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...or   f(x) = y = x^2 +8x + 15

roots at x = -3 and x = -5 :             (x+3)(x+5) = 0

                                              x^2 + 8x + 15 = 0

DIFFERENCE = 12 CDs

   difference per month 5-1 = 4 CD/mo

12 CDs/ 4 CDs/mo = 3 months

30  +  1M  =  18  +  5M

30 -  18 = 5M   - 1M

12  =  4M

M =  12/4  =   3   months

https://web2.0calc.com/questions/help-please_90002

This link shows the complete question, and my answer is there (post #2) 

240°  is a 60°  angle  in the 3rd quadrant...... so......sin  240   =   -sin 60  =  -sqrt (3) /  2

What does tell you that AE = 4?

AE is 4 so -AE=-4

You know it's best not to assume.

500 ( 1.025)²⁰ = $ 819.31

We notice that the angle of the square is 90 degrees, the angle measure of a equilateral triangle is 60 degrees, so therefore $BCE$ is $30 degrees$,

the square side and the equilateral triangle side are the same, so therefore $CE=BC$, making it isoceles

$180-30-2x=0$

x=75

$75$

1/4 * 3        +      1/3 * 4         +      1/2 *3

3/4                       4/3                         3/2

9/12            +       16/12        +         18/12

43/12 = 3   7/12   cups

To  find C  we have

[ 14 + 3(14 - 2) ,  4 + 3( 4 - - 2)  ]   =   [  14  + 3 ( 12)   ,  4 + 3 (6) ]  =  ( 50, 22)

Here is how to do one.....the rest are similar

c.)  a deposit at 4.4%/a, compounded quarterly, for 7 years

        .044 is interest in decimal

            4 periods per year    .044/4 = .011 interest PER PERIOD

                 7 years with QUARTERLY periods = 28 PERIODS
                       i =  (1 + .011)²⁸  - 1 = .358   35.8%

Your answer is based on the assumption that triangles ABC and ADE are not congruent.

Based on the given information, one can argue that these triangles are in fact congruent, and the answer will be a lot different. 

btw, where did the number 4 come from? Why not number 3?!? 

Don't listen to guests who don't give an explanation

I count 7 isosceles triangles.

I'm sorry guest but thet is wrong

Let $s$ and $\ell$ be the shorter and longer of the remaining sides of the triangle. We are told that $25+s+\ell=80$. By the Triangle Inequality,$$s+25>\ell.$$Adding $\ell$ to both sides of the inequality gives \begin{align*} s+25+\ell &> 2\ell \\ 80 &> 2\ell, \end{align*}so the largest value of $\ell$ is $39$. In that case, $s=80-(25+\ell)=80-64=\boxed{16}$.

Thanks so much!!!

no problemo

It says 7 is incorrect

(11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99) >>Total = 81 non-zero integers.

Their sums==(2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 18)==81 integers

There are 29 prime sums.

By using calculus, the minimum distance is 7.

Thanks