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2 years ago

Write the equation of the line with the following characteristics through the origin and the point (2,2)

1 answer:

4 0

Y = X

Because the origin is 0,0 and the point is 2,2.

In order to get from 0,0 to 2,2 with a line, it must have equal increments of the Y as the X.

In y=mx+b form, you’d have y = 1x+0 which just simplified to what I already stated: y=x

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What is the vertex and the axis of symmetry of the quadratic function graphed below?

Kazeer [188]

The answer is B ! as vertex is (6,3) and axis of symmetry lies on x=6 !

if you need explanation, comment !

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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 median number of cars sold by 11 sales representatives in a certain month is 6. The range of a number of cars sold by those

Luda [366]

It is given that the range of the number of cars sold is 4. Therefore if the fewest cars sold is 3, then the greatest number of cars sold will be 3 + 4 = 7.
The median number of cars sold is 6, so it is possible that the greatest number of cars sold is 7.
The statement is TRUE.

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2 years ago

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Anita had $400 in her savings account when she went to college. Her parents will add $200 to her account each month.

Stolb23 [73]

Anita's account had linear growth
Miguel's account had exponential growth.
Miguel's account grew faster because exponential growth is faster than linear growth

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2 years ago

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Preston is making cookies. He has fraction 4 over 5 cup of flour in a bag. He then used two fraction 1 over 10 cup scoops of flo

Art [367]

I'm pretty sure the answer will be 6/10

Hope this helps, best of luck, terribly sorry if I'm wrong if I am my apologies

~Animaljamissofab ♥

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2 years ago

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