Tutors Answer Your Questions about Geometric formulas (FREE)
Question 570478: hi
how would u be able to figure out the distance formula passing through the points (3,-2) and (6,4) step by step!!! please
Answer by richard1234(4789)   (Show Source):
Question 570164: find the geometric mean of 8 and 18
Answer by stanbon(48502) (Show Source):
Question 569553: Peter works as an electrical engineer for an electrical firm,His total salary for his first year of work at this firm is $60,000.peter's annual salary increases by 10% of his first year's salary,Find
I)His total salary after 10 years
II) the least value of 'n' fir which his total salary after 'n' years is more than 2milion dollars
b) John is an electrical engineer in a rival firm,His total salary for the first year is also $60,000.But his annual salary follows a geometric progession.If he earns $75,600 in his 4th year of work,find
i)his annual percentage increase in salary,
II) his total salary after 10 years
Answer by KMST(576)  (Show Source):
You can put this solution on YOUR website!I believe they mean that poor Peter, gets a raise of (0.10)($60,000)= $6,000 every year. His salary goes up in an arithmetic sequence (or arithmetic progression).
In the 10th year, after 9 raises, he gets $60,000+9($6,000)=$60,000+$54,000=$114,000.
The sum of an arithmetic progression is the average of first and last terms, multiplied times the number of terms.
I) Adding up Peter’s 10 years of salary we get 10($60,000+$114,000)/2=$870,000. I believe That’s what the problem means by “His total salary after 10 years.”
II) Another way to calculate the sum  of the first  terms of an arithmetic progression starting with  and increasing by  from term to term is
In Peter’s case,  and  , so
To find out when  we solve
 --->  --> 
 using the quadratic formula. We simplify to
 , which rounds to 18.01
That means that 18 years is not quite enough. In fact
Peter will have collected $2,000,000 in salary at some point during his 19th year, and after 19 years he will have totaled $2,166,000 in earnings, so I suspect the answer expected for part II) is 19.
b)John’s annual salary follows a geometric progression starting at $60,000, and earns $75,600 in his 4th year of work.
I) Let’s find his annual percentage increase in salary,
In a geometric sequence (or geometric progression), each term is the product of the term before times a common ratio, r. After raises at the end of the first 3 years, John’s salary for the fourth year is
$60,000  =$75,000, so =$75,000/$60,000=5/4=1.25 and
 = 1.0772 (rounded)
Each year end he gets a raise worth 0.0772 times the prior year salary, or  % of the prior year salary.
John may look at Peter in envy at the end of the first year, but his raise is always 7.72% of the latest salary, and keeps growing, while Peter’s raises are always the same $6,000 (10% of his starting salary). Peter had a salary of $60,000+3($6,000) =$78,000 for the fourth year, but soon John overtakes Peter in salary
II) Let’s find John’s total salary after 10 years
For the 10th year, John’s annual salary should be $60,000  =$60,000  =$117,187.50 (already ahead of Peter)
However, he is not yet ahead in terms of total earnings.
The sum of n terms of a geometric progression of common ratio  , starting with is calculated as
In this case $60,000  = $60,000  = $60,000  = $857,791.83 (rounded)
Question 567568: photocopiers can reduce or enlarged an item being copied. the scale factor of the copy to the original is expressed as a percent. if you want the original to be one fourth the side of the copy, at what percent do you set the copier?
Answer by josmiceli(6769)  (Show Source):
Question 498603: The sides of the outside square are 6 inches long. The corners of the next smaller squares are at the midpoints of the outside square and so on. Find the sum of the perimeters of the 3 squares. Imagine that the process of nesting squares continues forever. The sum of the perimeters approaches a finite number. What is that number?
Answer by jhardin(1) (Show Source):
Question 564179: Rearrange 1/u + 1/v = 1/f
to make u the subject of the formula.
Give your answer in its simplest form.
I know that uv is the common denominator, but i dont know how to rearrange.
Answer by mananth(10539)  (Show Source):
Question 559964: find the length of a = xi + 6j + 3k
this is a vector problem, sorry i had wrong category, I couldn't find it
Answer by Alan3354(21542)  (Show Source):
Question 559311: Round 952,123 to the nearest thousand.
Answer by nn-i(2) (Show Source):
Question 557664: If the formula for Volume of a cone is v=1/3*pi*r^2*h how do I find for h or r?
Answer by Earlsdon(6098) (Show Source):
You can put this solution on YOUR website! To solve for h, divide both sides by 
 Simplify:
To solve for r, divide both sides by  :
 Simplify:
 Now take the square root of both sides.
Question 557003: C:\Users\USER\Desktop\geometry.gif
Find the area of the shaded region.
Answer by solver91311(12114)  (Show Source):
You can put this solution on YOUR website!
Right. Any of us can get right into your local hard drive. Use your head for something besides a hat rack, please.
John
My calculator said it, I believe it, that settles it
Question 556921: on the coordinate plane plot point a whole coordinate are (-3,2)
Answer by JBarnum(1826)  (Show Source):
Question 555319: find the measure of each exterior angle of a regular octagon?
Answer by jim_thompson5910(21667) (Show Source):
Question 555179: I need help finding the perimeter, and area of a rectangle. The rectangle is 12in in width, and the length is x. I tired to figure it out several times,and just got weird confusing answers, and I've stressed myself out not knowing how to figure it out. Please please help me!
Answer by nerdybill(5403)  (Show Source):
You can put this solution on YOUR website!I need help finding the perimeter, and area of a rectangle. The rectangle is 12in in width, and the length is x. I tired to figure it out several times,and just got weird confusing answers, and I've stressed myself out not knowing how to figure it out. Please please help me!
width is 12 inches
length is x inches
.
Perimeter:
2(width + length) = 2(12 + x) = 24 + 2x inches
.
Area:
width * length = 12 * x = 12x square inches
Question 552625: A dodecagon is a polygon with 12 sides. How many degrees is each of the interior angles in a regular dodecagon? Show or explain how you got your answer.
Answer by jim_thompson5910(21667) (Show Source):
Question 551466: what is the slope of the line perpendicular to y= -3 over 2x +9?
Answer by Alan3354(21542) (Show Source):
Question 551398: two lines are parallel if the same side interior angles are_____________ angles.
f. complementary
h. congruent
g. supplementary
j. corresponding
Answer by Earlsdon(6098) (Show Source):
You can put this solution on YOUR website!If you were to draw a diagramm of this problem, two parallel lines crossed by a transversal, you would see that the same side interior angles would be supplementary. Try it!
Question 550886: what is the equation of the line that passes through (0, -2) and (4, 6)?
Answer by josmiceli(6769) (Show Source):
Question 550887: two sides of a 30 degrees -60 degrees -90 degrees triangle are 9 and 18. what is the length of the third side?
Answer by Alan3354(21542) (Show Source):
You can put this solution on YOUR website!two sides of a 30 degrees -60 degrees -90 degrees triangle are 9 and 18. what is the length of the third side?
---------------------------
The 18 side is the hypotenuse.
b =~ 15.588
Question 550678: 2a/(a+b)^2(a-b)+2b/(a+b)(a-b)^2-1/(a+b)^2-1/(a-b)^2
Answer by Maths68(1140)  (Show Source):
Question 550598: one of the base angles of an isosceles triangle is 40 degrees, Which is the triangle classification according to its angles?
Answer by JBarnum(1826) (Show Source):
You can put this solution on YOUR website!its an obtuse triangle
isosceles means 2 same sides and same angles
180-40-40=100
obtuse triangles have 1 angle thats greater then 90
Question 550602: a line passes through the points (5, -8) and (6, 2). what is the slope?
Answer by Alan3354(21542) (Show Source):
Question 550603: what is the equation of the line that passes through (9, -2) and (4,6)?
Answer by jim_thompson5910(21667) (Show Source):
You can put this solution on YOUR website!
First let's find the slope of the line through the points ) and )
Note: ) is the first point . So this means that  and  .
Also, ) is the second point . So this means that  and  .
 Start with the slope formula.
 Plug in , , , and
 Subtract  from  to get 
 Subtract  from  to get 
 Reduce
So the slope of the line that goes through the points and is
Now let's use the point slope formula:
 Start with the point slope formula
 Plug in , , and
 Rewrite  as 
 Distribute
 Multiply
 Subtract 2 from both sides.
 Combine like terms. note: If you need help with fractions, check out this solver.
So the equation that goes through the points and is
Question 550599: k is between J and L. JK= 3x-5, and KL=2X+1. If JL= 16, what is JK?
Answer by htmentor(580)  (Show Source):
You can put this solution on YOUR website!k is between J and L. JK= 3x-5, and KL=2X+1. If JL= 16, what is JK?
==========================
Given: JK = 3x - 5, KL = 2x + 1
The sum of the segments JK and KL will equal the length of the segment JL = 16
So we can write:
3x - 5 + (2x + 1) = 16 [JK + KL = JL]
Collect terms, solve for x:
5x - 4 = 16
5x = 20
x = 4
JK = 3x - 5 = 3*4 - 5 = 12 - 5 = 7
Ans: 7
Question 550604: one of the base angles of an isosceles triangle is 40 degrees. Which is the triangle classification according to its angles?
Answer by Edwin McCravy(6929)  (Show Source):
You can put this solution on YOUR website!
The smallest two angles in every triangle are acute angles (have measure
less than 90°). Sometimes the largest angle is also acute (has measure less
than 90°), sometimes it is right (has measure exactly 90°). and sometimes it is
obtuse (has measure greater than 90°).
If the largest angle is also an acute angle, the triangle is said to be "an acute triangle".
If the largest angle is a right angle, the triangle is said to be "a right
triangle".
If the largest angle is an obtuse angle, the triangle is said to be "an obtuse
triangle".
The triangle yoiu are talking about is isosceles with a base angle of 40°.
So we draw it:
Now since it is isosceles, we know that the other base angle is also 40°.
So we label it 40° also
They are both acute angles since 40° is less than 90°. So we need to
know about the largest angle, which is the vertex angle of the isosceles
triangle. We can look and see that it looks like it's obtuse, but in
geometry, we can't go by "what it looks like is true". We have to prove it.
Let's suppose the vertex angle is x°.
Since we know the three interior angles of every triangle totals 180°, we
have:
x° + 40° + 40° = 180°
We combine the terms 40° and 40° and get 80°
x° + 80° = 180°
We subtract 80° from both sides and get
x° = 100°
Since 100° is more than 90° the largest angle is obtuse, and so the
triangle is an obtuse triangle.
Edwin
Question 550500: what is the next term in the sequence? 729, -243, 81, -27
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(48502) (Show Source):
You can put this solution on YOUR website!what is the next term in the sequence? 729, -243, 81, -27
---
Common ratio: 729/(-243) = -3
----
next term -27/-3 = 9
next term 9/-3 = -3
==========================
Cheers,
Stan H.
===============
Answer by jim_thompson5910(21667) (Show Source):
Question 550496: if the complement of an angle measures 22 degrees, what is the measure of its supplement?
Answer by jim_thompson5910(21667) (Show Source):
You can put this solution on YOUR website!Let x = the unknown angle
The complement of angle x is 90-x and because the complement is 22 degrees, we know that 90-x = 22
Solve for x to get -x = 22-90 ---> -x = -68 ---> x = 68
So the original angle is 68 degrees and the supplement of 68 degrees is 180 - 68 = 112 degrees
Question 550498: where is the image of (-6, 2) reflected across the graph of y = -x?
Answer by stanbon(48502) (Show Source):
You can put this solution on YOUR website!where is the image of (-6, 2) reflected across the graph of y = -x?
-----------------
Ans: (-2,6)
======================
Cheers,
Stan H.
==================
Question 550480: the midpoint of a segment is (2, -5), and one of the endpoints is (3, 6). Where is the other endpoint?
Answer by jim_thompson5910(21667) (Show Source):
You can put this solution on YOUR website!(x+3)/2 = 2
x+3 = 4
x = 1
-------------------------------------------------------
(y+6)/2 = -5
y+6 = -10
y = -16
So the other endpoint is (1, -16)
Question 550457: Solve for x:
8
7
7
3
=
x +
Answer by JBarnum(1826) (Show Source):
Question 550461: Find the next term of the pattern: 3, 12, 147, . . .
Answer by JBarnum(1826) (Show Source):
You can put this solution on YOUR website!guess n check works...lol took me 1 min
i started with 3*4=12
but 12*4=48 not 147
12^2=144 and 147-144=3
so that pattern is  and 
i tried 3^2+3=12 then 12^2+3=147 so naturally its 147^2+3
Question 550463: Find the value of k so that the given points are 26 units apart. (–8, k ), (–7, 0)
Answer by josmiceli(6769) (Show Source):
Question 550456: Simplify: 9y + b- 7g + b- 8xg + b- 3yg - 2x
Answer by JBarnum(1826) (Show Source):
You can put this solution on YOUR website!wrong section but simply use the addition property and group like terms
 ask are there any other single y variables...nope
 are there any other single b variables...yess add them together 
 are there any other single g variables...nope
 are there any other xg variables...nope
 are there any other yg variables...nope
 are there any other single x variables...nope
now its simplified but it can be rearranged differently depending on what your teacher is looking for
1 possibility
2 possibility
there are a few more but i was just giving u the ideas
Question 550464: Simplify: 6x + 2(x + 4)
Answer by jim_thompson5910(21667) (Show Source):
Question 550462: What is the measure of each base angle of an isosceles triangle if its vertex angle measures 34 degrees
and its 2 congruent sides measure 21 units?
Answer by jim_thompson5910(21667) (Show Source):
Question 550460: Two intersecting planes __?__ intersect in more than one point.
Answer by jim_thompson5910(21667) (Show Source):
Question 550458: Find the sum of the measures of the interior angles of a pentagon.
Answer by jim_thompson5910(21667) (Show Source):
Question 549018: On a coordinate grid, line AB has end point B at (24,16). The midpoint at AB is P(4,-3). What is the y-coordinate of point A?
Answer by solver91311(12114) (Show Source):
Question 547227: Solve the equation or formula for the variable specified.  for r
Answer by mathie123(175) (Show Source):
You can put this solution on YOUR website!
We need to isolate r.
One trick I learned is do your BEDMAS backwards. So starting with S/A, we see that we have +9t we must get rid of.
Okay, now there is no more addition or subtraction on the same side of the equation as the r. the next step is looking for any division or multiplication. We have a 3 and a q multiplied with the r, so we must divide these out.
And there it is!
Question 544640: what temp in celsius is 1.5 times that of Fahrenheit?
Answer by Alan3354(21542) (Show Source):
Question 543272: suppose I added up a long list say thousands of natural numbers with the property that and even number of them are odd and an odd number of them are even. Can you determine whether the sum will be even or odd? Prove your answer
Answer by Edwin McCravy(6929) (Show Source):
You can put this solution on YOUR website!
Yes it's bound to be even.
PROOF:
Every even natural number can be written as 2p, where p is a natural number.
Every odd natural number can be written as 2q-1, where q is a natural number.
Suppose M and N are natural numbers and the list contains
the odd number 2M-1 of even natural numbers 2p1,2p2,...,2p2M-1
and
the even number 2N of odd natural numbers 2q1-1,2q2-1,...,2q2N-1.
Then the sum of the numbers in the list =
 +  =
 -  + =
2 - 2M + 2
2
which is an even number since it has a factor of 2.
[Note: We used 2p-1 for odd numbers rather than the usual 2p+1 because since
p is a natural number, the smallest odd natural number which 2p+1 can be is
3 when p=1, so to include 1, and some of the numbers in the list could be 1,
we must use 2p-1. The final result is positive since the first summation in
the parentheses above is greater than M.]
Edwin
Question 542767: c=F or F= 5/9 (F-32)
I need to know when the Celsius nemerical value & the Fahrenheit numerical value are the same.
Answer by solver91311(12114) (Show Source):
Question 542502: if the area of a trapezium is 28 m*m and two parallel sides are 8 m and60 dm respectively, find the altitude?
Answer by mananth(10539) (Show Source):
Question 153146: The Fibonacci sequence consists of the pattern 1,1,2,3,5,8,13...
What is the ninth term in the pattern?
Answer by octogirl(6)  (Show Source):
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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
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