Step-by-step explanation: Before multiplying two fractions together by multiplying across their numerators and multiplying across their denominators, you should always try to cross-cancel as your first step.

So in this problem, the 2 and 8 cross-cancel to 1 and 4.

Also, watch out for your signs. In this problem we have a negative times a positive so we know that our answer will be negative.

Now we can multiply across the numerators and across the denominators.

So we have 5 · 1 which is 5 and 4 · 3 which is 12.

So our answer is -5/12.

Be very careful with your signs!

7 0

3 years ago

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What is the solution to 2logg(x) = logg8+log,(x-2)? x=-4 x=-2 X=4 X= 8

astra-53 [7]

Answer:

x = 4

which agrees with the third listed answer among the given options

Step-by-step explanation:

We can re-write the logarithmic equation using the properties of logarithms:

$2\,log(x)=log(8)+log(x-2)\\log(x^2)=log(8*(x-2))\\log(x^2)=log(8x-16)$

Therefore, the arguments of the log functions must also be equal (and we can solve for "x" by noticing that this expression is the perfect square of a binomial:

$x^2=8x-16\\x^2-8x+16=0\\(x-4)^2=0$

and for this equation to verify, x must be 4

5 0

2 years ago

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How many gallons of a 20% acid solution should be mixed with 30 gallons of a 40% solution, to obtain a mixture of 30% acid solut

Alexeev081 [22]

Answer:

30 gallons of 20% acid solution should be mixed.

Step-by-step explanation:

Let x gallons of a 20% acid solution was mixed with 30 gallons of a 40% solution, to obtain a mixture of 30% acid solution.

Therefore, final volume of the solution will be (x + 30) gallons.

Now concept to solve this question is

20%.(x) + 40%.(30) = 30%.(x + 30)

0.20(x) + 0.40(30) = 0.30(x + 30)

0.20x + 12 = 0.30x + 9

0.30x - 0.20x = 12 - 9

.10x = 3

x = $\frac{3}{0.1}$

x = 30 gallons

Therefore, 30 gallons of the 20% acid solution should be mixed.

4 0

3 years ago