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Find the area of triangle RST.

xy+yz=zx

3n + n+16 = 32

4n = 16

n=4

xy=3n=3*4=12

I ran a regression analysis on your data, and the optimal location is Kansas City, Missouri, for a total distance of 28,762 miles.

Upstream speed = 45 miles per hour, downstream speed = 60 miles per hour

Wow... I really need to work on reading LaTeX!

first, the whole distance is 32, which is XZ.

then, write algebraic equation, XY+YZ = XZ, 3n + n+16 = 32

combine like terms: 4n = 16

n = 4 

and XY = 4*3 = 12

I do not know why it is blocked, there are a lot of bugs lately.

I have sent you a private message.

If AC is parallel to OB, that doesn't make BC parallel to AO.

There's not enough informatio for this problem to be solved!!!

Thanks guest, here is a little more insight for others to see what you have done.

(a) Compute the sum 101^2 - 97^2 + 93^2 - 89^2 + .... + 5^2 - 1^2

I paired them first

(101^2 - 97^2) + (93^2 - 89^2) + .... + (5^2 - 1^2)

then turned them around

(5^2 - 1^2)+ ..................   +  (93^2 - 89^2) +  (101^2 - 97^2) 

$T_1=(5^2 - 1^2) = [(3+2)^2 - (3-2)^2]\\ T_2=(13^2-9^2)= [(11+2)^2 - (11-2)^2]\\ ...\\ T_n= [((8n-5)+2)^2 - ((8n-5)-2)^2]\\ ...\\ T_{13}=(101^2-97^2)\\\quad= [(8*13-5+2)^2 - (8*13-5-2)^2]\\ \quad= [(99+2)^2 - (99-2)^2]\quad \text{just checking... it is good}\\ $

$T_n= [((8n-5)+2)^2 - ((8n-5)-2)^2]\\ T_n= [(8n-3)^2 - (8n-7)^2]\\ T_n= [(8n)^2-48n+9)] - [(8n)^2-112n+49)]\\ T_n= [-48n+9)] - [-112n+49)]\\ T_n= -48n+9 +112n-49\\ T_n= 64n-40\\ \text{This is an AP}\\ a=24, d=64,\;n=13\\ S_n=\frac{n}{2}(2a+(n-1)d]\\ S_{13}=\frac{13}{2}(2*24+12*64]\\ S_{13}=13(24+6*64]\\ S_{13}=13*408\\ S_{13}=5304\\$

LaTex:

T_1=(5^2 - 1^2) = [(3+2)^2 - (3-2)^2]\\
T_2=(13^2-9^2)=  [(11+2)^2 - (11-2)^2]\\
...\\
T_n= [((8n-5)+2)^2 - ((8n-5)-2)^2]\\
...\\
T_{13}=(101^2-97^2)\\\quad=  [(8*13-5+2)^2 - (8*13-5-2)^2]\\
\quad=  [(99+2)^2 - (99-2)^2]\quad \text{just checking... it is good}\\

T_n= [((8n-5)+2)^2 - ((8n-5)-2)^2]\\
T_n= [(8n-3)^2 - (8n-7)^2]\\
T_n= [(8n)^2-48n+9)] - [(8n)^2-112n+49)]\\
T_n= [-48n+9)] - [-112n+49)]\\
T_n= -48n+9 +112n-49\\
T_n= 64n-40\\
\text{This is an AP}\\
a=24, d=64,\;n=13\\
S_n=\frac{n}{2}(2a+(n-1)d]\\
S_{13}=\frac{13}{2}(2*24+12*64]\\
S_{13}=13(24+6*64]\\
S_{13}=13*408\\
S_{13}=5304\\

for some reason it isnt allowing me to give it a like, but thank you for your help!

Let m be the number of miles traveled so both rental costs for A and B are the same.

We form an equation:

110+0.4x=80+0.7x

30=0.3x

x=100 miles.

Oh...why are they blocked though? I could still type up the solution here though, but there won't be any diagrams.

FV = 7,700 *1.0575^24  

FV =7,700 *  3.82585957

FV =$29,459.12 - what $7,700 will be worth in 24 years.

b) See the answer in LaTex here:  https://web2.0rechner.de/mitglieder/heureka/?answerpage=531

2²,   3²,   and  4²    

Try this:       8x + 51 + 6x - 25 = 180  

a=0;b=0;c=0;d=0;e=0;p=0; cycle:n= a*10000+b*1000+c*100+d*10+e;if(n%2==1 and n*5+2*(n+4)==6*(n+2)+33, goto loop, goto next); loop:printn,", ",;p=p+1; next:e++;if(e<10, goto cycle, 0);e=0;d++;if(d<10, goto cycle, 0);e=0;d=0;c++;if(c<10, goto cycle,0);c=0;d=0;e=0;b++;if(b<10, goto cycle,0);e=0;d=0;c=0;b=0;a++;if(a<10, goto cycle,0);print"Total = ",p

OUTPUT: Your numbers are: 37, 39, 41

Im sorry. I was really skeptical about the other answer....but I didn't have a better way...so....

Let the distance travelled by the faster canoe =D

The distance travelled by the slower canoe =D - 5.25

Let the speed of the slower canoe =S

The speed of the faster canoe         =2S

S * 3.5 hours =D - 5.25

2S * 3.5 hours =D, solve for D, S

S =3/2 =1.5 mph - speed of the slower canoe.

1.5 * 2  =3 mph - speed of the faster canoe.

D =21/2 =10.5 miles travelled by the faster canoe.

a ) is wrong!

Here is your entire sequence grouped in "twos"

(10201 -9409, 8649 -7921, 7225 -6561, 5929 -5329, 4761 -4225, 3721 -3249, 2809 -2401, 2025 -1681, 1369 -1089, 841 -625, 441 -289, 169 -81, 25 -1)

What is the difference between each pair beginning with first? The following:

(792, 728, 664, 600, 536, 472, 408, 344, 280, 216, 152, 88, 24) - This is an arithmetic sequence.                    How do you sum it up?

[F + L] / 2 * N (number of terms) =Sum, where F=First term, L=Last term, N =Number of terms.

[792 + 24] / 2 * 13 =5,304 - And that is it!.

I'm sorry, but I am also quite confused on how the guest got the answer. I did it with difference of squares, which is a long, rigorous process... let me sent this to someone else...