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frozen [14]
3 years ago
10

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics
1 answer:
Zepler [3.9K]3 years ago
6 0

Answer:

first box is x+3

second box is 5

Step-by-step explanation:

To find the first f(x) equation , lets pick two points from the slanting line

(-3,0)(-2,1)

lets find the equation of this line

we need find equation y=mx +b

slope m = \frac{y_2-y_1}{x_2-x_1} = \frac{1-0}{-2-(-3)} =1

m=1  and point is (-3,0)

use formula y-y1=m(x-x1)

y-0 = 1(x-(-3))

y= 1(x+3)

y= x+3

another line is a horizontal line

for horizontal line , slope is always 0

we have line at 5 on y so equation is y=5


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the assumption being that "x" is a plain variable whilst "y" is a function, that matters because the chain rule would be needed for a function, not so for a plain variable.

4x^2+4x+xy=5\implies 8x+4+\stackrel{\textit{product rule}}{\left( 1\cdot y+x\cdot \cfrac{dy}{dx} \right)}=0 \\\\\\ x\cfrac{dy}{dx}=-8x-4-y\implies \cfrac{dy}{dx}=\cfrac{-8x-4-y}{x}

now, we know that y(5) = -23, which is another way of saying that when x = 5, y = -23, but we already knew that, we can get that by simply plugging it into the equation hmmm y'(5), well

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