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3 years ago

Can someone please show how to solve this ln(5x-1)+ln(x-6)=ln6 ???

2 answers:

8 0

When you add ln, you multiply
ln((5x-1)(x-6)=ln6 do now FOIL
ln(5x^2-30x-x+6)=ln6
therefore
5x^2-31x+6=6 and
5x^2-31x=0 furthermore
x(5x-31)=0
one solution is 0, which we will reject
the other solution is 5x=31
x=31/5

miv72 [106K]3 years ago

5 0

Ln(5x - 1) + ln(x - 6) = ln(6)
ln((5x - 1)(x - 6)) = ln(6)
 ln(5x(x - 6) - 1(x - 6) = ln(6)
ln(5x(x) - 5x(6) - 1(x) - 1(-6)) = ln(6)
ln(5x² - 30x - x + 6) = lm(6)
ln(5x² - 31x + 6) = ln(6)
 5x² - 31x + 6 = 6
5x² - 31x + 6 - 6 = 6 - 6
 5x² - 31x + 0 = 0
x = -(-31) +/- √((-31)² - 4(5)(0))
 2(5)
x = 31 +/- √(961 - 0)
 10
x = 31 +/- √(961)
 10
x = 31 +/- 31
 10
x = 31 + 31 x = 31 - 31
 10 10
x = 62 x = 0
 10 10
x = 6²/₅ x = 0

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The average reading score on certain tests is given by y = 0.153x + 255.4, where x is the number of years past 1970. In what yea

nirvana33 [79]

Average reading score is given by the expression,

y = 0.153x + 255.4

Here, x in the number of years past 1970.

To find the year in which the average reading score is 259.378, substitute the value of 'y' in the given expression.

y = 0.153x + 255.4

259.378 = 0.153(x) + 255.4

0.153x = 259.378 - 255.4

0.153x = 3.978

x = $\frac{3.978}{0.153}$

x = 26

That means given average reading score 259.378 will be 26 years after 1970.

Therefore, 1996 is the year in which the average reading score will be 259.378.

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2 years ago

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Mrrafil [7]

Answer:

We know that in the box there are:

4 twix

3 kit-kat

Then the total number of candy in the box is:

4 +3 = 7

Here we want to find the probability that we draw two twix.

All the candy has the same probability of being drawn from the box.

So, the probability of getting a twix in the first drawn, is equal to the quotient between the number of twix and the total number of candy in the box, this is:

p = 4/7

Now for the second draw, we do the same, but because we have already drawn one twix before, now the number of twix in the box is 3, and the total number of candy in the box is 6.

this time the probability is:

q = 3/6 = 1/2

The joint probability is the product of the individual probabilities, so here we have

P = p*q = (4/7)*(1/2) = 2/7

b) same reasoning than in the previous case:

For the first bar, the probability is:

p = 3/7

for the second bar, the probability is:

q = 2/6 = 1/3

The joint probability is:

P = p*q = (3/7)*(1/3) = 1/7

c) Suppose that first we draw a twix.

The probability we already know that is:

p = 4/7

Now we want another type, so we need to draw a kit-kat, the probability will be equal to the quotient between the remaining kit-kat bars (3) and the total number of candy in the box (6)

q = 3/6

The joint probability is:

P = p*q = (4/7)*(3/6) = 2/7

But, we also have the case where we first draw a kit-kat and after a twix, so we have a permutation of two, then the probability in this case is:

Probability = 2*P = 2*2/7 = 4/7

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