Questions on Geometry: Geometric formulas answered by real tutors!

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Just apply the distance formula, which is literally applied Pythagorean theorem.







Question 570164: find the geometric mean of 8 and 18
Answer by stanbon(48502) About Me  (Show Source):
You can put this solution on YOUR website!
find the geometric mean of 8 and 18
-----
x/8 = 18/x
---
x^2 = 8*18
----
x = 12
==============
Cheers,
Stan H.
==============


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) About Me  (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 S%5Bn%5D of the first n terms of an arithmetic progression starting with a%5B1%5D and increasing by d from term to term is
S%5Bn%5D=%28n%2F2%29%282+a%5B1%5D%2B%28n-1%29d%29
In Peter’s case, a%5B1%5D=60000 and d=6000, so
S%5Bn%5D=%28n%2F2%29%282+%2A60000%2B%28n-1%296000%29+=%28n%2F2%29%28120000%2B6000n-6000%29=%28n%2F2%29%28114000%2B6000n%29=57000n%2B3000n%5E2
To find out when S%5Bn%5D%3E=2000000 we solve
57000n%2B3000n%5E2=2000000 ---> 57n%2B3n%5E2-2000=0 --> 3n%5E2%2B57n-2000=0
n=%28-57+%2B-+sqrt%28+57%5E2-4%2A3%2A%28-2000%29+%29%29%2F%282%2A3%29+ using the quadratic formula. We simplify to
n=%28-57+%2B-+sqrt%28+3249%2B24000%29%29%2F6=%28-57+%2B-+sqrt%2827249%29%29%2F6 , which rounds to 18.01
That means that 18 years is not quite enough. In fact
S%5B18%5D=57000%2A18%2B3000%2A18%5E2=1998000
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.
S%5B19%5D=57000%2A19%2B3000%2A19%5E2=2166000
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
$60,000r%5E3=$75,000, so r%5E3=$75,000/$60,000=5/4=1.25 and
r=root%283%2C1.25%29= 1.0772 (rounded)
Each year end he gets a raise worth 0.0772 times the prior year salary, or highlight%287.72%29% 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%28%285%2F4%29%5E%281%2F3%29%29%5E9=$60,000%285%2F4%29%5E3=$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 r, starting with a%5B1%5D is calculated as
a%5B1%5D%28r%5En-1%29%2F%28r-1%29
In this case $60,000%28%281.077217%5E10-1%29%2F%281.077217-1%29%29= $60,000%28%282.10394-1%29%2F%281.077217-1%29%29= $60,000%281.10394%2F0.077217%29= $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) About Me  (Show Source):
You can put this solution on YOUR website!
Note that " percent " means " per one hundred ",
so "x" percent is +x%2F100+
given:
+x%2F100+=+1%2F4+
Multiply both sides by +400+
+4x+=+100+
+x+=+25+
se the copier to 25%


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) About Me  (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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
find the length of a = xi + 6j + 3k
----------
= sqrt%28x%5E2+%2B+6%5E2+%2B+3%5E2%29+=+sqrt%28x%5E2+%2B+45%29


Question 559311: Round 952,123 to the nearest thousand.
Answer by nn-i(2) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
V+=+%281%2F3%29pi%2Ar%5E2%2Ah To solve for h, divide both sides by %281%2F3%29pi%2Ar%5E2
h+=+V%2F%28%281%2F3%29pi%2Ar%5E2%29 Simplify:
h+=+3V%2F%28pi%2Ar%5E2%29
V+=+%281%2F3%29pi%2Ar%5E2%2Ah To solve for r, divide both sides by %281%2F3%29pi%2Ah:
r%5E2+=+V%2F%28%281%2F3%29pi%2Ah%29 Simplify:
r%5E2+=+3V%2F%28pi%2Ah%29 Now take the square root of both sides.
r+=+sqrt%283V%2F%28pi%2Ah%29%29


Question 557003: C:\Users\USER\Desktop\geometry.gif
Find the area of the shaded region.

Answer by solver91311(12114) About Me  (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
The Out Campaign: Scarlet Letter of Atheism



Question 556921: on the coordinate plane plot point a whole coordinate are (-3,2)
Answer by JBarnum(1826) About Me  (Show Source):
You can put this solution on YOUR website!
um theres only one point you can plot this


Question 555319: find the measure of each exterior angle of a regular octagon?
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of each exterior angle is 360/8 = 45 degrees.


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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
I = (180(n-2))/n

I = (180(12-2))/(12)

I = (180(10))/(12)

I = 1800/(12)

I = 150


So the measure of each interior angle of a 12-sided polygon is 150 degrees.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Question 551466: what is the slope of the line perpendicular to y= -3 over 2x +9?
Answer by Alan3354(21542) About Me  (Show Source):
You can put this solution on YOUR website!
what is the slope of the line perpendicular to y= -3 over 2x +9?
------
Is it y+=+-3%2F%282x+%2B+9%29 ?


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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Use the point-slope formula
+%28+y+-%28-2%29+%29+%2F+%28+x+-+0+%29+=+%28+6+-%28-2%29+%29+%2F+%28+4+-+0+%29+
+%28+y+%2B+2+%29+%2F+x+=+%28+6+%2B+2+%29+%2F+4+
+%28+y+%2B+2+%29+%2F+x+=+2+
+y+%2B+2+=+2x+
+y+=+2x+-+2+
Here's the plot:
+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+6%2C+2x+-+2+%29+


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) About Me  (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.
a%5E2+%2B+b%5E2+=+c%5E2
9%5E2+%2B+b%5E2+=+18%5E2
b%5E2+=+243
b+=+sqrt%28243%29+=+9sqrt%283%29
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) About Me  (Show Source):
You can put this solution on YOUR website!
=2a%2F%28a%2Bb%29%5E2%28a-b%29%2B2b%2F%28a%2Bb%29%28a-b%29%5E2-1%2F%28a%2Bb%29%5E2-1%2F%28a-b%29%5E2
Take LCD
=%282a%28a-b%29%2B2b%28a%2Bb%29-%28a-b%29%5E2-%28a%2Bb%29%5E2%29%2F%28a%2Bb%29%5E2%28a-b%29%5E2
=%282a%5E2-2ab%2B2ab%2B2b%5E2-%28a%5E2-2ab%2Bb%5E2%29-%28a%5E2%2B2ab%2Bb%5E2%29%29%2F%28a%2Bb%29%5E2%28a-b%29%5E2
=%282a%5E2-cross%282ab%29%2Bcross%282ab%29%2B2b%5E2-%28a%5E2-2ab%2Bb%5E2%29-%28a%5E2%2B2ab%2Bb%5E2%29%29%2F%28a%2Bb%29%5E2%28a-b%29%5E2
=%282a%5E2%2B2b%5E2-%28a%5E2-2ab%2Bb%5E2%29-%28a%5E2%2B2ab%2Bb%5E2%29%29%2F%28a%2Bb%29%5E2%28a-b%29%5E2
=%282a%5E2%2B2b%5E2-a%5E2%2B2ab-b%5E2-a%5E2-2ab-b%5E2%29%2F%28a%2Bb%29%5E2%28a-b%29%5E2
=%282a%5E2-2a%5E2%2B2b%5E2-2b%5E2%2B2ab-2ab%29%2F%28a%2Bb%29%5E2%28a-b%29%5E2
=%28cross%282a%5E2%29-cross%282a%5E2%29%2Bcross%282b%5E2%29-cross%282b%5E2%29%2Bcross%282ab%29-cross%282ab%29%29%2F%28a%2Bb%29%5E2%28a-b%29%5E2
=1%2F%28a%2Bb%29%5E2%28a-b%29%5E2


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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
a line passes through the points (5, -8) and (6, 2). what is the slope?
------
Slope, m = (change in y)/(change in x)


Question 550603: what is the equation of the line that passes through (9, -2) and (4,6)?
Answer by jim_thompson5910(21667) About Me  (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 x%5B1%5D=9 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=6.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%286--2%29%2F%284-9%29 Plug in y%5B2%5D=6, y%5B1%5D=-2, x%5B2%5D=4, and x%5B1%5D=9


m=%288%29%2F%284-9%29 Subtract -2 from 6 to get 8


m=%288%29%2F%28-5%29 Subtract 9 from 4 to get -5


m=-8%2F5 Reduce


So the slope of the line that goes through the points and is m=-8%2F5


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--2=%28-8%2F5%29%28x-9%29 Plug in m=-8%2F5, x%5B1%5D=9, and y%5B1%5D=-2


y%2B2=%28-8%2F5%29%28x-9%29 Rewrite y--2 as y%2B2


y%2B2=%28-8%2F5%29x%2B%28-8%2F5%29%28-9%29 Distribute


y%2B2=%28-8%2F5%29x%2B72%2F5 Multiply


y=%28-8%2F5%29x%2B72%2F5-2 Subtract 2 from both sides.


y=%28-8%2F5%29x%2B62%2F5 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%28-8%2F5%29x%2B62%2F5


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) About Me  (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) About Me  (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:

drawing%28400%2C200%2C-.1%2C2.1%2C-.1%2C1%2C%0D%0Alocate%28.15%2C.12%2C%2740%B0%27%29%2C%0D%0Atriangle%280%2C0%2Ccos%2840%2Api%2F180%29%2Csin%2840%2Api%2F180%29%2C2cos%2840%2Api%2F180%29%2C0%29+%29 

Now since it is isosceles, we know that the other base angle is also 40°.
So we label it 40° also

drawing%28400%2C200%2C-.1%2C2.1%2C-.1%2C1%2C%0D%0Alocate%28.15%2C.12%2C%2740%B0%27%29%2C+locate%281.25%2C.12%2C%2740%B0%27%29%2C%0D%0Atriangle%280%2C0%2Ccos%2840%2Api%2F180%29%2Csin%2840%2Api%2F180%29%2C2cos%2840%2Api%2F180%29%2C0%29+%29


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°.

drawing%28400%2C200%2C-.1%2C2.1%2C-.1%2C1%2C%0D%0Alocate%28.15%2C.12%2C%2740%B0%27%29%2C+locate%281.25%2C.12%2C%2740%B0%27%29%2C%0D%0Atriangle%280%2C0%2Ccos%2840%2Api%2F180%29%2Csin%2840%2Api%2F180%29%2C2cos%2840%2Api%2F180%29%2C0%29%2C%0D%0Alocate%28.73%2C.6%2C%27x%B0%27%29%0D%0A%0D%0A%0D%0A+%29

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.

drawing%28400%2C200%2C-.1%2C2.1%2C-.1%2C1%2C%0D%0Alocate%28.15%2C.12%2C%2740%B0%27%29%2C+locate%281.25%2C.12%2C%2740%B0%27%29%2C%0D%0Atriangle%280%2C0%2Ccos%2840%2Api%2F180%29%2Csin%2840%2Api%2F180%29%2C2cos%2840%2Api%2F180%29%2C0%29%2C%0D%0Alocate%28.67%2C.55%2C%27100%B0%27%29%0D%0A%0D%0A%0D%0A+%29



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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
You're dividing by -3 each time, so the next term is -27/(-3) = 9


Question 550496: if the complement of an angle measures 22 degrees, what is the measure of its supplement?
Answer by jim_thompson5910(21667) About Me  (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) About Me  (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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
not an equation please submitt correctly


Question 550461: Find the next term of the pattern: 3, 12, 147, . . .
Answer by JBarnum(1826) About Me  (Show Source):
You can put this solution on YOUR website!
guess n check works...lol took me 1 min
3%5E2%2B3=12
12%5E2%2B3=147
147%5E2%2B3=21612
i started with 3*4=12
but 12*4=48 not 147
12^2=144 and 147-144=3
so that pattern is x%5E2%2B3=yand y%5E2%2B3=z
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) About Me  (Show Source):
You can put this solution on YOUR website!
Applying the distance formula:
+26+=+sqrt%28+%28+k+-+0+%29%5E2+%2B+%28+-8+-%28-7%29+%29%5E2+%29+
+26+=+sqrt%28++k%5E2+%2B+%28+-1+%29%5E2+%29+
+26+=+sqrt%28+k%5E2+%2B+1+%29+
+26%5E2+=+k%5E2+%2B+1+
+676+=+k%5E2+%2B+1+
+k%5E2+=+675+
+k+=+25.98+
also
If k is assumed to be negative
+%28-k%29%5E2+=+675+
+-k+=+25.98+
+k+=+-25.98+
Hope I got it


Question 550456: Simplify: 9y + b- 7g + b- 8xg + b- 3yg - 2x
Answer by JBarnum(1826) About Me  (Show Source):
You can put this solution on YOUR website!
wrong section but simply use the addition property and group like terms
9y ask are there any other single y variables...nope
b are there any other single b variables...yess add them together b%2Bb%2Bb=3b
-7g are there any other single g variables...nope
-8xgare there any other xg variables...nope
-3ygare there any other yg variables...nope
-2xare there any other single x variables...nope
highlight%289y%2B3b-2x-7g-8xg-3yg%29
now its simplified but it can be rearranged differently depending on what your teacher is looking for
1 possibility
9y%2B3b-2x%2B%28-7g-8xg-3yg%29
9y%2B3b-2x-g%287%2B8x%2B3y%29
highlight%283%283y%2Bb%29-2x-g%287%2B8x%2B3y%29%29
2 possibility
3b-7g%28-2x-8xg%29%2B%289y-3yg%29
highlight%283b-7g-2x%281%2B4g%29%2B3y%283-g%29%29
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) About Me  (Show Source):
You can put this solution on YOUR website!
6x + 2(x + 4)


6x + 2(x) + 2(4)


6x + 2x + 8


8x + 8


So 6x + 2(x + 4) = 8x + 8


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) About Me  (Show Source):
You can put this solution on YOUR website!
Each base angle is (180-34)/2 = 73 degrees


Question 550460: Two intersecting planes __?__ intersect in more than one point.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Two intersecting planes __always__ intersect in more than one point.


Question 550458: Find the sum of the measures of the interior angles of a pentagon.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
S = 180(n-2)

S = 180(5-2)

S = 180(3)

S = 540

So the sum of the measures of the interior angles of a pentagon is 540 degrees.


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) About Me  (Show Source):
You can put this solution on YOUR website!


Use the mid-point formulas. You are given the coordinates of point 1, (Point B) and the mid-point, (Point P).





Substitute the given values and do the arithmetic to solve for and

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism



Question 547227: Solve the equation or formula for the variable specified. 3qr%2B9t=7u for r
Answer by mathie123(175) About Me  (Show Source):
You can put this solution on YOUR website!
3qr%2B9t=7u
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.
3qr%2B9t-9t=7u-9t
3qr=7u-9t
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.
3qr%2F3q=%287u-9t%29%2F3q
r=%287u-9t%29%2F3q
And there it is!


Question 544640: what temp in celsius is 1.5 times that of Fahrenheit?
Answer by Alan3354(21542) About Me  (Show Source):
You can put this solution on YOUR website!
C = 1.5F = 1.5*(C*1.8 + 32)
C = 2.7C + 48
C = -48/1.7 =~ -28.235 degs
-----------------


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) About Me  (Show Source):
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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 = 

sum%28%282p%5Bi%5D-1%29%2Ci=1%2C2M%29 + sum%28%282q%5Bj%5D%29%2Cj=1%2C2N-1%29 =

sum%28%282p%5Bi%5D%29%2Ci=1%2C2M%29 - sum%28%281%29%2Ci=1%2C2M%29 + sum%28%282q%5Bj%5D%29%2Cj=1%2C2N-1%29 =

2sum%28%28p%5Bi%5D%29%2Ci=1%2C2M%29 - 2M + 2sum%28%28q%5Bj%5D%29%2Cj=1%2C2N-1%29

2%28sum%28%28p%5Bi%5D%29%2Ci=1%2C2M%29+-+M+%2B+sum%28%28q%5Bj%5D%29%2Cj=1%2C2N-1%29%29

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) About Me  (Show Source):
You can put this solution on YOUR website!


Just solve the equation for

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism



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) About Me  (Show Source):
You can put this solution on YOUR website!
Area of trapezium = 1/2 * sum of parallel sides * height
=1/2 (8+6)*h
28=1/2 * 14 * h
28/7 = h
h= 4 m



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) About Me  (Show Source):
You can put this solution on YOUR website!
Just add the the number before the previous one and the previous one together
1,1,2,3,5,8,13,21,34,55


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