Determine whether the system is consistent, inconsistent, or dependent.
3x - 3y = -9
9x - 9y = -27 (Points : 1)
Consistent
Dependent
Inconsistent

There are only three possibilities for the solution of x and y for the system of two equations:

1. There is only one solution for x and y
2. There are an infinite number of solutions for x and y
3. There are no solutions to the system of equations (in this case, 2 equations)

In this case, there are an infinite number of solutions for x and y because the second equation is exactly 3 times the first equation.

A consistent system has least one solution.

Therefore, this system of two equations is CONSISTENT.

A dependent system means that every solution for one equation is also a solution for the other equation.

Therefore, this system is a DEPENDENT.


>>>The final answer is: This system is CONSISTENT and DEPENDENT.



--------------------------------------------

Feb 05, 2012
Potpourri of Functions
by: Staff


Part I

Question:


by Angel
(VA)

someone please help im lost


2. Adult tickets for a play cost $19 and child tickets cost $17. If there were 36 people at a performance and the theatre collected $646 from ticket sales, how many children attended the play? (Points : 1)
17 children
20 children
18 children
19 children

3. Find the coordinates of the x-intercept.
2x + y = -6 (Points : 1)
(-6, 0)
(0, -3)
(0, -6)
(-3, 0)

4. Find the vertex of the parabola.
y = -4x2 - 16x - 11

(Points : 1)
(5, 2)
(2, 5)
(-2, 5)
(5, -2)

5. Determine whether the system is consistent, inconsistent, or dependent.
3x - 3y = -9
9x - 9y = -27 (Points : 1)
Consistent
Dependent
Inconsistent

6. Find the domain and range of the relation, and state whether or not the relation is a function.
{(3, 9), (3, 10), (3, 11), (3, 12)} (Points : 1)
Domain = {9, 10, 11, 12}, Range = {3}
The relation is a function.
Domain = {9, 10, 11, 12}, Range = {3}
The relation is not a function.
Domain = {3}, Range = {9, 10, 11, 12}
The relation is not a function.
Domain = {3}, Range = {9, 10, 11, 12}
The relation is a function.

7. Determine whether or not the network is traversable.
(Points : 1)
No, it is not traversable.
Yes, it is traversable.

8. Determine whether or not the relation is a function.
{(1, 9), (2, 10), (3, 11), (4, 12)} (Points : 1)
No
Yes

9. Identify the quadrilateral.
(Points : 1)
Rhombus
Rectangle
Trapezoid
Parallelogram

10. The triangles in the figure below are similar. Use the proportional property of similar triangles to find the measure of x.

(Points : 1)
34.2 km
29.2 km
25.2 km
19.2 km

11. Find the slope of the line passing through the points (10, 0) and (0, 3). (Points : 1)
-10/3
10/3
3/10
-3/10

12. The amount of revenue a company makes per day by selling x items is given by the function f(x) = 14x - 0.2x2. How many items should be sold if the company wants to maximize their profit? (Points : 1)
30 items
35 items
70 items
40 items


13. Identify angles 2 and 7 as alternate interior, alternate exterior, corresponding, or vertical.
(Points : 1)
Alternate exterior
Vertical
Alternate interior
Corresponding




15. Find the measure of the supplement of 58°. (Points : 1)
32°
148°
302°
122°

16. Carla invested $23,000, part at 16% and part at 15%. If the total interest at the end of the year is $3,500, how much did she invest at 16%? (Points : 1)
$4,000
$18,000
$6,000
$5,000

= 3.14.π17. Find the circumference of the circle. Use
(Points : 1)
113.04 cm
18.84 cm
56.52 cm
37.68 cm


--------------------------------------------

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