While testing a new pesticide, an agricultural scientist uses two functions to predict the yields of two same-sized potato farms that have different soil conditions. the scientist's predicted yield, in tons, of the first farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. his predicted yield, in tons, of the second farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. if the scientist uses the same amount of pesticide on the two farms, select the function that accurately represents the predicted combined yield from both farms.
f(x)= -2.43x^2+10.37x+9 and g(x)= -3.43^2+13x+25

a. h(x)= -5.86x^2 + 23.37x + 34
b. h(x)= -5.86x^2 + 2.63x + 34
c. h(x)= -x^2 + 2.63x + 16
d. h(x)= x^2 + 2.63x - 16

A. h(x)= -5.86x^2 + 23.37x + 34

Step-by-step explanation:

If the scientist uses the same amount of pesticide on the two farms then the x's of the functions are the same.

Then, the combined yield of the two farms is just the yield of the first farm plus the yield of the second farm:

.

Now, since

and

,

then

we add the coefficients of the  corresponding terms to get:

Which is choice A.

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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