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2 years ago

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I am planning to attend a company-paid conference. My charges will include $412.00 for airfare, $378.00 for conference registrat

ion, and $210.00 for food.”
Supervisor: “Please submit an expense form for a total of __________ when you return.”

1 answer:

Anna007 [38]2 years ago

4 0

Answer:

$1000.00

Step-by-step explanation:

The supervisor is asking for an expense form of a <u>total (?) </u>when you return.

Given the charges given in the word problem, it is only logical to assume the supervisor wants a expense form of how much you spent (total) on the trip. Thus, you add!

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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>

4 0

2 years ago

Ben uses 3/12 pound of strawberries and 2/12 pound of blueberries

Gennadij [26K]

Answer:

what's the rest of the question

Step-by-step explanation:

:/

4 0

2 years ago

Read 2 more answers

In circle Y, what is m∠SZT?

lara31 [8.8K]

We first solve for angle TZU which is determined by the formula:
mTZU = 0.5(arcTU + arcSR)
mTZU = 0.5(72°+100°) = 86°

By vertical angle, mTZU = mSZR = 86°

We note that the sum of all angles formed is 360°. Solving for the remaining angles:
360° - 86° - 86° = 188°

Since mSZT is equal to mRZU by vertical angle, we divide 188° by 2.
188°/2 = 94°

m∠SZT = 94°

4 0

2 years ago

Read 2 more answers

RESTAURANTS In 2012, a popular pizza franchise had 2483 restaurants. In 2017, there were 2606 franchised

lisabon 2012 [21]

y - 2483 = 24.6(x - 2)

Let x represent the number of years after 2010

Let y represents the number of restaurants in x years

2012 is 2 years after 2010

2017 is 7 years after 2010

Number of restaurants owned by RESTAURANTS in 2012 = 2483

This can be represented in coordinate form as (2, 2483)

Number of restaurants owned by RESTAURANTS in 2017 = 2606

This can be represented in coordinate form as (7, 2606)

The equation of a line in point-slope form is:

$y-y_{1} = m(x - x_{1} )$

where m represents this slope, and is calculated as:

$m = \frac{y_{2} - y_{1} }{x_2-x_1} \\m = \frac{2606-2483}{7-2} \\m = \frac{123}{5} \\m = 24.6$

Substitute x₁ = 2, y₁ = 2483, and m = 24.6 into the point-slope equation

The equation in point-slope form becomes:

y - 2483 = 24.6(x - 2)

Learn more here: brainly.com/question/6497976

5 0

2 years ago

Butoxors [25]

Answer:

The correct answer is E. The person who got down at Meritland is older than Yahu, who in turn is older than the person from Lambda.

Step-by-step explanation:

We can conclude that there are three managers, two pilots, and one scientist from the information we're given. Since the youngest among the passengers is Zane, a scientist, his age must be 31. The passengers from Beta and Alpha are pilots, whereas the people from Gamma, Delta, and Kappa are all managers. This means that the passenger who is the scientist must be from Lambda. The passenger who got down at Station X is a manager and is under 34 years old.

The passengers from Delta and Alpha are 35 years old. The person from Beta got down at Station Y, while the person from Lambda got down at Station Z. Here’s the final distribution in the attachment:

4 0

2 years ago