The function r(x) = –0.000345(x – 50)2 + 2.1 can be used to model the curve of a road designed to allow for water to run off in rainstorms depending on the distance from the shoulder of the road, x, in feet. A European firm studying these curves is going to convert feet to meters using the function m(x) = 0.3048x. Which composition can be used to model the curve of the road in terms of meters?

9514 1404 393

Answer:

Step-by-step explanation:

We can define a couple of linear functions as ...

  f(x) = x

  g(x) = -2x+1

Then the reflected function -g(x) is ...

  -g(x) = -(-2x +1) = 2x -1

And the difference from f(x) is ...

  f(x) -(-g(x)) = x -(2x -1) = -x +1 . . . . f(x) -(-g(x))

We want to compare that to the sum of the functions:

  f(x) +g(x) = x +(-2x +1) = -x +1 . . . . f(x) +g(x)

The two versions of the function expression have the same value.

These results are a property of addition, so do not depend on the nature of f(x) or g(x). They will hold for every function.

Answer:

f(x) = x

g(x) = -2x+1

f(x) -(-g(x)) = -x+1

f(x) +g(x) = -x+1

f(x)-(-g(x)) = (f+g)(x) is true for all functions f and g, linear or not

Step-by-step explanation:

We can define a couple of linear functions as ...

 f(x) = x

 g(x) = -2x+1

Then the reflected function -g(x) is ...

 -g(x) = -(-2x +1) = 2x -1

And the difference from f(x) is ...

 f(x) -(-g(x)) = x -(2x -1) = -x +1 . . . . f(x) -(-g(x))

We want to compare that to the sum of the functions:

 f(x) +g(x) = x +(-2x +1) = -x +1 . . . . f(x) +g(x)

The two versions of the function expression have the same value.

These results are a property of addition, so do not depend on the nature of f(x) or g(x). They will hold for every function.

Answer:

The number: 85     factors: 17, 1

Step-by-step explanation:

136-51=85

85 and 51

Common factors of 85 and 51

17,1

Answer:

18/25

Step-by-step explanation:

Answer:

72%, or, 18/25

Step-by-step explanation:

I just converted 0.72 into a percentage and a fraction. I hope this helps! :P

Answer:

The time it takes to hit a target that is 3 feet above ground is approximately 0.35 seconds

Step-by-step explanation:

The given parameters are;

The height of the arrow above the ground = 5 ft.

The height of the target above the ground = 3 ft.

The time it takes the arrow to fall to 3 ft. from 5 ft. above the ground is given by the free fall formula, since the arrow has no vertical velocity component

The equation for free fall is h = 1/2·g·t²

Where;

h = The height of fall = 5 - 3 = 2 feet

g = The acceleration due to gravity = 32.17405 ft/s²

t = How long it takes to fall (to its target)

∴ 2 = 1/2 × 32.17405 × t²

t² = 2/(1/2 × 32.17405) ≈ 0.1243

t = √0.1243 ≈ 0.353

t = 0.35 seconds, to the nearest hundredth

Therefore, the time it takes to fall 2 ft to hit a target that is 3 feet above ground = 0.35 seconds.

The time to hit the target is simply the period the arrow gets to the target from the arch.

The time to hit the target is 0.35 seconds

The height of a parabola is calculated as:

[tex]\mathbf{h = \frac{1}{2}gt^2}[/tex]

Where:

[tex]\mathbf{h =5 - 3 = 2}[/tex] --- the difference between the height of the arrow and the height of the target.

[tex]\mathbf{g = 32.2 fts^{-2}}[/tex] --- acceleration due to gravity

So, we have:

[tex]\mathbf{2 = \frac{1}{2} \times 32.2 \times t^2}[/tex]

Multiply both sides by 2

[tex]\mathbf{4 = 32.2 \times t^2}[/tex]

Divide both sides by 32.2

[tex]\mathbf{0.124 = t^2}[/tex]

Take square roots

[tex]\mathbf{0.35 = t}[/tex]

Rewrite as:

[tex]\mathbf{t = 0.35s}[/tex]

Hence, the time to hit the target is 0.35 seconds

Read more about rates and time at:

https://brainly.com/question/18798899

Answer:

[tex]3(x - 1)^2 - 11= 0[/tex]

Step-by-step explanation:

Given

[tex]3x^2 - 6x = 8[/tex]

Required

Rewrite in form of [tex]3(x - p)^2 + q = 0[/tex]

[tex]3x^2 - 6x = 8[/tex]

Subtract 8 from both sides

[tex]3x^2 - 6x - 8 = 8 - 8[/tex]

[tex]3x^2 - 6x - 8 = 0[/tex]

Express -8 as 3 - 11;

So, we have:

[tex]3x^2 - 6x + 3 - 11= 0[/tex]

Expand [tex]3x^2 - 6x + 3[/tex]

[tex]3(x^2 - 2x + 1) - 11= 0[/tex]

Factorize the expression in the bracket;

[tex]3(x^2 - x -x + 1) - 11= 0[/tex]

[tex]3(x(x - 1) -1(x - 1)) - 11= 0[/tex]

[tex]3((x - 1)^2) - 11= 0[/tex]

[tex]3(x - 1)^2 - 11= 0[/tex]

By comparison: [tex]3(x - p)^2 + q = 0[/tex]

[tex]p= 1[/tex]

[tex]q = -11[/tex]

Answer:

i just want points to upload a post sry

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

because 8-2= 6

now multiply 6*5 and you get 30

Answer:

In expanded form:

2^3 = 2 * 2 * 2 = 8

In standard form :

2^3

Step-by-step explanation:

Given the numbers in range (0 to 10)

Write an exponential expression :

Choosing from the range for the Base and the exponent

Base = 2

Exponent = 3

where ; 2 = base. ; 3 = exponent

In expanded form:

2^3 = 2 * 2 * 2 = 8

In standard form :

2^3

Answer:

e total surface area (TSA) of a cuboid is the sum of the areas of its 6 faces, which is ... 1: Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm. ... Example 2: Find the surface area of a cuboid of dimensions 4.8 cm, 3.4 cm ... Example 4: The length, breadth and height of a cuboid are 16cm, 14cm and ...

Step-by-step explanation:

Where's the cuboid? You left it out.

In any case, use the following formula:

SA = 2(front + side + top)

Answer:

Jared transfers $55 to his checking account from his savings account.

Jared spends $55 from his checking account to purchase a college Algebra textbook

Jared withdraws $55 from his checking account

Hope this helps!

Step-by-step explanation:

The variables can be represented as x and y for the two books.

y=3x+4

x+y=72

Use substitution or elimination to solve the problem. I would personally go with substitution, but its all personal preference.

Answer:

1/4 books per month.

Step-by-step explanation:

1 book in 4 months means you have to do 1 divided by 4 which equals .25. After converting to a fraction you get 1/4.

Answer:

1 and 4/5 mile or 1.8 miles

Step-by-step explanation:

You would multiply 3/5 by 3 because in 1/3 day she can walk 3/5 miles, you want to find out how much she can walk in a day! Hope this helps! If you liked this answer, a brainliest would much be appreciated!

Answer:

9/5 i believe ( or 1 4/5 )

Step-by-step explanation:

multiply 3/5 by 3, since 1/3 is only a part of the day

( im sorry if this is wrong :( )

Answer:

796p

Step-by-step explanation:

If three cartens come in a sigle packege you see how many cartons you need so that would 26/3 wich is some what 8, so you do 90*8 to see how much you'ev spent so far. Now you know that you have 24 cartons so far because you multiply 3 and 8. Lastly, you just add 76 because you need two more cartons. :)

Answer:

r = 8

Step-by-step explanation:

Given

r + 6 = 14 ( subtract 6 from both sides )

r = 8

y^3/4x

Step-by-step explanation:

here,

6x^2/5y *(y^3/4x)

3xy^2/10

Answer:

x=−y−1

Step-by-step explanation:

y=−x−1

Step 1: Flip the equation.

−x−1=y

Step 2: Add 1 to both sides.

−x−1+1=y+1

−x=y+1

Step 3: Divide both sides by -1.

−x

−1

=

y+1

−1

x=−y−1

Answer:

A

Step-by-step explanation:

Speed= Distance/time

20m/10s=2 m/s

Answer:

;)

Step-by-step explanation:

Answer:

you did not out the full equation so I am not able to solve your problem.

If you put the full problem I will try to solve and walk you through it.

Answer:

e then m 4

Step-by-step explanation:

cause thats how it goes

Answer:

l = [tex]\frac{P-2w}{2}[/tex]

Step-by-step explanation:

Given

P = 2(l + w) ← distribute right side

P = 2l + 2w ( subtract 2w from both sides )

P - 2w = 2l ( isolate l by dividing both sides by 2 )

[tex]\frac{P-2w}{2}[/tex] = l

Answer:

l=‒2w+p/2

Step-by-step explanation:

p=2(L+w)

p=2L+2w(add ‒2w on both sides)

‒2w+p=2L+2w-2w

‒2w+p=2L

‒2w+p/2=2L/2

L=‒2w+p/2

i hope it helps you.

Answer:

<X= 111 , <Y= 69, <Z 111

Step-by-step explanation:

X and Z are corresponding

solve for Y

180-111= 69

Answer:

Somebody once told me the world is gonna roll me

I ain't the sharpest tool in the shed

She was looking kind of dumb with her finger and her thumb

In the shape of an "L" on her forehead

[Pre-Chorus]

Well, the years start coming and they don't stop coming

Fed to the rules and I hit the ground running

Didn't make sense not to live for fun

Your brain gets smart but your head gets dumb

So much to do, so much to see

So what's wrong with taking the backstreets?

You'll never know if you don't go

You'll never shine if you don't glow

[Chorus]

Hey now, you're an all star

Get your game on, go play

Hey now, you're a rock star

Get the show on, get paid

And all that glitters is gold

Only shooting stars break the mold

[Verse 2]

It's a cool place, and they say it gets colder

You're bundled up now, wait 'til you get older

But the meteor men beg to differ

Judging by the hole in the satellite picture

The ice we skate is getting pretty thin

The water's getting warm so you might as well swim

My world's on fire, how 'bout yours?

That's the way I like it and I'll never get bored

[Chorus]

Hey now, you're an all star

Get your game on, go play

Hey now, you're a rock star

Get the show on, get paid

All that glitters is gold

Only shooting stars break the mold

[Interlude]

Go for the moon

Go for the moon

Go for the moon

Go for the moon

[Chorus]

Hey now, you're an all star

Get your game on, go play

Hey now, you're a rock star

Get the show on, get paid

And all that glitters is gold

Only shooting stars

[Verse 3]

Somebody once asked, “could I spare some change for gas?

I need to get myself away from this place"

I said, "Yep, what a concept

I could use a little fuel myself and we could all use a little change"

[Pre-Chorus]

Well, the years start coming and they don't stop coming

Fed to the rules and I hit the ground running

Didn't make sense not to live for fun

Your brain gets smart but your head gets dumb

So much to do, so much to see

So what's wrong with taking the backstreets?

You'll never know if you don't go (Go!)

You'll never shine if you don't glow

[Chorus]

Hey now, you're an all star

Get your game on, go play

Hey now, you're a rock star

Get the show on, get paid

And all that glitters is gold

Only shooting stars break the mold

[Outro]

And all that glitters is gold

Only shooting stars break the mold

Step-by-step explanation:

Answer:

4,000%

Step-by-step explanation:

You can solve this problem by using a proportion.

So to start the proportion draw one line then put an equal sign and draw another line.

Then start filling out the proprtion. in proprtions  your is and of can make it easier to solve the problem

is $10,000_________= ______________

of 5%                                     100%    

First multiply $10,000 dollars by 100%, you get 200,000%

Then divide 200,000% by 5% and you get 4,000%

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

m∠1 = 65°

Since. ∠1 and ∠2 are the angles of linear pair,

m∠1 + m∠2 = 180°

65° + m∠2 = 180°

m∠2 = 115°

m∠1 = m∠3 [Vertical angles]

m∠3 = 115°

Since, ∠1 and ∠4 is the linear pair of angles,

m∠1 + m∠4 = 180°

65° + m∠4 = 180°

m∠4 = 180 - 65 = 115°

m∠4 + m∠5 = 180° [Consecutive interior angles between the parallel lines]

115° + m∠5 = 180°

m∠5 = 180° - 115° = 65°

m∠5 + m∠6 = 180° [Linear pair of angles]

65° + m∠6 = 180°

m∠6 = 115°

m∠5 = m∠7 [Vertical angles]

m∠5 = m∠7 = 65°

m∠6 = m∠8 [Vertical angles]

m∠6 = m∠8 = 115°

Answer:

c 78

Step-by-step explanation:

Answer:

you should ask us what color your pillow is

Step-by-step explanation: