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I assume that what you meant was d=s+s2/20, which is s2/20+s-d=0 or s2+20s-1500=0 (s-30)(s+50)=0 so that s=30, the negative result is rejected.

A+B+C=180 B=2A C=A+20  substituting the values for B and C in the first equation we have A+2A+A+20=180 4A+20=180 or 4A=160 gives A=40 B=2A=80 C=A+20=60

2N+5≥45 so that 2N≥40 or N≥20

The pattern you seem to be looking at is for every integer n, the number g you seek is such that n/g = n+g This gives g2+ng-n=0 or that g=(-n±√(n2+4n))/2 If you use the plus sign you get n= 1     g=0.618033989 n=2     ...

After 1 year the car is worth 21000-.0937×21000=21000×.9063 After 2 years the car is worth (21000×.9063)×.9063 carry on

Let the lesser odd integer be 2n-1, and so the greater is 2n+1 2n-1+87, the lesser +87, is 2n+86 6 times the greater is 6(2n+1)=12n+6 2n+86=12n+6 gives 80=10n and so 8=n The numbers are 16-1=15 and 16+1=17

The line you have (2/3)x-2 has a slope of 2/3, as will the line you want.  Its equation will be y=(2/3)x+b, where the b is chosen so that the line passes through (5,3).  3=(2/3)5+b or 3=10/3+b or b=-1/3.  The equation is y=(2/3)x-1/3

I assume that you mean log8x-log810=log84.  That is log8(x/10)=log84.  Raise 8 to the power of each of the equal sides and have x/10=4, or x=40.

The  formula is S=P(1+r/k)nk, where k is the number of compounding periods per year and n the number of years, In our case we seek P for S=50000, k=12, r=.06 50000=P(1+.06/12)72=P(1.005)72 and so P=50000/1.00572=34915.12

Let A be the amount after n years of annual compounding at rate r of initial principal P. A=P(1+r)n.  Solving this for P we have P=A/(1+r)n.  The particular numbers for our case are P=28,500/1.035=28500/1.159274074=24584.35035 Feel free to round as needed.

Assuming that the area, length times width = x4+10x2+9=(x2+9)(x2+1) and assuming that one of these factors is the height and the other the width, and that the width is the larger number, then it is x2+9 which is, for any real number greater than x2+1

x2-2x+y2-24=0 (x-1)2-1 +y2=24 (x-1)2+y2=25 center (1,0)  radius 5

The border is of uniform width w. (13-2w)(9-2w)=45  the area of the painting is 45 ft2 117-44w+4w2=45 4w2-44w+72=0  divide by 4 w2-11w+18=0 (w-9)(w-2)=0 w=2 is only possible answer

f(x)= 3x2 - x +2 f(x+h)= 3(x+h)2 - (x+h) +2 f(x+h)=3(x2+2xh+h2)-x-h+2=3x2+6xh+3h2-x-h+2 f(x+h)-f(x)=3x2+6xh+3h2-x-h+2-3x2+x-2=6xh+3h2-h (f(x+h)-f(x))/h=6x+3h-1=6x-1+3h

The sum of the angles of a triangle is 180 degrees. Draw triangle ABC.  Make BC horizontal, for convenience. Through point A draw a line parallel to the opposite side, namely BC. Mark a point L on this line to the left of A, and a point R on this line to the right of A. ∠LAB...

.5×7 + x = the acid in the final soloution 7+x is the amount of the final solution (3.5+x)/(7+x)=.7 3.5+x=.7(7+x) 3.5+x=4.9+.7x .3x=1.4 x=14/3=4 2/3 gal Note:3 1/2 + 4 2/3 = 8  1/6  total acid after addition of acid 7+4...

x6-19x3-216=0 Let y=x3 and have y2-19y-216=0 which may be factored as (y-27)(y+8)=0 which gives that y=27, y=-8 and so that x=3 or x=-2

l = long side, w = short side l+w=11           half the perimeter l2+w2=101      Pythagoras l+w=11 gives that (l+w)2=l2+2lw+w2=121 or that 2lw=20 2lw=20 or lw=10 l+w=11 lw=10...

Things equal to the same thing are equal to each other, or equality is transitive.  Which, for angles says that if angle A is congruent to angle D and angle D is congruent to angle E then angle A is congruent to angle E.  This is more about the nature of equality than that of...