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2 years ago

8

Shelby, Allen, and Denise printed their digital photos. Each requested the same size prints. Shelby paid $2.70 for 5 prints. All

en paid $3.24 for 11 prints. Denise paid $4.05 for 20 prints

2 answers:

Pepsi [2]2 years ago

8 0

Answer:

wrote the ordered pairs (5, 2.70), (11, 3.24), and (20, 4.05)

used two of the ordered pairs to find the slope

wrote the point-slope form for a linear equation

substituted the slope and the coordinates of one of the points to write the equation of the line

Step-by-step explanation:

tekilochka [14]2 years ago

4 0

Person: Number of prints Total Cost
Shelby 5 2.70
Allen 11 3.24
Denise 20 4.05

To solve for the variable cost:
11 - 5 = 6
3.24 - 2.70 = 0.54
0.54 / 6 = 0.09 per print

To solve for the fixed cost
0.09 x 5 = 0.45
2.70 - 0.45 = 2.25

y = 2.25 + 0.09x

y = 2.25 + 0.09(5) = 2.25 + 0.45 = 2.70
y = 2.25 + 0.09(11) = 2.25 + 0.99 = 3.24
y = 2.25 + 0.09(20) = 2.25 + 1.8 = 4.05

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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

Gus has skydived four more times than Niko Emma has skydive twice as many times as Nico if Emma has skydived 16 times, how many

ad-work [718]

Answer: Gus skydived 32 times

Step-by-step explanation:

G = number of times that Gus skydives

N = number of times that Nico skydives

E= number of times that Emma skydives

Gus skydives 4 times as much as Nick

This means G = 4N

Emma skydives 2 times as much as Nick.

This means E= 2N

If Emma has skydived 16 times,

That means E = 16

Put E = 16 in E= 2N,

16 =2N

N= 16/2 = 8

Put N= 8 in G = 4N

G =4×8 = 32

Gus skydived 32 times

Check

Nick skydived 8 times

Emma skydived 16 times

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2 years ago

A frequent flyer was interested in the relationship between dollars spent on flying and the distance flown. She sampled 20 frequ

marshall27 [118]

Answer:

c) 44000 miles

Step-by-step explanation:

The regression line has the following format:

$y = bx + a$

In which b is the slope(how much each mile costs) and a is the fixed number of miles flown.

In this problem, we have that:

$a = 24000, b = 10$ . So

$y = 10x + 24000$

A person who spent $ 2000 is predicted to have flown:

This is y when x = 2000.

$y = 10(2000) + 24000$

$y = 44000$

So the correct answer is:

c) 44000 miles

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2 years ago

Tyler needs to complete the table for his consumer science class. He knows that 1 tablespoon contains 3 teaspoons and that 1 cup

olga_2 [115]

Answer:

1 cup = 48 teaspoons

C = 48t

Step-by-step explanation:

Given:

1 tablespoon = 3 teaspoons

1 cup = 16 tablespoon

Write an equation that represents the number of teaspoons, t, contained in a cup, C.

Since

1 tablespoon = 3 teaspoons

And

1 cup = 16 tablespoon

Then

1 cup = 3 teaspoons × 16

1 cup = 48 teaspoons

Let

cup = C

Teaspoons = t

Therefore,

C = 48t

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