Tutors Answer Your Questions about Geometric formulas (FREE)
Question 281785: Choose the most efficient strategy for solving the following problem: A group of surveyors left their base camp and traveled 50 km east, then 20 km north, then 10 km west, then 50 km south. How far were they from their base camp?
a. look for a pattern
b. draw a diagram
c. work backward
d. make a chart
Next question is to solve this problem.
a. 50km
b. 130km
c. 92 km
d. they were back at their base camp.
Click here to see answer by richwmiller(9135)   |
Question 287297: Will you please help with this problem with great detail. Thank You
One side of an equilateral triangle is four yards less than the side of a square. The perimeter of the triangle is twenty-eight yards shorter than the perimeter of the square. Find the length of the sides of the triangle and square.
Click here to see answer by richwmiller(9135) |
Question 292469: A boy standing on the shore of a lake 1 mile wide wants to go to the store 3 miles down the shore on the opposite side of the lake. If he swims at 2 miles per hour, and walks at 4 miles per hour, is it quicker for him to swim directly across the lake and then walk to the store, or is it quicker for him to swim directly to the store? Prove this mathematically.
Click here to see answer by richwmiller(9135) |
Question 292469: A boy standing on the shore of a lake 1 mile wide wants to go to the store 3 miles down the shore on the opposite side of the lake. If he swims at 2 miles per hour, and walks at 4 miles per hour, is it quicker for him to swim directly across the lake and then walk to the store, or is it quicker for him to swim directly to the store? Prove this mathematically.
Click here to see answer by Alan3354(30993)  |
Question 297848: An inflated beach ball with radius r=25 centimeters hold approximately 65.400 cubic centimeters of air. When the ball is compressed, the radius is 2/3 the original size. Approximately how much air does the partially deflated ball now hold?
Click here to see answer by Alan3354(30993) |
Question 300735: I have a geometry study guide that I honestly do not understand at all. I need answers with an explanation? :( please..here is the information
These are the shapes that go with the problems:
http://i43.tinypic.com/10wr02b.png
Here are the possible answers (not all of them will be used):
A. 476
B. 6
C. 7
D. 6.5
E. 2 / 3
F. 176
G. 12
H. 96
I. 48
J. 2 sqrt(3)
K. 16 sqrt(2)
L. 30
M. 30sqrt(6)
N. 3
O. 3, 8
P. 8
Q. 10 pi
R. 17.5
S. 4, 6
T. 69
U. pi
V. 108
W. 32
X. 3 sqrt(2)
Y. 16
Z. 14 pi
Here are the questions...
Question 1
1: Find the area of a rectangle with length 5 sqrt(2) and width 3 sqrt(2).
_____ square units
Question 2
2: A walk 2 meters wide surrounds a rectangular grass plot 30 m long and 10 m wide. Find the area of the walk.
_____ square meters
Question 3
3: Find the area of the polygon in Figure 1.
_____ square units
Question 4
4: A square has diagonals of length 8 cm. Find the area.
_____ square cm
Question 5
5: Find the lengths of the sides of a rectangle of area 24 square units and perimeter 22.
Question 6
6: Find the height of a triangle with base length 4 and area 12 square units.
Question 7
7: Find the area of a triangle with base length 3 sqrt(2) and height 2 sqrt(2).
_____ square units
Question 8
8: Find the area of the triangle in Figure 2, if a = 8 and b = 4.
_____ square units
Question 9
9: Find the area of the triangle in Figure 2, if a = 5 and c = 13.
_____ square units
Question 10
10: Find the area of the triangle in Figure 3.
_____ square units
Question 11
11: A parallelogram of area 78 square units has one side of length 12. Find the length of an altitude to that side.
Question 12
12: Find the area of the parallelogram ABCD in Figure 4, if m Ang A = 30 deg, AB = 12, and AD = 8.
_____ square units
Question 13
13: Find the area of the parallelogram ABCD in Figure 4, if m Ang A = 45 deg, AB = 10 sqrt(3), and AD = 6.
_____ square units
Question 14
14: Find the area of the parallelogram ABCD in Figure 4, if DC = 12 and the height = 9.
_____ square units
Question 15
15: Find the area of the trapezoid with base lengths 12 and 4 and height 6.
_____ square units
Question 16
16: Find the height of a trapezoid with area 40 square units and base lengths 7 and 3.
Question 17
17: A trapezoid of area 150 square units has one base of length 18 and height 12. Find the length of the other base.
Question 18
18: Find the area of the trapezoid in Figure 5 if m Ang A = m Ang D = 45 deg, AB = 4 sqrt(2), and BC = 4.
_____ square units
Question 19
19: Find the circumference of a circle with a diameter of 10.
Question 20
20: Find the radius of a circle with circumference 4 sqrt(3)(pi).
Question 21
21: Find the radius of a circle with area (4/9) (pi).
Question 22
22: What is the circumference of a circle with area 49(pi)?
Please and thank you SO much! :(
Click here to see answer by Fombitz(13828)  |
Question 300737: I need major help on how to answer these questions and what they are. Here is the info...
* The slash / represents a fraction bar and division. For example, one half = 1/2.
* The notation sqrt( ) is used to denote the square root of a number.
To answer some of the following questions you will need to refer to the figures below:
Figure 1: The three horizontal lines are parallel.
Figure 3: The two horizontal lines are parallel.
Figure 7: JM and JP are chords of the circle. JK is a diameter.
Figure 8: GH and JK are chords of the circle.
Use Figure 3 below for the following proof:
Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°.
Prove: lines a and b are parallel.
1. m ang 1 + m ang 3 = 180o : Given
2. m ang 3 + m ang 5 = 180° : Definition of straight angle
3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________
4. m ang 1 = m ang 5 : __________
5. Lines a and b are parallel: __________
Here are the figures that go with the questions:
http://i44.tinypic.com/s153m1.png
And here are the questions:
11.) Find the measure of the supplement of the angle with measure 85 degrees.
5 degrees
105 degrees
95 degrees
58 degrees
12.) If CG is an altitude of Triangle ABC, then _______.
CG is perpendicular to AB
CA is perpendicular to AB
G is the midpoint of AB
CG is parallel to BC
13.) What is the equation of the line through points (-3, 2) and (-4, 5)?
y = (2/3)x - 6
y = 2x - 4
y = 2x + 2
y = -3x - 7
14.) Given Triangle RST is similar to Triangle DEF. If m Ang E = 38°, m Ang R = 43°, and m Ang T = (7x + 8)°, then x = ?
13
14.14
4.29
15
15.) With only a compass and a straightedge it is possible to construct a square.
True
False
Neither
Both
16.) If the sides of one angle are opposite rays of the sides of another angle, then the two angles are vertical angles.
True
False
Neither
Both
17.) In Figure 7, if m Ang PJK = 37° and m Arc PM = 41°, then m Ang MJK =
16.5°
9°
33°
12°
18.) If two polygons are similar, then they are congruent.
True
False
Neither
Both
19.) Use Figure 1 above. If m Ang 1 = 30°, then m Ang 11 = _______.
30°
60°
120°
150°
20.) A trapezoid of area 150 square units has one base of length 18 and height 12. Find the length of the other base C
3.5
7
3 sqrt(2)
14
21.) Refer to triangle DEF in Figure 5, if m Ang D = 30o, m Ang E = 60°, and DF = 12, what is ME in simplest form?
2 sqrt(3)
6
6 sqrt(3)
12
:( this is an ungraded study guide but counted as an incomplete if not done. please help? :( I don't understand how to do this.
Click here to see answer by Fombitz(13828) |
Question 300741: I need major help on how to answer these questions and what they are. :( this is an ungraded study guide but counted as an incomplete if not finished. I don't understand how to do these so I would love help:( Here is the info...
* The slash / represents a fraction bar and division. For example, one half = 1/2.
* The notation sqrt( ) is used to denote the square root of a number.
To answer some of the following questions you will need to refer to the figures below:
Figure 1: The three horizontal lines are parallel.
Figure 3: The two horizontal lines are parallel.
Figure 7: JM and JP are chords of the circle. JK is a diameter.
Figure 8: GH and JK are chords of the circle.
Use Figure 3 below for the following proof:
Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°.
Prove: lines a and b are parallel.
1. m ang 1 + m ang 3 = 180o : Given
2. m ang 3 + m ang 5 = 180° : Definition of straight angle
3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________
4. m ang 1 = m ang 5 : __________
5. Lines a and b are parallel: __________
Here are the figures that go with the questions:
http://i44.tinypic.com/s153m1.png
And here are the questions:
42.) In the proof above, the reason for step 4 is
substitution
angle addition
equal corresponding angles
parallel postulate
43.) For Figure 4, find DE.
6
8
10
12
44.) If two triangles are congruent, then the _______ corresponding parts are congruent.
3
6
4
2
45.) Lines p and q are parallel. The slope of p is 5 and the slope of q is 10/v. What is v?
2 sqrt(13)
4
4 sqrt(2)
2
46.) For Figure 6, 0A = 3 and AC = 12, what is OB?
3sqrt(9)
3 sqrt(3)
7
sqrt(153)
47.) Classify the angle with measure 75 degrees.
Acute
Obtuse
Straight
Right
48.) A parallelogram of area 78 square units has one side of length 12. Find the length of an altitude to that side.
3
2 sqrt(3)
6
6.5
49.) Refer to Triangle DFE in Figure 5, if DM = 4 and ME = 8, what is FM in simplified form?
4 sqrt(2)
12
2 sqrt(3)
16
50.) In elliptic or spherical geometry, there can be _____ right angle(s) in a triangle.
zero
one
two
three
51.) For right triangle ACB with right angle C, if m Ang A = 45° and BC = 3, what is the length of AC?
3 sqrt(3)
3
3 sqrt(2)
1.5
52.) Opposites sides of a parallelogram are parallel and congruent.
True
False
Neither
Both
53.) In the proof above, the reason for step 3 is
substitution
angle addition
parallel postulate
equal corresponding angles
Click here to see answer by Fombitz(13828) |
Question 300740: I need major help on how to answer these questions and what they are. :( this is an ungraded study guide but counted as an incomplete if not finished. I don't understand how to do these so I would love help:( Here is the info...
* The slash / represents a fraction bar and division. For example, one half = 1/2.
* The notation sqrt( ) is used to denote the square root of a number.
To answer some of the following questions you will need to refer to the figures below:
Figure 1: The three horizontal lines are parallel.
Figure 3: The two horizontal lines are parallel.
Figure 7: JM and JP are chords of the circle. JK is a diameter.
Figure 8: GH and JK are chords of the circle.
Use Figure 3 below for the following proof:
Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°.
Prove: lines a and b are parallel.
1. m ang 1 + m ang 3 = 180o : Given
2. m ang 3 + m ang 5 = 180° : Definition of straight angle
3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________
4. m ang 1 = m ang 5 : __________
5. Lines a and b are parallel: __________
Here are the figures that go with the questions:
http://i44.tinypic.com/s153m1.png
And here are the questions:
31.) At five o'clock the measure of the angle formed by the hands of the clock is?
60°
210°
150°
180°
32.) In angle ABC, A is the vertex.
True
False
Neither
Both
33.) A regular polyhedron is a polyhedron with faces that are congruent squares.
True
False
Neither
Both
34.) In Figure 7 if m Arc PM = 40° and m Arc JKM = 210°, then m Ang PJK =
70°
35°
55°
40°
35.) If a triangle has sides of lengths 8, 4, and 4 sqrt(3), is the triangle right?
Yes
No
Maybe
Sometimes
36.) A triangle with at least two sides of equal length is called _______.
Scalene
Isosceles
Equilateral
Regular
37.) A polygon is regular if and only if the sides are congruent (“if and only if” states a condition but does not necessitate it to be the sole condition).
False
True
Neither
Both
38.) In the proof above, the reason for step 5 is
substitution
parallel postulate
equal corresponding angles
angle addition
39.) What is the center of the circle with equation (x + 1)^2 + (y + 3)^2 = 9/4?
(-1, -3)
(-1, -1)
(-3/2, 4)
(1, 3)
40.) Use Figure 2 above. If m Ang B = 53° and m Ang C = 62°, which side(s) of Triangle ABC is(are) the longest?
AB
BC
AC
AB & BC
41.) What is the equation of the line with slope 2/3 and passes through the midpoint of the segment joining points (-1, 6) and (-7, -4)?
y = -3x - 9
y = (2/3)x + (11/3)
y = -3x - 7
y = (2/3)x - 6
Click here to see answer by Fombitz(13828) |
Question 300738: I need major help on how to answer these questions and what they are. :( this is an ungraded study guide but counted as an incomplete if not finished. I don't understand how to do these so I would love help:( Here is the info...
* The slash / represents a fraction bar and division. For example, one half = 1/2.
* The notation sqrt( ) is used to denote the square root of a number.
To answer some of the following questions you will need to refer to the figures below:
Figure 1: The three horizontal lines are parallel.
Figure 3: The two horizontal lines are parallel.
Figure 7: JM and JP are chords of the circle. JK is a diameter.
Figure 8: GH and JK are chords of the circle.
Use Figure 3 below for the following proof:
Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°.
Prove: lines a and b are parallel.
1. m ang 1 + m ang 3 = 180o : Given
2. m ang 3 + m ang 5 = 180° : Definition of straight angle
3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________
4. m ang 1 = m ang 5 : __________
5. Lines a and b are parallel: __________
Here are the figures that go with the questions:
http://i44.tinypic.com/s153m1.png
And here are the questions:
22.) A square has diagonals of length 8 cm. Find the area. ___ square cm
32
16 sqrt(2)
12
3 sqrt(2)
23.) the measure of the complement of the angle with measure 45 degrees.
315 degrees
45 degrees
55 degrees
135 degrees
24.) Use Figure 1. The exterior angles of Angle 3 are _______.
Angles 1 and 2
Angles 5, 6, and 7
Angles 2 and 4
Angles 1, 2, and 4
25.) In Figure 8, if GI = 3, IH = 8, JK = 10, what is JI (if it is longer than IK)?
8
12
6
4
26.) All opposite sides of a trapezoid are parallel.
True
False
Neither
Both
27.) What is the volume of a right cone with radius 3 and height 4? ___ (pi) cubic units
16
24
12
27
28.) For Figure 4, find AC.
26 2/3
9.5999999999999996447286321199499070644378662109375
10
15
29.) The converse of the statement: "If you are baking brownies, then the kitchen smells good", is "If the kitchen smells good, then you are baking brownies."
True
False
Neither
Both
30.) The radius of a Circle O is 4, if radii OA and OB form 90° angle, AB = ?
4 sqrt(2)
4
16 sqrt(2)
8
Click here to see answer by Fombitz(13828) |
Question 300736: I need major help on how to answer these questions and what they are. Here is the info...
* The slash / represents a fraction bar and division. For example, one half = 1/2.
* The notation sqrt( ) is used to denote the square root of a number.
To answer some of the following questions you will need to refer to the figures below:
Figure 1: The three horizontal lines are parallel.
Figure 3: The two horizontal lines are parallel.
Figure 7: JM and JP are chords of the circle. JK is a diameter.
Figure 8: GH and JK are chords of the circle.
Use Figure 3 below for the following proof:
Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180°.
Prove: lines a and b are parallel.
1. m ang 1 + m ang 3 = 180o : Given
2. m ang 3 + m ang 5 = 180° : Definition of straight angle
3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________
4. m ang 1 = m ang 5 : __________
5. Lines a and b are parallel: __________
Here are the figures that go with some of the questions:
http://i44.tinypic.com/s153m1.png
And here are the questions:
The point where the three altitudes of a triangle intersect is called the
intersection point
altocenter
centroid
orthocenter
2.) Classify the angle with measure 180 degrees.
Acute
Obtuse
Straight
Right
3.) In Figure 8, if GH = 8, JI = 8, IK = 2, what is GI?
8
4
6
10
4.) If we wanted to draw a median of Triangle ABC coming from vertex C, then our line would _______.
cross BC at its midpoint
cross AB at its midpoint
cross and be perpendicular to BC
cross and be perpendicular to AB
5.) The base of a pyramid is a square with sides of length 4 cm. If the volume = 80 cm3, what is the height? ___ cm
16 / 3
12
15
5 sqrt(3) / 3
6.) Find the value of x: (2x) / 7 = (x - 1) / 3
1
13/7
7
5/7
7.) A line that intersects a circle in a single point.
chord
secant
tangent
diameter
8.) A circle of area 49(pi) has a circumference of what?
7 pi
17.5
10
14 pi
9.) If two sides and the _______ angle of one triangle are congruent to two sides and the _______ angle of another triangle, then the triangles are congruent.
Smallest
Opposite
Included
Acute
10.) When constructing the median of a triangle, it is possible that the median may lie exterior to the triangle.
True
False
Neither
Both
Thank you so much! :( this is just a study guide (ungraded but counted as an incomplete if not done.
Click here to see answer by Fombitz(13828) |
Question 306293: Please help. My son is having a terrible time in geometry and I never took it so I'm of no help.
Given: the angle of BCA = 50 degrees. The arc of CD = 80 degrees
How do I find the arc of AD? (in layterms please)
Thanks so much for any help you can offer.
Click here to see answer by Alan3354(30993) |
Question 306617: Sorry for the lact of picture...I don't know how to post it. I do know that it is an oblique triangle where a is the bottom (width) and b and c are on the left and right side, respectively. a = 5, b = 6, and angle between a and b = 1/3pi. Find c. Thank you in advance.
Click here to see answer by stanbon(57314) |
|
Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710
|
