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AI = 2*sqrt(3) - 2.

AE = 5 + sqrt(3), so a + b = 8.

The formula for the sum is \({s \over {1 - r}} \), where s is the starting term, and r is the common ratio. 

The starting term is \({b \over 7} \), and the common term is \({b \over 7}\). This means that we have the equation \({{b \over 7} \over {1 - {b \over 7}}} = 1\). 

Solving for b, we find \(b = {7 \over 2} = \color{brown}\boxed{3.5}\)

\(\color{brown}\boxed{10,002}\)

https://web2.0calc.com/questions/graphing-parabolas-part-2

\(-t^2 + 8t + 10 = 12\)

\(-t^2 + 8t - 2 = 0\)

\(t = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(t = {-8 \pm \sqrt{-8^2-(4 \times -1 \times -2)} \over 2 \times -1}\)

\(t= {-8 \pm \sqrt{56} \over -2}\)

\(t = {-8 \pm 2\sqrt{14} \over -2}\)

\(t = {4 \pm \sqrt{14}}\)

\(t = \color{brown}\boxed{4 - \sqrt{14}}\)

Why don't you try it out? 

Pick any number with a remainder of 3, compute \(n^2 + 1\), and find the remainder when it is divided by 7. 

The radius of the circle is \(\text{Area} \over \text{semiperimeter}\). 

The semiperimeter is half of the perimeter, and find the area using Heron's formula: \(\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}\), where s is the semiperimeter. 

Company A:

360 / 12 ==30 packs of 12 pencils each

30  x  $1.60 ==$48.00 - cost of 360 pencils from Company A

Company B:

360 / 18 ==20 packs of 18 pencils each

20  x  $3.00==$60 - cost of 360 pencils from Company B

Abs[60 - 48]==$12 - absolute difference between the the 2 Companies.

The distance is 5*sqrt(11)/3.

ans is 11, Thx so much @BuilderBoi

Here's a similar problem: https://web2.0calc.com/questions/help-geometry_3429#r6

Just make a list...

It would look like this: AAA, AAB, AAC, ABA, ABB, ABC, ACA, ACB, ACC, ... , CCB, CCC.

Because it is converging to 1, therefore:

sumfor(n, 1, infinity, ((b)^n) / (7^n))==1

b ==7 / 2 ==3.5

a_1 = 15/2.

There are 10 ways of arranging the people.

The side length of the square is 8.

1.75 ==1  x  R^3

1.75 ==R^3

R ==1.75^(1/3) ==1.20507113 - hourly rate of growth

Future population==200  x  1.20507113^10

                                 ==200  x  6.4584281

                                 ==1,292 - number of yeast cells 10 hours after 9:00 AM.

Reflect the point across \(x = 5\).

I think your question is missing the numbers...

Here's another way: 

The area of the 2 triangles is \(12 \times (5 + 4) \div 2 = 54 \)

The area of the white triangle is \(12 \times 5 \div 2 = 30\)

This means that the area of the shaded region is \(54 - 30 = \color{brown}\boxed{24}\)

I solved it and got 12/7.