Step-by-step explanation:
they're is a neat little trick.
but first of all, "roots" means the 0 solutions of the equation. like
ax² + bx + c = 0
there are 2 solutions for x to make the whole expression equal 0.
these are the "roots".
now to the little trick :
when is a multiplication resulting in 0 ?
when at least one of the factors is 0.
and any quadratic expression can be written as multiplication of 2 factors. like
c(x - a)(x - b) = cx² - cax - cbx + cab
what are the "roots" or 0 points ?
either
c = 0
x - a = 0 | x = a
x - b = 0 | x = b
the leading coefficient = 3.
that means nothing else than c = 3.
root = 1 means (x - 1) is one factor.
root = -5 means (x + 5) is the other factor.
so, we have
3(x - 1)(x + 5) = 3x² + 12x - 15
and the equation is
3x² + 12x - 15 = 0
or
3x² + 12x = 15
Since that is a triangle the expression would be b x h / 2. So 12*12 = 144 / 2 = 72. The answer is 72.
A = pi * r^2.....r = radius and pi = 3.14
A = (3.14)(13^2)
A = 3.14(169)
A = 530.66
Answer:
x = 4
Step-by-step explanation:
Using the sine ratio on right triangle KJL
and the exact value sin30° = 
sin30° = 
= 
= 
= ( cross- multiply )
2JL = 8
( divide both sides by 2 )
JL = 4
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Using the sine ratio in right triangle JLM
and the exact value sin45° = 
sin45° = 
= 
= 
= ( cross- multiply )
x × = 4 ( divide both sides by
x = 4
