Tutors Answer Your Questions about Geometric formulas (FREE)
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+10x120=0
divide by 2
x^2+5x60=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 r13

(r+13)*(r13) = 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):
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=2S10
.
L+S=38
L=38S
.
38S=2S10
48=3S
16=S
ANSWER !: The smaller number is 16.
.
L=38S=3816=22
ANSWER 2: the larger number is 22.
.
CHECK:
.
L=2S10
22=2(16)10
22=3210
22=22
Question 991444: Find the next five terms, then write a conjecture.
1, 8, 27, 64, ___, ___, ___, ___, ___
Answer by solver91311(20879) (Show Source):
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^216k+100=k^24k+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^216k+100=k^24k+85
Answer by josgarithmetic(13975) (Show Source):
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=30w. And the expression for the area in terms of the width : A=w^2 +30w
Answer by josgarithmetic(13975) (Show Source):
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:
 Crossmultiplying
 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): Answer by MathLover1(11324) (Show Source):
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):
Question 986695: angle ABC is 25 degrees
angle ABD = 2xy
angle DBC = 3yx
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 = 2xy
angle DBC = 3yx
ray BD bisects angle ABC, so 2xy = 3yx

find the equation
2xy = 3yx
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.
, onehalf 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): Answer by Tatiana_Stebko(1470) (Show Source):
Question 984839: Draw a line ab intercept plane q at w
Answer by Alan3354(47455) (Show Source):
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):
Question 984455: How do you do midpoint and distance?
Answer by Fombitz(25151) (Show Source):
Question 984356: find a if given c and theta
Answer by Timnewman(249) (Show Source):
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+4y4z=5
Answer by Edwin McCravy(13211) (Show Source):
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):
Question 982744: Find the value of the acute angle, if the obtuse angle is 136 degrees.
Answer by Alan3354(47455) (Show Source):
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 slopeintercept 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):
Question 980491: in geometric progression please solve for r: S = rL a / r  1
thank you
Answer by solver91311(20879) (Show Source):
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): Answer by josgarithmetic(13975) (Show Source):
Question 979054: The diagonal of a rectangle is 10.what is the area of rectangle
Answer by Alan3354(47455) (Show Source):
Question 978137: standard equation with a focus at 6,8 and directrix at y=2
Answer by josgarithmetic(13975) (Show Source):
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 + x2, find f(a1)
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):
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):
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)

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, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025
