<span>log(x-3)+log(x) = 2 + log(x+2)
---------------------------
log[(x-3)x] - log(x+2) = 2
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log[(x^2-3x)/(x+2)] = 2
----
(x^2-3x)/(x+2) = 2^2
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x^2-3x = 4x+8
x^2 - 7x - 8 = 0
Factor:
(x-8)(x+1) = 0
Positive solution:
x = 8</span>
<span>Turn the percent to a decimal by moving the decimal point over 2 places to the left. then multiply. so, 1425 * 375</span> = 53.44
(x-h)^2=4P(y-k), vertex is (h,k)
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k
nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix
I will only convert the 1st one fully, you should be able to do the rest
1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
(-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)
k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5
basically completee the square with x and find P by force factoring a 4 out
2. directix: y=-1.75
3. directix: y=1.5
4. directix: y=17.25
5. d: -37.5
6. d: 9.25
7. d=2.625
order them yourself
Option 2: 
is the correct answer.
Step-by-step explanation:
The radical expressions like these are simplified by using fractional exponents
given
![\frac{\sqrt{4}}{\sqrt[3]{4} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B4%7D%7D%7B%5Csqrt%5B3%5D%7B4%7D%20%7D)
Converting radicals into exponents
When there is no base the exponent is 1/2 and as the base is 3, the exponent will be 1/3
So
As the bases of numerator and denominator is same, the exponents can be subtracted
Hence,
Option 2: is the correct answer.
Keywords: Exponents, radicals
Learn more about radicals at:
#LearnwithBrainly
Answer:
1 10/12
Step-by-step explanation:
Take the fractions and get them to the same bottom number, 12. So it would be 5 4/12 - 3 6/12.
Take 1 away from 5 to get 4 and the one you pulled would be 12/12(also equal to 1). 4 16/12 - 3 6/12 would be 1 10/12
