Answer:
Step-by-step explanation:
-6x²+15x+9=0
divide by -3
2x²-5x-3=0
2x²+x-6x-3=0
x(2x+1)-3(2x+1)=0
(2x+1)(x-3)=0
either x=-1/2
or x=3
First term ,a=4 , common difference =4-7=-3, n =50
sum of first 50terms= (50/2)[2×4+(50-1)(-3)]
=25×[8+49]×-3
=25×57×-3
=25× -171
= -42925
derivation of the formula for the sum of n terms
Progression, S
S=a1+a2+a3+a4+...+an
S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d] → Equation (1)
S=an+an−1+an−2+an−3+...+a1
S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n−1)d] → Equation (2)
Add Equations (1) and (2)
2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)
2S=n(a1+an)
S=n/2(a1+an)
Substitute an = a1 + (n - 1)d to the above equation, we have
S=n/2{a1+[a1+(n−1)d]}
S=n/2[2a1+(n−1)d]
The answer is (C) the middle one
Number of zids=x
number of zods=y
number of zid legs=5x
number of zod legs=7y
so
5x+7y=140
try to get it into slope intercept from so you can graph is (y=mx+b)
5x+7y=140
subtract 5x from both sides
7y=140-5x
divide both sides by 7
y=20-5/7x
y=-5/7x+20
plug in numbers for x and get numbers for y (you can only plug in multiples of 7 for x so that there are a whole number of zids and since you are counting, x and y must never be negative)
lets try 0 for x
y=-5/7(0)+20
y=20
so x=0 and y=20 is an answer (if you can have only one of that species)
lets try 7 for x
y=-5/7(7)+20
y=-5+20
y=15
so x=7 and y=15 is an answer
lets try 14 for x
y=-5/7(14)+20
y=-10+20
y=10
so x=14 and y=10 is another answer
lets try 21 for x
y=-5/7(21)+20
y=-15+20
y=5
so x=21 and y=5 is another answer
lets try 28 for x
y=-5/7(28)-20
y=-20+20
y=0
so x=28 and y=0 is an answer (if there can be only one of a species)
if we go further, then y will be negative so the answers are
(x,y)
(0,20)
(7,15)
(14,10)
(21,5)
(28,0)
if it is allowed that only one species exists then there are 5 possible answers
if both must exist simultaneously, then there are only 3 answers
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ln9 = y can be rewritten into an exponential function as y = e^9
