y = 3(x + 4)^2 + 31
Step-by-step explanation:
We can convert the given quadratic equation into its vertex form by completing the square:
y = 3x^2 + 24x + 43
= 3(x^2 + 8x) + 43
= 3(x^2 + 8x + 4) + 31
= 3(x + 4)^2 + 31
This is the vertex form of the given quadratic equation with (-4, 31) as its vertex
So
lets say we have
a/b=2a/2b
we know that if we invert one and multiply it by the other (divide them), we get 1 because a/a=1 where a=a
so
2/3 and 4/6 are equivelent because if you divide them we get 12/12=1
2/3 and 8/12 are equivilent because if you divide them we get 24/24=1
and sinde 2/3=4/6 and 2/3=8/12, 2/3=4/6=8/12
they are equivlent
Answer:
- width: 18 in
- length: 27 in
Step-by-step explanation:
The relations between length (L) and width (W) are ...
W +9 = L
LW = 486
Substituting gives ...
(W+9)W = 486
W^2 +9W -486 = 0 . . . put in standard form
(W +27)(W -18) = 0 . . . . factor
W = 18 . . . . the positive solution
The width of the rectangle is 18 inches; the length is 27 inches.
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<em>Comment on factoring</em>
There are a number of ways to solve quadratics. Apart from using a graphing calculator, one of the easiest is factoring. Here, we're looking for factors of -486 that have a sum of 9.
486 = 2 × 3^5, so we might guess that the factors of interest are -2·3² = -18 and 3·3² = 27. These turn out to be correct: -18 +27 = 9; (-18)(27) = -486.
Answer:
6^2
Step-by-step explanation:
We know a^b / a^c = a^(b-c)
6^5 / 6^3 = 6^(5-3) = 6^2