Questions on Geometry: Geometric formulas answered by real tutors!

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Question 1179190: Find the slope of the line through (-5,3) and (x+1, x-2).
Click here to see answer by ikleyn(53560)

Question 1201106: A vertical aerial AB 9.6m high stands on ground which is inclined 12 degrees to the horizontal. A stay connects the top of the aerial A to a point C on the ground 10m downhill from B the foot of the aerial. Determine the length of the stay and the angle the stay makes with the ground.
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Question 67218: Log(base 3)9- log(base 5)5^3 + log(base 7) 7 ^2 - log (base 11)1
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Question 67382: Simplify:
log(base 2)8 + 3 log(base 3)3 - log(base 2)1 + log(base 4)(1/4)
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Question 447845: The total number of seats in a basketball sports arena is 12,000. The arena is divided into three sections, court sides, end zone and balcony, and there are twice as many balcony seats as court side seats. For the conference championship game, ticket price were $10.00 for court side, $8.00 for balcony and $7.00 for end-zone. If the arena was sold out for the game and the total receipts were $99,000 how many seats were court-side???.... thank you ^^
Click here to see answer by ikleyn(53560)

Question 729557: how do you determine the length and width when you are given the difference of two similar objects
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Question 1209200: The volume of a right cone is 4125π units. If its diameter measures 30 units, find its height? please help I'm really stuck...
Click here to see answer by greenestamps(13292)

Question 1209200: The volume of a right cone is 4125π units. If its diameter measures 30 units, find its height? please help I'm really stuck...
Click here to see answer by ikleyn(53560)

Question 1160338: The clients have 6m tall tree in their back yard that is leaning 8 degrees to the vertical.
To prevent it from leaning any further, until it can be properly dug up and replanted, A support pole is placed 1M from the top of the tree at a 75 degrees angle with the ground.
How far from the base of the tree is the support pole placed on the ground?
Click here to see answer by ikleyn(53560)

Question 1177064: In quadrilateral ABCD, AB=BC=1,m∠B=100degrees,m∠D=130degrees, Find BD.
No picture is associated with this question.
Click here to see answer by ikleyn(53560)

Question 1177064: In quadrilateral ABCD, AB=BC=1,m∠B=100degrees,m∠D=130degrees, Find BD.
No picture is associated with this question.
Click here to see answer by CPhill(2189)

Question 1209547: Find the surface area of the regular pyramid.
A triangular pyramid. The base triangle has a base of 7 centimeters and a height of 6 centimeters. The height of a triangular face is labeled 9 centimeters.
cm2
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Question 1209548: Find the surface area of the regular pyramid.
A triangular pyramid. The base triangle has a base of 30 millimeters and a height of 26 millimeters. The height of a triangular face is labeled 20 millimeters.
mm2
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Question 1209550: A farmer has 114 feet of fencing. Which shape would give the most area?
(a) Equilateral triangle
(b) Circle
(c) Square
(d) Non-square rectangle
Click here to see answer by math_tutor2020(3830)

Question 1192321: 1. Suppose you have n points, no three of which are collinear. How many lines contain two of these n points?
2. If no four of the n points are coplanar, how many planes contain three of the n points?
Hint: (for 3 and 4, generalize in a form of a formula)
3.Prove theorem 1.1.4. The steps in the proof are already given: you just have to supply the reasons for each step.
Theorem 1.1.4. If two lines intersect, then their union lies in exactly one plane.
Proof: Let and be two intersecting lines.
a. A ∩ B is a point p.
b. B contains a point q ≠ p.
c. There is a plane E, containing A and q.
d. E contains A ∪ B.
e. No other plane contains A ∪ B.
Click here to see answer by CPhill(2189)

Question 1192322: 1. Suppose you have n points, no three of which are collinear. How many lines contain two of these n points?
2. If no four of the n points are coplanar, how many planes contain three of the n points?
Hint: (for 3 and 4, generalize in a form of a formula)
3.Prove theorem 1.1.4. The steps in the proof are already given: you just have to supply the reasons for each step.
Theorem 1.1.4. If two lines intersect, then their union lies in exactly one plane.
Proof: Let and be two intersecting lines.
a. A ∩ B is a point p.
b. B contains a point q ≠ p.
c. There is a plane E, containing A and q.
d. E contains A ∪ B.
e. No other plane contains A ∪ B.
Click here to see answer by CPhill(2189)

Question 1193334: EF is the median of trapezoid ABCD in the figure below. Use the following theorems to answer the questions.
If three (or more) parallel lines intercept congruent line segments on one transversal, then they intercept congruent line segments on any transversal.
The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side.
Suppose that AB = 11.4 and DC = 17.2.
Find MF.
Find EM.
Find EF.
Find
1/2(AB + DC).

Click here to see answer by proyaop(69)

Question 1193343: a ∥ b ∥ c and B is the midpoint of AC.
AB = 2x + 5, BC = x + 7, and DE = 3x + 6.
x =
Find the length of
DE.
DE =
Because a ∥ b ∥ c and B is the midpoint of
AC,E is the midpoint of
DF and EF =
.
Find the length of
EF.
Click here to see answer by proyaop(69)

Question 1193592: Assume that AD is the geometric mean of BD and DC in △ABC Suppose BD = 3 and DC = 6.
Write a proportion involving AD that can be used to solve for AD.
3/AD
AD=

Find AD.
AD =

Suppose AD = 3 and DC = 6.
Write a proportion involving BD that can be used to solve for BD.
=
3/6
Find BD.
BD =

Click here to see answer by ikleyn(53560)

Question 1193686: Find the missing lengths. Give your answers in both simplest radical form and as approximations correct to two decimal places.
Given: right △RST with
RT = 8radical 2
and m∠
STV = 150°
Find: RS and ST
simplest radical form RS=
approximation RS =
simplest radical form ST =
approximation ST=
Click here to see answer by ikleyn(53560)

Question 1209264: How can I prove a square is the largest rectanglar area possible? I'm really stuck. Thanks for any help
Click here to see answer by math_tutor2020(3830)

Question 1209187: A homeowner has 80 feet of fence to enclose a rectangular garden. What dimensions for the garden give the maximum area?
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Question 1209009: Farmer Jessie has a field shaped as quadrilateral ABCD. She measures three of the sides AB = 50 meters, BC = 65 meters, and CD = 80 meters. She also determines that angle ABC = 130 degrees and BCD = 52 degrees.
(a) What is the distance between points A and C?
(b) Show one way to find the area of triangle ABC.
(c) Show a different way to find the area of triangle ABC.
(d) What is the area of quadrilateral ABCD?
Round each result to 3 decimal places.
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Question 1208432: when pipe is transported it is bundled into regular hexagons for stability during shipment. let n be the number of pieces of pipe on any side of the regular hexagon. write a rule for this situation. how many pieces of pipe are in a bundle when n = 12
the photo : imgur.com/a/3GF6R6G (IT IS NUMBER 2)
Click here to see answer by greenestamps(13292)

Question 1207940: The tangent line to a circle may be defined as the line that intersects the circle in a single point, called the point of tangency. If the equation of the circle is x^2 + y^2 = r^2 and the equation of the tangent line is y = mx + b, show that:

A. r^2(1 + m^2) = b^2

B. The point of tangency is [(-r^2 m)/b, (r^2/b)]

C. The tangent line is perpendicular to the line containing the center of the circle and point of tangency.

Click here to see answer by mananth(16949)

Question 1207806: A hot-air balloon, headed due east at an average speed of 15 miles per hour and at a constant altitude of 100 feet, passes over an intersection. Find an expression for the distance d (measured in feet) from the balloon to the intersection t seconds later.
Click here to see answer by Alan3354(69443)

Question 1207807: A Dodge Neon and a Mack truck leave an intersection at the same time.The Neon heads east at an average speed of 30 miles per hour, while the truck heads south at an average speed of 40 miles per hour. Find an expression for their distance apart d (in miles) at the end of t hours.
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Question 1207590: In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $QR$, and let $Y$ be the foot of the perpendicular from $X$ to side $PR$. If $PQ = 10,$ $QR = 10,$ and $PR = 12,$ then compute the length of $XY$.
Click here to see answer by greenestamps(13292)

Question 1207592: In triangle $ABC$, point $X$ is on side $BC$ such that $AX = 13,$ $BX = 13,$ $CX = 5,$ and the circumcircles of triangles $ABX$ and $ACX$ have the same radius. Find the area of triangle $ABC$.
Click here to see answer by ikleyn(53560)

Question 1206650: △ABC with m∠A = m∠B = 45° and
BC = 4
Find: AB approximation

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Question 1206551: Harold Johnson lives on a four-sided, 50,000-square-foot lot that is bounded on two sides by parallel streets. The city has assessed him $1,000 for curb repair, $2 for each foot of property bordering on these two streets. How far apart are the streets?
Click here to see answer by math_tutor2020(3830)