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3 years ago

Which statement is true regarding the graphed functions?

Mathematics

1 answer:

vaieri [72.5K]3 years ago

5 0

Answer:

probably b

Step-by-step explanation:

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3 years ago

What is the perimeter of a triangle with vertices of (5,1) (-3,3) (-7,-3)

timurjin [86]

$Vertices:\\
A(5,1)\\B(-3,3)\\C(-7,-3)\\\\ You\ must\ find\ length\ of\ AB,\ BC,\ AC.\\\\
A(5,1)\ \ \ \ \ \ B(-3,3)\\\\Distance\ between\ A \ and\ B:\\AB=\sqrt{(x_B-x_A)^2+(y_A-y_B)^2}\\\\AB=\sqrt{(-3-5)^2+(3-1)^2}\\AB=\sqrt{8^2+2^2}\\AB=\sqrt{64+4}\\AB=\sqrt{68}
$ $
 B(-3,3)\ \ \ \ C(-7,-3)\\\\Distance\ between\ B \ and\ C:\\BC=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\\\BC=\sqrt{(-7-(-3))^2+(-3-3)^2}\\BC=\sqrt{(-4)^2+(-6)^2}\\BC=\sqrt{16+36}\\BC=\sqrt{52}$ $A(5,1)\ \ \ \ \ \ C(-7,-3)\\\\Distance\ between\ A \ and\ C:\\AC=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\\\AC=\sqrt{(-7-5)^2+(-3-1)^2}\\AC=\sqrt{(-12)^2+(-4)^2}\\AC=\sqrt{144+16}\\AC=\sqrt{160}$ $Perimeter\ of\ triangle=\ AB+AC+BC=\\\sqrt{68}+\sqrt{52}+\sqrt{160}=2\sqrt{17}+2\sqrt{13}+2\sqrt{40}$

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3 years ago

Jake has 1/4 of his paycheck left . He plans ro spend this money to buy a present for each of his 3 kids . he will spend the sam

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4 years ago

Someone answer plzzzzzzz

sergiy2304 [10]

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3 years ago

Plz I can’t do this

zheka24 [161]

Answer: f(g(x))=x and g(f(x)) = x

f⁻¹(x) = g(x) YES ARE INVERSES

f⁻¹(x) ≠ g(x) NOT INVERSES

<u>Step-by-step explanation:</u>

Inverse is when you swap the x's and y's and then solve for y.

If f⁻¹(x) = g(x), then they are inverses of each other.

Similarly, if g⁻¹(x) = f(x), they are inverses of each other.

<em>NOTE: You can also use composition to determine if they are inverses --> If (fog)(x) = x, then they are inverses of each other.</em>

$f(x) = \dfrac{1}{x+4}-9\\\\\\\text{Swap the x's and y's. NOTE: f(x) is y}\\x=\dfrac{1}{y+4}-9\\\\\\\text{Add 9 to both sides}\\x+9=\dfrac{1}{y+4}\\\\\\\text{Flip the fractions}\\\dfrac{1}{x+9}=y+4\\\\\\\text{Subtract 4 from both sides}\\\dfrac{1}{x+9}-4=y\\\\\\\boxed{f^{-1}(x)=g(x)\text{ so f(x) and g(x) are inverses of each other}}$

$f(x) = 3x+27\\\\\\\text{Swap the x's and y's NOTE f(x) is y}\\x=3y+27\\\\\\\text{Subtract 27 from both sides}\\x-27=3y\\\\\\\text{Divide everything by 3}\\\dfrac{1}{3}x-\dfrac{27}{3}=y\\\\\\\text{Simplify}\\\dfrac{1}{3}x-9=y\\\\\\\boxed{f^{-1}(x)\neq g(x)\text{ so f(x) and g(x) are NOT inverses of each other}}$

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3 years ago