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2 years ago

11

he time spent dancing (minutes) and the amount of calories burned can be modeled by the equation c = 5.5t. Which table of values

matches the equation and includes only viable solutions? Image for option 1 Image for option 2 Image for option 3

4 answers:

Vladimir [108]2 years ago

4 1

the image option 3 would be it

Kruka [31]2 years ago

4 1

Answer:

0 0

5 27.5

10 55

15 82.5

Step-by-step explanation:

Guest1 year ago

1 0

Image two is right. I just got three wrong. It doesn't make sense to include negative amounts of time.

Guest1 year ago

0 0

2nd option

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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

8. The ratio of students in Arts, Science and Commerce Faculties is 5: 4: 3. If the number

N76 [4]

Answer:

Arts=295, Commerce=177

Step-by-step explanation:

That the three subjects have a common ratio implies that there is some common factor between them that relates to the actual number of students in each area, so 5:4:3 means 5x:4x:3x for some value of x

We know that there are 236 science students, so 4x = 236 or x = 59

so the number of arts students is 5(59) and the number of commerce students is 3(59)

Arts = 5*59 = 295

Commerce = 3*59=177

3 0

1 year ago

Which shows the four-term polynomial and factored form of x2 + 6x-27?

blsea [12.9K]

Answer:

0x2+9x-3x-27 6x-27

Step-by-step explanation:

7 0

2 years ago

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Write a expression that shows 3 times the sixth power of 10

user100 [1]

(10 raised to the power of 6)×3

(10*6) ×3

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2 years ago

Given: line AB is congruent to line CD and line AD is congruent to line BC. Prove: angle D is congruent to angle B

Taya2010 [7]

AD = BC ----> Parallel lines
AC = AC -----> Reflexive property
<A = <C -----> Congruent angles
<D = <B -----> Congruent angles

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2 years ago