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3 years ago

100 Points for this

Mathematics

2 answers:

4vir4ik [10]3 years ago

7 0

Answer:

l(x,y) = (-4y, -4x - 3)

Step-by-step explanation:

Let's start with function (x, y)

Transformations in the given order result in following

A dilation by a factor of 4 with the origin as the center of dilation

This results in both coordinates multiplied by 4
(x, y) → (4x, 4y)

A reflection across the y-axis

This results in x-coordinate changing sign to opposite
(4x, 4y) → (-4x, 4y)

A 90° counterclockwise rotation about the origin

This results in x-coordinate swapping with negative y-coordinate
(-4x, 4y) → (-4y, -4x)

A translation 3 units down

This results in y-coordinate change by -3
(-4y, -4x) → (-4y, 4x - 3)

The final function is:

l(x) = (-4y, -4x - 3)

Temka [501]3 years ago

5 0

Answer:

l(x) = (-4y, -4x - 3)

I got the same answer as Mhanifa and if you want the explanation check his, because mine sucks :(

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The graph below shows the value of Edna's profits f(t), in dollars, after t months:

umka21 [38]

Since we know that the graph of our quadratic function has x-intercepts at (6,0) and (18,0), $x=6$ and $x=18$ are the zeroes of our quadratic. To find our quadratic we are going to factor each zero backwards and multiply them:
$x=6$
$x-6=0$
$x=18$
$x-18=0$

$(x-6)(x-18)=x^{2}-6x-18x+108$
$=x^{2}-24x+108$

Now that we have our quadratic function, we are going to use the average formula: $m= \frac{f(9)-f(3)}{9-3}$
$where$
$f(9)$ is the function evaluated at the 9th month
 $f(3)$ is the function evaluated at the 3rd month

$m= \frac{f(9)-f(3)}{9-3}$
$m= \frac{[9^{2}-24(9)+108]-[3^{2}-24(3)+108]}{9-3}$
$m= \frac{-27-45}{6}$
$m= \frac{-72}{6}$
$m=-12$

We can conclude that the closest approximate average rate of change for Edna's profits from the 3rd month to the 9th month is: B. −11.63 dollars per month.