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REY [17]
2 years ago
14

PLS PLS help!

Mathematics
1 answer:
Leto [7]2 years ago
4 0

9514 1404 393

Answer:

  y = 3x^2 +30x +69

Step-by-step explanation:

Transformations work this way:

  g(x) = k·f(x) . . . . vertical stretch by a factor of k

  g(x) = f(x -h) +k . . . . translation (right, up) by (h, k)

__

So, the translation down 2 units will make the function be ...

  f(x) = x^2  ⇒  f1(x) = f(x) -2 = x^2 -2

The vertical stretch by a factor of 3 will make the function be ...

  f1(x) = x^2 -2  ⇒  3·f1(x) = f2(x) = 3(x^2 -2)

The horizontal translation left 5 units will make the function be ...

  f2(x) = 3(x^2 -2)  ⇒  f2(x +5) = f3(x) = 3((x +5)^2 -2)

The transformed function equation can be written ...

  y = 3((x +5)^2 -2) = 3(x^2 +10x +25 -2)

  y = 3x^2 +30x +69

__

The attachment shows the original function and the various transformations. Note that the final function is translated down 6 units from the original. That is because the down translation came <em>before</em> the vertical scaling.

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The graph shows the relationship between a gift card balance and the number of visits to a smoothie shop.
enyata [817]

Answer: $3.00

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
dybincka [34]

What you should do first is simplify the equation into the y = mx + b format. Move 2x to the other side. Know that in doing this, 2x must become the opposite of what it currently is (-2) in order for the equation to remain true. We also have to take away the '10' because the line is parallel, not exactly the same, which means a different y intercept. This looks like:

5y = -2x + b

Next, simplify y to make things easier. This can be done by dividing both sides by 5, like so:

\frac{5}{5}y = -\frac{2}{5}x + b

What you should also know is that if a line is parallel to another, then this means the slope has to be the same because they both have the same changes in rise and run. With this in mind, simply plug in the x and y values.

(-4) = -\frac{2}{5} * (5) + b

--> -4 = \frac{10}{5} + b

---> -4 = -2 + b

Add 2 to both sides to isolate b.

-4 + 2 = b

Which means that -2 = b.

Now that we have the y intercept, we can write the equation of the line, which is y = -\frac{2}{5}x - 2.

Hope this was helpful.

3 0
3 years ago
What is the area of the rectangle above?
FrozenT [24]
=13 x 6
=78 unit squares
5 0
2 years ago
Allie wants to arrange her flower garden in eight equal rows.
Shalnov [3]
So depending on the amount of Flowers in a row or feet in a row you would divide the total by eight.
7 0
3 years ago
Triangle MNP is dilated according to the rule DO,1.5 (x,y)Right arrow(1.5x, 1.5y) to create the image triangle M'N'P, which is n
Vikki [24]

Given:

The vertex of a triangle MNP are M(-4, 6), N(2, 6), and P(-1, 1).

The rule of dilation is:

(x,y)\to (1.5x,1.5y)

The image of triangle MNP after dilation is M'N'P'.

To find:

The coordinates of the endpoints of segment M'N'.

Solution:

The end points of MN are M(-4, 6) and N(2, 6).

The rule of dilation is:

(x,y)\to (1.5x,1.5y)

Using this rule, we get

M(-4,6)\to M'(1.5(-4),1.5(6))

M(-4,6)\to M'(-6,9)

And,

N(2,6)\to N'(1.5(2),1.5(6))

N(2,6)\to N'(3,9)

The endpoints of M'N' are M'(-6, 9) and N'(3, 9).

Therefore, the correct option is B.

8 0
3 years ago
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