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3 years ago

Which function represents a parabola that is translated 2 units to the left and 6 units down from the parent function, f(x)=x^2

Mathematics

1 answer:

Luda [366]3 years ago

4 0

Translation involves moving a function along its coordinates

The image of the function is $g(x) = (x + 2)^2 - 6$

<h3>How to determine the new function</h3>

The parent function is given as:

$f(x) = x^2$

When the function is translated 2 units left, we have:

$f'(x) = (x + 2)^2$

When the function is translated 6 units down, we have:

$f"(x) = (x + 2)^2 - 6$

Rewrite as:

$g(x) = (x + 2)^2 - 6$

Hence, the image of the function is $g(x) = (x + 2)^2 - 6$

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Serena has attached a 10 inch ribbon to the corners of a frame to hang it on the wall. The frame 9 inches wide. How far above th

kherson [118]

Answer: The hook would be 2.2 inches (approximately) above the top of the frame

Step-by-step explanation: Please refer to the picture attached for further details.

The top of the picture frame has been given as 9 inches and a 10 inch ribbon has been attached in order to hang it on a wall. The ribbon at the point of being hung up would be divided into 5 inches on either side (as shown in the picture). The line from the tip/hook down to the frame would divide the length of the frame into two equal lengths, that is 4.5 inches on either side of the hook. This would effectively give us two similar right angled triangles with sides 5 inches, 4.5 inches and a third side yet unknown. That third side is the distance from the hook to the top of the frame. The distance is calculated by using the Pythagoras theorem which states as follows;

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse (longest side) and AB and BC are the other two sides

5^2 = 4.5^2 + BC^2

25 = 20.25 + BC^2

Subtract 20.25 from both sides of the equation

4.75 = BC^2

Add the square root sign to both sides of the equation

2.1794 = BC

Rounded up to the nearest tenth, the distance from the hook to the top of the frame will be 2.2 inches

4 0

3 years ago

Pentagon TEXAS has vertices at T(1, 8), E(3, 8), X(6, 2), A(3, 2), and S(1, 4). What is the area of Pentagon TEXAS?

Tamiku [17]

The area of the pentagon is 19 square units

The coordinates of the pentagon are given as:

$T = (1, 8)$

$E =(3, 8)$

$X =(6, 2)$

$A=(3, 2)$

$S = (1, 4)$

The area of the pentagon is then calculated using:

$Area = \frac 12|(x_1y_2+x_2y_3+x_3y_4+x_4y_5+x_5y_1) -(y_1x_2+y_2x_3+y_3x_4+y_4x_5+y_5x_1)|$

So, we have:

$Area = \frac 12|(1 \times 8 +3 \times 2+6\times2+3 \times 4 + 1 \times 8) -(8\times3+8\times6+2\times3+2\times1+4\times1)|$

Simplify the expressions in both brackets

$Area = \frac 12|46 -84|$

$Area = \frac 12|-38|$

Remove absolute bracket

$Area = \frac 12 \times 38$

$Area = 19$

Hence, the area of the pentagon is 19 square units

Read more about areas at:

brainly.com/question/1423568

7 0

2 years ago

there are 239 people in the first six rows of the movie theater if the same number of people are in the next six rows about how

bija089 [108]

Answer:

478 people

Step-by-step explanation:

All you need to do for this problem is simply multiply 239 by 2. If the first 6 rows are 239 people, and so are the next 6, that's all you need to do.

239*2=478

8 0

3 years ago

Parking in a student lot costs $2 for the first half hour and $1.75 for each hour thereafter. A partial hour is charged the same

Masteriza [31]

An easier way to think of this problem is just keep adding for each additional hour:

0.5 hours --> $2

1.5 hrs --> $3.75

2.5 hrs --> $5.50

3.5 hrs --> $7.25

and since you can only spend $7, the maximum time is 2.5 hours

3 0

3 years ago

Read 2 more answers

Jazz buys a bag of lolipops from the store, where each lolipop costs $0.45. She wants to sale them at school and marks up the pr

NeX [460]

Answer:

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You're face to face with greatness

And it's strange

You don't even know how you feel

It's adorable

It's nice to see that humans never change

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I know it's a lot, the hair, the bod

When you're staring at a demigod

So what can I say except

You're welcome

For the tide, the sun, the sky

Hey, it's okay, it's okay

You're welcome

I'm just an ordinary demiguy

What can I say except

You're welcome

For the tide, the sun, the sky

Hey, it's okay, it's okay

You're welcome

I'm just an ordinary demiguy

Honestly, I can go on and on

I could explain every natural phenomenon

The tide, the grass, the ground

Oh, that was me I was messing around

I killed a snake, I buried its guts

Sprouted a tree, now you've got coconuts

What's the lesson?

What is the takeaway?

Don't mess with Maui when he's on a breakaway

And the tapestry here in my skin

Is a map of the victories I win

Look where I've been, I make everything happen

Look at that mean mini Maui just tikkity tappin'

Singing and scratchin'

Flipping and snappin'

People are clappin', hearing me rappin'

And bring the chorus back in

Well anyway, let me say you're welcome

For the wonderful world you know

Hey, it's okay, it's okay

You're welcome

Well, come to think of it, I gotta go

Hey, it's your day to say

You're welcome

'Cause I'm gonna need that boat

I'm sailing away, away

You're welcome

'Cause Maui's the ultimate guy

You're welcome!

Step-by-step explanation:

4 0

3 years ago