# Questions on Geometry: Geometric formulas answered by real tutors!

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Question 994045: the length of a garden is 10 m more than twice the width. The are is 120m2. What are the dimensions of the garden to the nearest tenth metre?
Answer by Boreal(1464)   (Show Source):
You can put this solution on YOUR website!
W=x
L=2x+10
area is 120 m^2
Therefore, (2x+10)(x)=120
2x^2+10x=120
2x^2+10x-120=0
divide by 2
x^2+5x-60=0
x=(1/2) { -5 +/- sqrt (25+240)}, and use positive root only
sqrt 265=16.279
x=(1/2)(-5+16.279)=(1/2)(11.279)=5.64 m
2x+10=21.28
convert to nearest tenth of a meter
5.6*21.3=119.28
rounded to two decimal places it is 120.02.
The dimensions are 5.6 m x 21.3 m

Question 993703: A chord of length 24cm is 13cm from the centre of the circle.calculate the radius of the circle
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
A chord of length 24cm is 13cm from the centre of the circle.calculate the radius of the circle
-------------
13 cm from the center --> segments of r+13 and r-13
---
(r+13)*(r-13) = 12*12 = 144

r =~ 17.6918 cm

Question 993396: An angle measure 69
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(47455)   (Show Source):
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
Thx for letting us know.

Question 991463: the larger of two numbers is 10 less than twice the smaller number.If the sum of the two numbers is 38,find the two numbers.
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
L=larger number; S=smaller number
.
L=2S-10
.
L+S=38
L=38-S
.
38-S=2S-10
48=3S
16=S
ANSWER !: The smaller number is 16.
.
L=38-S=38-16=22
ANSWER 2: the larger number is 22.
.
CHECK:
.
L=2S-10
22=2(16)-10
22=32-10
22=22

Question 991444: Find the next five terms, then write a conjecture.
1, 8, 27, 64, ___, ___, ___, ___, ___

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

Each term is the cube of the term number.

John

My calculator said it, I believe it, that settles it

Question 990111: You are watching a pitcher who throws two types of pitches, a fastball(F) and a curveball(C). You notice that the order of pitches was F,C,F,F,C,C,F,F,F. Assuming that this pattern continues, predict the next five pitches
Answer by farohw(153)   (Show Source):
You can put this solution on YOUR website!

Hello,

It appears that the pattern is in the order of 1,2,3,4... for each type of pitch.

F,C,F,F,C,C,F,F,F,(C,C,C),(F,F,F,F, C,C,C,C,)...

Best,
Farohw

Question 989633: k^2-16k+100=k^2-4k+85 (Sorry if I have sent this already, I don't know if the first one was sent!)
Answer by rothauserc(2272)   (Show Source):
You can put this solution on YOUR website!
k^2 -16k +100 = k^2 -4k +85
subtract k^2 from both sides of =
-16k +100 = -4k +85
add 16k to both sides of =
100 = 12k +85
subtract 85 from both sides of =
15 = 12k
divide both sides of = by 12
k = 15 / 12 = 5 / 4 = 1.25
************************************
check answer by substituting for k in original equation
(1.25)^2 - 16(1.25) + 100 = (1.25)^2 -4(1.25) + 85
−18.4375 +100 = −3.4375 +85
81.5625 = 81.5625
our answer checks

Question 989630: k^2-16k+100=k^2-4k+85
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!

Both members have a k^2 term...

Question 989072: Hello, I am a junior in high school looking for help to get a formula. I need this formula to solve an equation in which I want to know the number of sides in a regular polygon, where I am given the circumradius and a side length.
Thanks in advance,
Tyler

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Hello, I am a junior in high school looking for help to get a formula. I need this formula to solve an equation in which I want to know the number of sides in a regular polygon, where I am given the circumradius and a side length.
==========================
s = side length
r = radius
n = # of sides
-----
angle = asin(s/2r)
n = 360/(2*angle)
-->

Question 988965: please help me on this one....A farmer has 60m of fencing to make a rectangular pen for his goat, find the maximum possible area of the pen.... i tried to derive the expression : l=30-w. And the expression for the area in terms of the width : A=-w^2 +30w
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
length L
width w
A for AREA
perimeter is 60 feet, equal to the amount of fencing.

------Just as you have.

Your question is, what is w and L for maximum area A ?

w and L must be each greater than 0.
A is a parabola function and has a maximum point for its vertex; and A has two x-axis intercepts. The maximum value for A occurs in the exact middle of the roots. w is really the HORIZONTAL number line and A is for the vertical number line.

Roots for A?

Solve for w, and find what is the value in the middle?
Now, what is A at that middle value of w?

Question 988607: The fourth term of a geometric progression exceeds the third term by 54, and the sum of the second and third term is 36. Find the common ratio if it is positive
Found 3 solutions by MathTherapy, KMST, MathLover1:
Answer by MathTherapy(4047)   (Show Source):
You can put this solution on YOUR website!
The fourth term of a geometric progression exceeds the third term by 54, and the sum of the second and third term is 36. Find the common ratio if it is positive
Since , then , , and

Since  exceeds  by 54, then we can say that:

---------- eq (i)

Since the sum of  and  is 36, then we can say that:

--------- eq (ii)

Since  and , we can then say that:
------ Cross-multiplying
-------- Factoring out GCF, 18

(r - 3)(2r + 1) = 0
Common ratio, or 		OR           (ignore, since r MUST be > 0)



Answer by KMST(3791)   (Show Source):
You can put this solution on YOUR website!
= the common ratio.
= the second term.
= the third term.
= the fourth term.
The fourth term of a geometric progression exceeds the third term by 54 translates as
<--><--> .
The sum of the second and third term is 36 translates as
<--><--> .
The ratio both equations tells us that
-->-->-->}--> .
The equation is a quadratic equation.
As is true for all quadratic equations, it can be solved by "completing the square, or by using the quadratic formula.
This particular quadratic equation can also be solved by factoring:
--->--->}--->---> .
If the common ratio is positive, it must be .

Answer by MathLover1(11324)   (Show Source):
You can put this solution on YOUR website!
if the fourth term exceeds the third term by , we have
....eq.1
if the sum of the second and third term is , we have
....eq.2
By using we have:

....eq.1
....eq.2
---------------------------------------------------add eq.2 and eq.1

.............substitute in eq.2

....eq.2

......divide by

=> one solution will be: =>
=> another solution will be: =>=>
now we can find first term:
if
....eq.2

if :
....eq.2
......multiply by

so, there are two solutions:
1. and
2. and

then the second term is:
if and :

third term is

fourth term

the terms of sequence are:=>

if ,

.
third term is

and fourth term is

the terms of sequence are:=>

now, check given data:
for =>
....eq.1

....eq.2

for =>
....eq.1

....eq.2

Question 987483: How many elements does each of these sets have where a and b are distinct elements?
A) P ({a, b, {a, b} })
B) P ({0, a, {a} , { {a} })
C) P (P { ( ) }

Answer by farohw(153)   (Show Source):
You can put this solution on YOUR website!

Hello,
a)This set has 3 elements and the power set can be calculated as
P({a,b,{a,b}}) = 2^3 = 8.

b) P({∅,a,{a},{{a}}}) = 2^4 = 16.

c) An empty set has 0 elements, so the power set is P({ }) = 2^0 = 1. Hence, P P({ }) is 2^1 = 2.

Cheers,
Farohw

Question 986915: Please help with this geometry question!
http://www.intervisualtechnology.us/data/1/13918/unit_4_5_q2.png
a)15
b)70
c)55
d)105

Answer by Fombitz(25151)   (Show Source):
You can put this solution on YOUR website!
Since it's an isosceles triangle, the two base angles are identical.
So,

Question 986695: angle ABC is 25 degrees
angle ABD = 2x-y
angle DBC = 3y-x
ray BD bisects angle ABC
find the equations

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
angle ABC is 25 degrees
Sketch ang ABC with C as the vertex.
-------
angle ABD = 2x-y
angle DBC = 3y-x
ray BD bisects angle ABC, so 2x-y = 3y-x
-----
find the equation
2x-y = 3y-x
3x = 4y
----------
Cheers,
Stan H.
----------

Question 986224: A square and an equilateral triangle have equal perimeters. The area of the triangle is 163 square centimeters. How long, in centimeters, is a diagonal of the square? Express your answer in simplest radical form.
Thank you

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Triangle, side length s.
Altitude cuts triangle into two special 30 60 90 triangles.
A, the area of The equilateral triangle,
A/2, area of one of the special triangles.
a, altitude of the triangle.

, one-half base times height, twice

substitute for a,

Solve for s

The SQUARE
Let x be the edge of square shape.

because perimeter of square is given as equal to perimeter of the equilateral triangle.

The diagonal of the square is d.

-
Substitute for x to get better formula for d.

Substitute for s to get yet a better formula for d.

Rationalize the expression, the denominator...

and remember, given A=163....

Question 984951: Trapezoid TRAP has bases TR= y + 7 and AP= 3y + 5. If the median of TRAP has length 6y- 10, find y
Found 2 solutions by solver91311, Tatiana_Stebko:
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

The measure of the median of a trapezoid is the mean of the measures of the bases, so:

John

My calculator said it, I believe it, that settles it

Answer by Tatiana_Stebko(1470)   (Show Source):
You can put this solution on YOUR website!

multiply by 2

Question 984839: Draw a line ab intercept plane q at w

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Ok, I did that.
Now what?

Question 984567: Hi! I am finite mathematics and we are studying "sets". Here is my question.
U= {1,2,3,4,5,6,7,8,9,10}
A={1,3,5,7,9}
B={2,4,6,8,10}
C={1,2,4,5,8,9}

QUESTION: (AuBuC)^C

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!
Already answered this one.

Question 984455: How do you do midpoint and distance?
Answer by Fombitz(25151)   (Show Source):
You can put this solution on YOUR website!
The midpoint of two points is the average of the x and y values.
Example : The midpoint of the line between (1,2) and (3,4) is

and

So the midpoint is (2,3).
.
.
.
The distance between two points is,

So the distance between (1,2) and (3,4) is,

Question 984356: find a if given c and theta
Answer by Timnewman(249)   (Show Source):
You can put this solution on YOUR website!
This is not a question.
Maybe you ommitted some important aspect of what you wanted to ask;
please repost your question.

Question 984081: Find the equation of the line joining (1,-1,3) to (3,3,-1). Show that it is perpindicular to the plane
2x+4y-4z=5

Answer by Edwin McCravy(13211)   (Show Source):
You can put this solution on YOUR website!
A parametric equation for a line through the point

parallel to the vector

is:

A symmetric equation for the line is

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

When given two points on a line:

and

we can find a vector

parallel to the line by subtracting coordinates as components.

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

The above is all the information you need to find an equation of the
line, whether you want a parametric or symmetric equation.

--------------------------------------
Then for the second part, you need:

A normal vector to the plane whose equation is

is

So all you need do is to show that the vector

that is parallel to the line that you got in the first part is either the same
or a scalar multiple of the normal vector to the plane

If you have any questions, be sure to ask them in the thank-you note form below,
and I'll get back to you by email.

Edwin

Question 982715: An infinite geometric series has first term 70 and common ratio -0.23.
To 2 decimal places, what is the sum to infinity of this series?

Answer by KMST(3791)   (Show Source):
You can put this solution on YOUR website!
For a geometric sequence with first term and common ratio ,
the sum of the first terms is

When , gets progressively smaller as increases, approaching zero,
so the sum of an infinite geometric series with first term and common ratio is

In this case,
rounded to two decimal places.

Question 982744: Find the value of the acute angle, if the obtuse angle is 136 degrees.
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
How are the 2 angles related?

Question 982064: if three sides of trapezoid are 18.318mm, 17.02296 and 17.02296 the what is the length of fourth side??
Answer by Edwin McCravy(13211)   (Show Source):
You can put this solution on YOUR website!
That's not enough information to determine a trapezoid.  You must be
given which two sides are parallel, and something else, perhaps the
perpendicular height.

Question 981832: The segment joining (-3,-2) and (-1/2,3) is extended a distance equal to 4/5 of its own length. Find the terminal point.
Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
Label (-3,-2) A, (-1/2, 3) B and Terminal point T.
Distance between A and B = 5
Distance between B and T = 4
AB/BT = 5/4
b - a/t - b = 5/4
Cross multiply
5(t - b) = 4(b - a)
5t - 5b = 4b - 4a
Collect like terms
5t = 4b - 4a + 5b
5t = 9b - 4a
T = 1/5(9b - 4a)
T = 1/5( 9(-1/2,3)) - 4(-3 -2))
T = 1/5(-9/2 , 27) + (12 ,8)
T = 1/5(15/2, 35)
T = (3/2,7)
This is the Terminal point.
Hope this helps :-)

Question 981643: When the coordinates (1, 1), (7, 3), (8, 0), and (2, -2) are joined, which shape is formed?
A. Parallelogram
B. Rectangle
C. Rhombus
D. Square
C????

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
When the coordinates (1, 1), (7, 3), (8, 0), and (2, -2) are joined, which shape is formed?
A. Parallelogram
B. Rectangle
C. Rhombus
D. Square
=================
Why do you think it's C?
============
By definition, it's A and B
A rectangle is a special case of A.

Question 981640: Point A is located at (0, 4), and point B is located at (−2, −3). Find the point that is 1 over 4 the distance from point A to point B.
A. (−1, 0.75)
B. (−0.75, 2)
C. (−0.5, 2.25)
D. (−0.25, 3)

i think its C??

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
(1) Find equation of the line containing the given points. Put into slope-intercept form.
(2) Distance formula, to find distance AB.
(3) Distance formula again, using the unknown point (x,y) to be of distance from (0,4). y will be in terms of x, according to the equation of the line found. Solve for x, and use it to find corresponding y.

That is the plan and description of the process, which YOU can do.

SOLUTION PROCESS DETAILS

(1)

-

pick either point
----but y intercept already given as one of the points.

(2)

(3)
The general unknown point on the line is (x,y) or (x,(7/2)x+4).
Point A is (0,4).
You want (x,y) so that

-
The steps to simplify that equation

Notice that x is already isolated in one term and no need to square both sides as
part of this simplification!....
because sqrt(x^2) might be positive or negative x;

--------------one of these will make sense and one will not make sense.
-
What then is the y coordinate?
,......

Question 981637: Line AB contains points A (0, 1) and B (1, 5). The slope of line AB is
A) −4
B)negative 1 over 4
C)1 over 4
D) 4
i think its B???

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Line AB contains points A (0, 1) and B (1, 5). The slope of line AB is
---------------
Slope = diffy/diffx

Question 980491: in geometric progression please solve for r: S = rL -a / r - 1
thank you

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

John

My calculator said it, I believe it, that settles it

Question 979691: A line passes through a circle at two points. Another line passes through the same circle at two points. These two lines intersect at a point on a circle. In how many parts is the circle divided?
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
3, if it's all the same circle.
4 if the intersection is on some other circle.

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Visualize this mentally or draw the description to help. The intersecting lines will cut the circle into four parts.

Question 979054: The diagonal of a rectangle is 10.what is the area of rectangle
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
The diagonal of a rectangle is 10.what is the area of rectangle
-------------
Not enough info.

Question 978137: standard equation with a focus at 6,8 and directrix at y=-2
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Distance Formula, and Definition of Parabola.

Question 975312: the length of a rectangle is 5 ft longer than its width. if its area is 36 ft, what are its dimensions?
Answer by algebrahouse.com(1579)   (Show Source):
You can put this solution on YOUR website!
x = width
x + 5 = length {length is 5 longer than width}

Area of a rectangle = width x length

x(x + 5) = 36 {substituted width and length into area formula}
x² + 5x = 36 {used distributive property}
x² + 5x - 36 = 0 {subtracted 36 from each side}
(x + 9)(x - 4) = 0 {factored into two binomials}
x + 9 = 0 or x - 4 = 0 {set each factor equal to 0}
x = -9 or x = 4 {solved each equation}

x = 4 {width cannot be negative}
x + 5 = 9 {substituted 4, in for x, into x + 5}

width = 4 ft
length = 9 ft

To ask a question, visit: www.algebrahouse.com

Question 974473: a plane travels 79 mi at a bearing of 37 degree 19'. how far north did the plane travel during that time.
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
a plane travels 79 mi at a bearing of 37 degree 19'. how far north did the plane travel during that time.
--------------
= 79*cos(37° 19')

Question 974474: The radius of a circle is 32.4 m. find the length of an arc of the circle intercepted by a central angle of 7pi/6 radians
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
The radius of a circle is 32.4 m. find the length of an arc of the circle intercepted by a central angle of 7pi/6 radians
------------
Length = 32.4*7pi/6 m

Question 974471: f(x) = x^2 + x-2, find f(a-1)
Answer by algebrahouse.com(1579)   (Show Source):
You can put this solution on YOUR website!
f(x) = x² + x - 2

f(a - 1)
= (a - 1)² + (a - 1) - 2 {substituted (a - 1) for x}
= (a - 1)(a - 1) + a - 1 - 2 {when squaring a binomial, multiply it by itself}
= a² - 2a + 1 + a - 1 - 2 {used the foil method to square the binomial}
= a² - a - 2 {combined like terms}

To ask a question, visit: www.algebrahouse.com

Question 973185: Twenty water tanks are decreasing in size in such a way that the volume of each tank is 0.5 the volume of the previous tank. The first tank is empty, but the other 19 tanks are full of water. Would it be possible for the first water tank to hold all the water from the other 19 tanks? Motivate your answer.

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Twenty water tanks are decreasing in size in such a way that the volume of each tank is 0.5 the volume of the previous tank. The first tank is empty, but the other 19 tanks are full of water. Would it be possible for the first water tank to hold all the water from the other 19 tanks? Motivate your answer (¿que?).
--------------
Yes, it will hold all the water.
-----
Use binary counting.
1111111111111111111 = 2^20 - 1
10000000000000000000 = 2^20 which is greater than the 19 1's.

Question 973153: Please Help
Generate a formula for the nth Octagonal number by relating to one or more figurate numbers with fewer than seven sides(by relating to hexagonal, pentagonal, square, oblong or triangular numbers).

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

Triangle:

Square:

Pentagonal:

Hexagonal:

Heptagonal:

The pattern looks like octagonal should be

And that is indeed the correct formula.

John

My calculator said it, I believe it, that settles it

Question 972411: Question:
Gabe's garden is in the shape of a triangle with a base of 28 ft and height of 24 ft. Gabe has plants that require 6 ft 2 to grow properly. What is the area of the garden? What is the greatest number of these plants that Gabe can fit into the garden?

Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
b=base=28 ft; h=height=24 ft; A=area
.

ANSWER 1: The area of the garden is 336 square feet.
.

ANSWER 2: The greatest number of plants that will fit with adequate space is 56.

Question 970770: Jason is attempting to rest a piece of wood on a cement ball so that the angle of elevation of the resulting ramp is exactly 18 degrees. Jason draws the sketch below to model this situation. He labels the point of tangency between the ramp and the cement ball, A, the center of the ball, B, and the point of tangency between the flat ground and the ball, C, and the point where the ramp will touch the ground, D. If the radius of the cement ball is 21 inches, find the distance between points C and D so the damp will have the desired angle of elevation. Round your answer the the nearest inch.
Answer by jim_thompson5910(33401)   (Show Source):
You can put this solution on YOUR website!
Hint: Draw out the picture to get

Then erase all of the extra unneeded parts of the drawing and you will be left with this

The ultimate goal is to find the value of x (the length of CD)