Answer: 84.5%
Step-by-step explanation:
15.2 × 15.2 = 231.04 cm² (area of the entire large square)
5.98 × 5.98 = 35.76 cm² (area of the small square)
large square - small square = area of the blue region
231.04 - 35.76 = 195.28 cm² (area of the blue region)
= percentage of time that the point will be in the blue region
= 0.845 --> 84.5%
6x² + 24x - 72
Divide all the terms by the greatest common of factor of 6. Makes factoring easier. We will need to put this 6 on at the end so keep it in mind.
(6x² + 24x - 72) / 6 = x² + 4x - 12
Your simplified equation is x² + 4x - 12
Now to factor we must find out what two factors of - 12 can be added together to equal 4. The factors are 6 and -2:
x² - 2x + 6x - 12
Now we must group and factor.
(x² - 2x) + (6x - 12)
We can pull an x out of the first binomial because both terms have that in common:
x(x - 2) + (6x - 12)
We can pull a 6 out of the second binomial for the same reason:
x(x - 2) + 6(x - 2)
The terms inside the parentheses match each other, this means (x- 2) is one of the factors of the original trinomial. The other comes from the terms on the outside x and + 6. Put them together, (x + 6)
So your factors are (x - 2)(x + 6); this isn't it though. We need the 6 from the top, the one we divided out to make factoring easier. We will put it on the outside of whichever factor you list first so that your final answer reflects that to get back to the original trinomial, you would have to multiply the whole thing by 6.
Your final answer is:
6(x - 2)(x +6)
B
36 is the radius so
The formula for circumference is radius times two and take that answer times pi
So 36×2 is 72 and 72 times pi is 226.194671058
6x^2-7x-3=0
Solve by completing the square:
x^2-7/6x-1/2=0 (divided everything by 6)
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of bb, the coefficient of x.<span>(b/2)2=<span>(−7/12)<span>2
</span></span></span>x2−7x/6+<span>(−7/12)2</span>=1/2+<span>(−7/12)<span>2
(simplify)
</span></span><span><span>x2−<span>7x6</span>+49144=121144</span><span>x2-<span>7x6</span>+49144=121144</span></span>Factor the perfect trinomial square into <span><span>(x−7/12)</span>2</span><span><span><span>(x−7/12)</span>2</span>=<span>121/144
x-7/12=squ. root of +/- 121/144
x-7/12= +/- 11/12
Solution1:
x-7/12=11/12
x=18/12
x=3/2
Solution 2:
</span></span>x-7/12=-11/12
x=-4/12
<span>x=-1/3
</span>Answers: 3/2, -1/3
