The expression −
20
r
2
+
1
,
400
r
−
12
,
000
represents the total profit made by a company when selling a certain product for
r
dollars. Which inequality represents the sale price, in dollars, when the total profit will be at most
10
,
000
dollars?

−
20
r
2
+
1
,
400
r
−
12
,
000
>
10
,
000

− − 20 r 2 + 1 , 400 r − − 12 , 000 > 10 , 000

−
20
r
2
+
1
,
400
r
−
12
,
000
≥
10
,
000

− − 20 r 2 + 1 , 400 r − − 12 , 000 ≥ ≥ 10 , 000

−
20
r
2
+
1
,
400
r
−
12
,
000
<
10
,
000

− − 20 r 2 + 1 , 400 r − − 12 , 000 < 10 , 000

−
20
r
2
+
1
,
400
r
−
12
,
000
≤
10
,
000

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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