So it is enclosed by 200 m of fence
perimiter=200 m
it is a rectangle to
p=legnth+legnth+width+width or
p=l+l+w+w or
p=2l+2w or
p=2(l+w)
so
p=200
200=2(l+w)
divide both sides by 2
100=l+w
area=l times w
area=2275
lw=2275
l+w=100
combine and solve
l+w=100
subtract w
l=100-w
subisutute 100-w for l in other eqution
(100-w)(w)=2275
distribute
-w^2+100w=2275
add (w^2-100w) to both sides
0=w^2-100w+2275
factor
find what 2 numbers add up to -100 and multiply to get 2275
guess (or factor 2275 and find factors that add up to -100)
figure out that they are -65 and -35
0=(w-65)(w-35)
set each to zero
0=w-65
0=w-35
solve for w
w=65 or 35
65>35 so
65 m=legnth
35 m=width
Answer:
use logarithms
Step-by-step explanation:
Taking the logarithm of an expression with a variable in the exponent makes the exponent become a coefficient of the logarithm of the base.
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You will note that this approach works well enough for ...
a^(x+3) = b^(x-6) . . . . . . . . . . . variables in the exponents
(x+3)log(a) = (x-6)log(b) . . . . . a linear equation after taking logs
but doesn't do anything to help you solve ...
x +3 = b^(x -6)
There is no algebraic way to solve equations that are a mix of polynomial and exponential functions.
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Some functions have been defined to help in certain situations. For example, the "product log" function (or its inverse) can be used to solve a certain class of equations with variables in the exponent. However, these functions and their use are not normally studied in algebra courses.
In any event, I find a graphing calculator to be an extremely useful tool for solving exponential equations.
Do cross multiply or butterfly.
For example first one.
18/x=6/10 So cross multiply 18×10 =6x
180=6x
Divide both sides by 6 to get x alone
180÷6=30
So x =30 Do the same to rest
Rise over run is -2/4 or simplified as -1/2
The second one is
