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2 years ago

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Sakeem is a landscape architect. When he creates a lawn, his supplier charges $.43 per square foot for sod. Sakeem charges his c

ustomers $2.00 per square foot to lay the sod. The profit Sakeem makes when creating a lawn varies directly as the number of square feet of sod. Recall that profit is the difference of the amount earned and the amount spent.

2 answers:

Alina [70]2 years ago

7 0

Answer:

y/x = 1.57

Step-by-step explanation

Y=kx

k=$1.57

y=1.57x

divid by x

y/x=1.57

IRISSAK [1]2 years ago

4 0

Answer:

profit = $1.57

Step-by-step explanation:

2.00-0.43=1.57

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Roberto's toy car travels at 30 centimeters per second (cm/sec) at high speed and 20 cm/sec at low speed. If the car travels for

igomit [66]

Answer:

1200 cm

Step-by-step explanation:

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2 years ago

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F(x)=3x 2 +9f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 9 and g(x)=\dfrac{1}{3}x^2-9g(x)= 3 1 x 2

34kurt

Answer:

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

$g(f(x)) = 3x^4 + 18x^2 + 18$

<em>f(x) and g(x) and not inverse functions</em>

Step-by-step explanation:

Given

$f(x) = 3x^2 + 9$

$g(x) = \dfrac{1}{3}x^2 - 9$

Required

Determine f(g(x))

Determine g(f(x))

Determine if both functions are inverse:

Calculating f(g(x))

$f(x) = 3x^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)(\frac{1}{3}x^2 - 9) + 9$

Expand Brackets

$f(g(x)) = (x^2 - 27)(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = x^2(\frac{1}{3}x^2 - 9) - 27(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = \frac{1}{3}x^4 - 9x^2 - 9x^2 + 243 + 9$

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

Calculating g(f(x))

$g(x) = \dfrac{1}{3}x^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)(3x^2 + 9) - 9$

$g(f(x)) = (x^2 + 3)(3x^2 + 9) - 9$

Expand Brackets

$g(f(x)) = x^2(3x^2 + 9) + 3(3x^2 + 9) - 9$

$g(f(x)) = 3x^4 + 9x^2 + 9x^2 + 27 - 9$

$g(f(x)) = 3x^4 + 18x^2 + 18$

Checking for inverse functions

$f(x) = 3x^2 + 9$

Represent f(x) with y

$y = 3x^2 + 9$

Swap positions of x and y

$x = 3y^2 + 9$

Subtract 9 from both sides

$x - 9 = 3y^2 + 9 - 9$

$x - 9 = 3y^2$

$3y^2 = x - 9$

Divide through by 3

$\frac{3y^2}{3} = \frac{x}{3} - \frac{9}{3}$

$y^2 = \frac{x}{3} - 3$

Take square root of both sides

$\sqrt{y^2} = \sqrt{\frac{x}{3} - 3}$

$y = \sqrt{\frac{x}{3} - 3}$

Represent y with g(x)

$g(x) = \sqrt{\frac{x}{3} - 3}$

Note that the resulting value of g(x) is not the same as $g(x) = \dfrac{1}{3}x^2 - 9$

<em>Hence, f(x) and g(x) and not inverse functions</em>

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2 years ago

the number of rainbow smelt in Lake Michigan had an average rate of change of −19.76 per year between 1990 and 2000. The bloater

Nataly_w [17]

Initial population of rainbow smelt: 227.
Initial population of bloater fish: 1,052.
t - number of the years;
The equation is:
227 - 19.76 t = 1,052 - 92.57 t
92.57 t - 19.76 t = 1,052 - 227
72.81 t = 825
t = 825 : 72.81
t = 11.33 years = 11 1/3 years = 11 years 4 months
Answer: After 11 years and 4 months.

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romanna [79]

Answer:

20

Step-by-step explanation:

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2 years ago

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