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MAT. 126 - definition of sin A
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MAT. 126 - definition of sin A

by T
(ATLANTA)










































Ashford 4 : - Week 3 - Quiz


Time Remaining:


1. What is the definition of sin A for the following triangle?
(Points : 1)










2. Which quadrilateral is a trapezoid? (Points : 1)










3. Determine whether the system is consistent, inconsistent, or dependent.
3x + 2y = 15
6x + 4y = 30 (Points : 1)
Consistent
Dependent
Inconsistent


4. 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


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


6. Which triangle is obtuse? (Points : 1)










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


8. 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


9. Classify the angle as acute, right, obtuse, or straight.
(Points : 1)
Obtuse
Right
Straight
Acute


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


11. Classify the triangle according to sides.
(Points : 1)
Scalene
Isosceles
Equilateral


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


13. In triangle ABC, angle C is a right angle. Find the measure of angle B if side b = 105 m and side c = 139 m. (Points : 1)
49°
59°
53°
47°


14. Identify angles 6 and 7 as alternate interior, alternate exterior, corresponding, or vertical.
(Points : 1)
Vertical
Alternate interior
Alternate exterior
Corresponding


15. Find the perimeter.
(Points : 1)
25 inches
45 inches
40 inches
35 inches


16. The difference between the ages of two friends is 2 years. The sum of their ages is 74 years. Find the age of the older friend. (Points : 1)
38
36
39
37


17. Which of the following is not a way to name the angle shown?
(Points : 1)










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


19. Find the domain and range of the relation, and state whether or not the relation is a function.
{(7, 2), (8, 2), (9, 2), (10, 2)} (Points : 1)
Domain = {2}, Range = {7, 8, 9, 10}
The relation is not a function.
Domain = {2}, Range = {7, 8, 9, 10}
The relation is a function.
Domain = {7, 8, 9, 10}, Range = {2}
The relation is not a function.
Domain = {7, 8, 9, 10}, Range = {2}
The relation is a function.


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





Time Remaining:

Comments for MAT. 126 - definition of sin A

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Jun 11, 2012
Ashford 4 - Week 3 - Quiz
by: Staff


Part I



Answer:


1. What is the definition of sin A for the following triangle?
(Points : 1)



To view the triangle, open the following link:


(1) If your browser is Firefox, click the following link to VIEW the VENN Diagram; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page

http://www.solving-math-problems.com/images/definition-sin-a-triangle-2012-06-11.png




>>> Sin A = a/c








2. Which quadrilateral is a trapezoid? (Points : 1)


To view the diagram, open the following link:


http://www.solving-math-problems.com/images/trapezoid-2012-06-11.png





>>> Answer: “B” is the trapezoid




3. Determine whether the system is consistent, inconsistent, or dependent.

3x + 2y = 15
6x + 4y = 30 (Points : 1)

Consistent
Dependent
Inconsistent


Definitions:

Inconsistent linear systems: No solutions at all. Graphically, inconsistent systems are parallel lines.

Consistent linear systems: A consistent system has at least one solution.

There are two categories of Consistent Systems:

1) Dependent Systems (also called underdetermined systems): there are an infinite number of solutions. There is not enough information to find a single, unique solution. Graphically, dependent systems are the same line.

2) Independent Systems (also called uniquely determined systems): Independent systems have “one”solution. Graphically, the solution is the point where the two lines described by the equations intersect.


Your two equations form a “consistent” system because there is a least one solution.

Your two equations are also a “dependent” system because the second equation is merely two times the first equation. Graphically your two equations are the same line. There are an infinite number of solutions.


>>> The final answer to your question is: system is consistent and dependent.

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

Jun 11, 2012
Ashford 4 - Week 3 - Quiz
by: Staff


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

Part II






4. 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


To view the diagram, open the following link:


http://www.solving-math-problems.com/images/trapezoid-2012-06-11.png








When two triangles are similar, the ratio of any two corresponding line segments will have the same numerical value.

x/12 = 27.3/13

12*(x/12) = 12*(27.3/13)

x*(12/12) = 12*(27.3/13)

x*(1) = 12*(27.3/13)

x = 12*(27.3/13)

x = 25.2

>>> answer: 25.2


= 3.14.5. Find the circumference of the circle. Use
(Points : 1)
113.04 cm
18.84 cm
56.52 cm
37.68 cm

To view the diagram, open the following link:


http://www.solving-math-problems.com/images/circle-2012-06-11.png





Circumference = 2*pi*r

Circumference = 2*3.14*6

Circumference = 37.68 cm

>>> Circumference = 37.68 cm




6. Which triangle is obtuse? (Points : 1)


>>> An obtuse triangle has one angle which is GREATER than 90°






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


This question is similar to question 3.


Your two equations form a “consistent” system because there is a least one solution.

Your two equations are also a “dependent” system because the second equation is merely two times the first equation. Graphically your two equations are the same line. There are an infinite number of solutions.


>>> The final answer to your question is: system is consistent and dependent.







8. 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


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

Jun 11, 2012
Ashford 4 - Week 3 - Quiz
by: Staff

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

Part III


9. Classify the angle as acute, right, obtuse, or straight.
(Points : 1)
Obtuse
Right
Straight
Acute


To view the diagram, open the following link:


http://www.solving-math-problems.com/images/classify-angle-2012-06-11.png




>>> Angle: acute

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


To view the diagram, open the following link:


http://www.solving-math-problems.com/images/identify-angles-2-and-7-2012-06-11.png






>>> ∠2 & ∠7 are Alternate Exterior angles

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

Alternate Exterior angles are the angle pairs that are on opposite sides of the transversal, and outside the two parallel lines (l₁ and l₂)

Pairs of Alternate Exterior angles: ∠2 & ∠7, ∠1 & ∠8


Corresponding angles are the angle pairs that are in the same position relative to the transversal.

Pairs of corresponding angles: ∠2 & ∠6, ∠1 & ∠5, ∠3 & ∠7, ∠4 & ∠8


Vertical Angles are the angle pairs that share the same vertex.

Pairs of Vertical angles: ∠1 & ∠4, ∠2 & ∠3, ∠5 & ∠8, ∠6 & ∠7



Alternate interior Angles ate the angle pairs that are on opposite sides of the transversal, but inside the two parallel lines (l₁ and l₂)

Pairs of Alternate interior Angles: ∠3 & ∠6, ∠4 & ∠5


11. Classify the triangle according to sides.
(Points : 1)
Scalene
Isosceles
Equilateral


To view the diagram, open the following link:


http://www.solving-math-problems.com/images/scalene-and-acute-triangle-2012-06-11.png








>>> Scalene and acute









12. 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°





13. In triangle ABC, angle C is a right angle. Find the measure of angle B if side b = 105 m and side c = 139 m. (Points : 1)


49°
59°
53°
47°


Sin B = b/c

∠B = Sin⁻¹(b/c)

∠B = Sin⁻¹(105/139)

∠B = Sin⁻¹(105/139)

∠B = Sin⁻¹(0.755396)

∠B = 49.0599834137644°

>>> ∠B = 49°


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

Jun 11, 2012
Ashford 4 - Week 3 - Quiz
by: Staff


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

Part IV


14. Identify angles 6 and 7 as alternate interior, alternate exterior, corresponding, or vertical.
(Points : 1)
Vertical
Alternate interior
Alternate exterior
Corresponding


This is similar to question 10.

To view the diagram, open the following link:


http://www.solving-math-problems.com/images/identify-angles-2-and-7-2012-06-11.png




>>> ∠6 & ∠7 are Vertical Angles

Vertical Angles are the angle pairs that share the same vertex.





15. Find the perimeter.
(Points : 1)
25 inches
45 inches
40 inches
35 inches


To view the diagram, open the following link:


http://www.solving-math-problems.com/images/perimeter-of-octagon-2012-06-11.png




Perimeter of octagon = 8 sides * 5 in

Perimeter of octagon = 40 in

>>> perimeter = 40 in



16. The difference between the ages of two friends is 2 years. The sum of their ages is 74 years. Find the age of the older friend. (Points : 1)
38
36
39
37

x + y = 74
x – y = 2

add the two equations

x + y = 74
x – y = 2
-------------
x + x + y - y = 74 + 2

2x + 0 = 76

2x = 76

2x / 2 = 76 / 2

x * (2 / 2) = 76 / 2

x * (1) = 76 / 2

x = 76 / 2

x = 38

x + y = 74

38 + y = 74

38 - 38 + y = 74 - 38

0 + y = 74 - 38

y = 74 - 38

y = 36

>>> older friend: 38 years old; younger friend: 36 years old



17. Which of the following is not a way to name the angle shown?
(Points : 1)

To view the diagram, open the following link:


http://www.solving-math-problems.com/images/name-the-angle-shown-2012-06-11.png



>>> ∠P



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

>>> the relation is a function






19. Find the domain and range of the relation, and state whether or not the relation is a function.
{(7, 2), (8, 2), (9, 2), (10, 2)} (Points : 1)


Domain = {7, 8, 9, 10}, Range = {2}
The relation is not a function.



20. 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





Thanks for writing.

Staff
www.solving-math-problems.com



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