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There are two circles, and they both symmetric with respect to the y-axis.  One is externally tangent to both circles (so the unit circles are outside), and the other is internally tangent to both circles (so the unit circles are inside).  You can draw both cases, but they're easy to understand.

HINT: We could x root every number

From 30-60-90 triangle, tan(pi/3) = sqrt(3).  I will let you finish.

Each item ends in 99 cents.  Does that help?

thats wrong

wrong

By Vieta, a + b = 4 and ab = 7.  Can you solve it now?

Set up a system:

3t + 7c = 376

8t + 2c = 486

Can you solve it now?

Look at these numbers and see if they meet your conditions. If they don't, please let know where I went wrong.

4000  4005  4010  4015  4020  4025  4030  4035  4040  4045  4050  4055  4060  4065  4100  4105  4110  4115  4120  4125  4130  4135  4140  4145  4150  4155  4160  4165  4200  4205  4210  4215  4220  4225  4230  4235  4240  4245  4250  4255  4260  4265  4300  4305  4310  4315  4320  4325  4330  4335  4340  4345  4350  4355  4360  4365  5000  5005  5010  5015  5020  5025  5030  5035  5040  5045  5050  5055  5060  5065  5100  5105  5110  5115  5120  5125  5130  5135  5140  5145  5150  5155  5160  5165  5200  5205  5210  5215  5220  5225  5230  5235  5240  5245  5250  5255  5260  5265  5300  5305  5310  5315  5320  5325  5330  5335  5340  5345  5350  5355  5360  5365  Total =  112

that is wrong.. try again!

Equation of line: y - 1 = -2(x + 1)

Standard form: 2x + y + 3 = 0.

BBJJ sometimes the simplest answers are also the correct ones.

You can give back his/her point now and a show of appreciation would be good.

No, just the digits \(b\) and \(c\) have to follow the third condition. The problem only said that the total number \(N\) had to follow the first condition.

Let the population of the city =P
0.6P =Women
0.4P =Men
0.3 * 0.6P =0.18P =Girls.
0.4 * 0.18P =0.072P are girls between 5-7 years old.

0.25 * 0.4P =0.1P are boys
0.20 * 0.10P =0.02P are boys between 5-7 years old.
0.02P = 2000
P =2000 / 0.02
P =100,000 People - the population of the city.
0.072 * 100,000 = 7,200 girls between 5-7 years old.

Compute

\(S = 1^2/(1.3) + 2^2/(3.5) + 3^2/(5.7) + 4^2/(7.9) +............+ 500^2/(999.1001)\)

I took the "." in the denominators to mean "times" or "*" : if that is the case, then your sequence sums up to:

sumfor(n, 1, 500, (n^2 / (4*n^2 - 1))=125,250 / 1001 

If each side of a square were increased by seven feet the area would be 315 square feet larger. What is the length of a side of the square

The trapezoid ABCD is 1/4 of the total increase of the area of a square.   315 / 4 = 78.75 sq ft 

My diagram may help you find the side length of the square

Here's a start:

Can you take it from here? (i.e. you have two simultaneous equations that you can solve for h and x).

As follows: