The Cleveland Art Institute has eight paintings by a local artist they plan to display. If the paintings are hung in one horizontal line, how many different ways can they be arranged if order is important? A.10,880 B.20,160 C.1 D.40,320

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Explanation:

A graph is a nice addition (and it will likely help us see the vertex directly), but it isn't necessary because we can use the equation given to us. Though I recommend using a graphing calculator to confirm the answer.

The original function is the same as y = 1x^2+8x + (-2). We see that it is in the form y = ax^2+bx+c where

a = 1

b = 8

c = -2

Use the values of 'a' and b to get the value of h, which is the x coordinate of the vertex.

h = -b/(2a)

h = -8/(2*1)

h = -4

The x coordinate of the vertex is x = -4. Plug this into the original equation to get

f(x) = x^2+8x-2

f(-4) = (-4)^2 + 8(-4) - 2

f(-4) = -18

Plugging x = -4 into f(x) leads to y = -18. The point (-4, -18) is on the parabola. Furthermore, this is the vertex (h,k)

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Alternatively, you can complete the square as shown below

y = x^2 + 8x - 2

y = (x^2 + 8x) - 2

y = (x^2 + 8x + 0) - 2

y = (x^2 + 8x + 16 - 16) - 2

y = (x^2 + 8x + 16) - 16 - 2

y = (x+4)^2 - 18

y = 1(x+4)^2 - 18

y = 1(x-(-4))^2 - 18

The last equation is in the form y = a(x-h)^2 + k with (h,k) = (-4,-18) being the vertex. The 16 is the result of taking half of 8 and squaring that result. We have 16-16 = 0 to make sure that we don't change the equation and keep things balanced. This is the same as adding 16 to both sides. All of this is done so we can end up with the (x+4)^2 perfect square portion.You can expand out (x+4)^2 - 18 and you should get x^2+8x-2 again.

Answer:

A ≈ 312.1

Step-by-step explanation:

[tex]A = \pi r(r+\sqrt{h^2 + r^2})[/tex]

r = 5

h = 14

[tex]A = \pi 5(5+\sqrt{14^2+5^2})[/tex]

A = 312.055478161

Answer:

  Your table is filled in below.

Step-by-step explanation:

The scale factor is the ratio of image size to original size. In part (d), the image height is "blocks" while the original height is "feet". So, the units of the scale factor are "blocks/ft".

Sometimes a scale factor has units, like this, and sometimes it is expressed as a pure number. A map scale factor might be the pure number ratio 1 : 62500, or it could also be expressed with units as 1 in : 1 mile.*

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* actually, these are slightly different scales. 1:62500 is about 0.98643 inches per mile.

Answer: Image

Step-by-step explanation:

took the test

Answer:

1. A=3x^4y^4 2.B= 2^6=64

Step-by-step explanation:

hope this helps pls mark brainliest

Answer:

  (3.5, 17)

Step-by-step explanation:

It would be nice to see the whole graph, so we can see where the functions cross.

Without that information, we can still eliminate unreasonable choices.

A) the quadratic at y=3.5 is well above the exponential

B) the most likely choice (3.5, 17)

C) at x=-8, the quadratic is above the exponential

D) neither graph goes anywhere near y = -8

Answer:

642/125

Step-by-step explanation:

and the other person got it

Answer:

C. Two lines are perpendicular if they have opposite slopes

Step-by-step explanation:

Hey there!

Well 2 lines that are perpendicylar have reciprocal slopes for example,

2 and 1/2 are 2 slopes that are perpendicular.

Hope this helps :)

Answer:

d

Step-by-step explanation:

Answer:

approximately 5.36

Step-by-step explanation

20 - 9.28 = 10.72

BD = EC

10.72/2 = 5.36

Answer:

The tragedy of the commons in fourteenth-century England was overcome by the common lands being enclosed and privatized.

Step-by-step explanation:

The Commons tragedy refers to a popular economic narrative that explains why common assets appear to be overused from a social point of view. The story-line is focused on the premise that each person tries to get as much profit as possible from the available resource. As per the question, the land available for grazing was limited and solution can be opted through enforcing regulations, auctioning out a limited number of licenses, or transforming the common good into a private good.

Answer:

Part A : see composition process below

Part B :    [tex]Domain=\{x\,|\,x\neq 0\}[/tex]

Step-by-step explanation:

Part A

Let's use the composition of functions to find if they give the identity : [tex]f(g(x))=x[/tex]  thus proving they are the inverses of each other:

[tex]f(g(x))=f(\frac{5x+1}{x} )=\frac{1}{\frac{5x+1}{x}-5} =\frac{1}{\frac{5x+1-5x}{x}} =\frac{1}{\frac{1}{x} } =x[/tex]

So we have proved they are the inverses of each other.

Part B

Given that the composition is:

[tex]f(g(x))=\frac{1}{\frac{1}{x} }[/tex]

the Domain must exclude x=0, for which this quotient is undefined.

The Domain is then:

[tex]Domain=\{x\,|\,x\neq 0\}[/tex]

Answer:

1425 square kilometer.

Step-by-step explanation:

2900 - 8.5% = 2653.5

2653.5 - 8.5% = 2427.9525

2427.9525 - 8.5% = 2221.5765375

2221.5765375 - 8.5% = 2032.74253181

2032.74253181 - 8.5% = 1859.95941661

1859.95941661 - 8.5% = 1701.8628662

1701.8628662 - 8.5% = 1557.20452257

1557.20452257 - 8.5% =1 424.84213815 ≈ 1425

Answer:

[tex]5\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]4*1\frac{2}{5} = 4 * \frac{7}{5} = \frac{28}{5} = 5\frac{3}{5}[/tex]

Answer:

[tex]\boxed{ 5\frac{3}{5}}[/tex]

Step-by-step explanation:

[tex]\displaystyle 4 \times 1\frac{2}{5}[/tex]

[tex]\sf Convert \ mixed \ fraction \ into \ improper \ fraction.[/tex]

[tex]\displaystyle 4 \times \frac{7}{5}[/tex]

[tex]\sf Multiply.[/tex]

[tex]\displaystyle \frac{28}{5}[/tex]

[tex]\sf Convert \ improper \ fraction \ into \ mixed \ fraction.[/tex]

[tex]\displaystyle 5\frac{3}{5}[/tex]

Answer:

x = -4

Step-by-step explanation:

16 + x = 12

16 - 16 + x = 12 - 16

x = -4

Answer:

John ran at a faster rate

Step-by-step explanation:

If john runs 1/2 mile in 5 minutes, then for him to run 1 mile it would take 10 minutes because it takes john 5 minutes for every half of a mile. Now Al runs 1/3 mile in 4 minutes. If he would run 1 mile, it would take him 12 minutes because it takes him four minutes every third mile.  

1/3 : 4    =       3/3 : 12        Al

1/2 : 5    =     2/2 : 10           John

From both of the rations John ran faster

Answer:

2 sqrt(2)

Step-by-step explanation:

h(x) = 2x-8

g(x) = sqrt( x-4)

g(h(10))

First find h(10)

h(10) = 2*10 -8 = 20-8 =12

Then find g(h(10) = g(12) = sqrt( 12-4)

                                = sqrt(8) = sqrt(4*2) = sqrt(4) sqrt(2) = 2 sqrt(2)

Answer:

a

Step-by-step explanation:

edge 2021

Answer:

5.36

Step-by-step explanation:

tan 15 = x / 20

x = 40 - 34.64

x = 5.36

Answer:

Table B represents a linear function.

Step-by-step explanation:

Table B is a linear function because y goes up by a constant, steady rate of 4 every time x goes up by one.

Answer:

y<-8

Step-by-step explanation:

y<-1 - 7

y<-8

Answer:

y < -8

Step-by-step explanation:

To solve an inequality, we must get the variable, y, isolated on one side of the inequality.

[tex]y+7 < -1[/tex]

7 is being added to the variable, y. The inverse of addition is subtraction. Subtract 7 from both sides of the inequality.

[tex]y+7-7< -1-7[/tex]

[tex]y < -1-7[/tex]

[tex]y < -8[/tex]

The solution to the inequality is: y< -8

Hey there!

5/8 + 14 = ?

We can say 14 is equal to 14/1 beause it doesn't have a denominator and we will need to solve for your equation

14 * 8 = 112 (upcoming numerator for now)

8 * 1 = 8 (upcoming denominator for now)

5 stays alone

New equation 5 + 112 / 8

5 + 112 = 117 (numerator)

8 = 8 (demominator)

Answer: 117/8 (if you're looking for the improper fraction version) ; 14 5/8 (if you're looking for the mixed number version) ; 14.625 (if you're looking for the decimal version of it)

⬆ ANY one of these choices SHOULD work

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

parallel

Step-by-step explanation:

We are cutting in the same direction as the base, so the slices is parallel to the base

Answer:

x = 1 ±[tex]\sqrt{119i}[/tex]/ 4

Step-by-step explanation:

[tex]2x^{2} -x +15[/tex] = 0

Use the quadratic formula:

x = 1 ±[tex]\sqrt{119i}[/tex]/ 4

I hope this helps...

And plz mark me brainliest!!1

Answer: I dont know if this is right but the is 8 Ive never done this before.

Step-by-step explanation:

1 =

4 =

1 =

4 =

r− 5 ⋅ 2 = 1 = r = 11

8 = r = 11

Answer:

1/24

Step-by-step explanation:

Answer:

1/24 makes this equation true

Answer:

Step-by-step explanation: I hope it helps :)

[tex]-1.5(4-r)=-12\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\\\-1.5\left(4-r\right)\cdot \:10=-12\cdot \:10\\\\= -15\left(4-r\right)=-120\\\\\mathrm{Divide\:both\:sides\:by\:}-15\\\\\frac{-15\left(4-r\right)}{-15}=\frac{-120}{-15}\\\\4-r=8\\\\\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}\\\\4-r-4=8-4\\\\-r=4\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-r}{-1}=\frac{4}{-1}\\\\r=-4[/tex]

Answer:

r = -4

Step-by-step explanation:

-1.5(4-r)=-12

Divide each side by -1.5

-1.5/-1.5(4-r)=-12/-1.5

(4-r)=8

Subtract 4 from each side

4-r-4 = 8-4

-r = 4

Divide each side by -1

r = -4

Answer:

Tan D = 7 / 4

Sin D = 7 / 8.1

Cos D = 4 / 8.1

IG = 4.95 Cm

Step-by-step explanation:

In question number 3

Tan D = Perpendicular / Base

Tan D = 7 / 4

Sin D = Perpendicular / hypotenuse

Sin D = 7 / 8.1

Cos D = Base / hypotenuse

Cos D = 4 / 8.1

In question number 4

Tan 68° = IG / GH

2.475 = IG / 2

IG = 4.95 Cm

Answer:

3/4 of the whole day(24 hours)

Step-by-step explanation:

1/3 of 24 hours equal to 8 hours. He slept for 8 hours. So his waking time equals 24-8=16

5/8 of his waking time (16 hours ) equal to 10 hours.

now total time spent in his house 10 + 8 = 18

in fraction 18/24 = 3/4

He slept 1/3 of the day, and is awake 2/3 of the day (note that 1/3 + 2/3 = 3/3 = 1)

2/3 of 5/8 = (2/3)*(5/8) = (2*5)/(3*8) = 10/24 = 5/12 of the day is spent at home when he is awake

Add 1/3 and 5/12 to get

1/3 + 5/12 = 4/12 + 5/12 = (4+5)/12 = 9/12 = 3/4

He spent 3/4 of a whole day at home (equivalent to 18 hours)

Answer:

  P(-3) = -2

Step-by-step explanation:

Substitution

P(-3) = 4(-3)^2 +10(-3) -8 = 36 -30 -8

P(-3) = -2

__

Long Division

See the working below. The remainder is -2, so ...

  P(-3) = -2

A-

1 box --- 6 minutes

y boxes --- 1 minute

y = 1/6

B-

1 box --- 9 minutes

t boxes --- 1 minute

t = 1/9

So...

r - used time

r(1/9 + 1/6)=100

r=(100.18)/5

r= 360 minutes

1/6 . 360 = 60 boxes

answer: 60 boxes

In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.

Let's use the concept of the rate of work to solve this problem. The rate of work is the amount of work done per unit of time.

Machine A's rate of work is 1 box of nails every 6 minutes.

Machine B's rate of work is 1 box of nails every 9 minutes.

Let's assume that machine A filled x boxes, and machine B filled y boxes. Since they worked for the same amount of time, the total number of boxes filled by both machines is 100.

So, the equation representing the total work is:

x (boxes filled by A) + y (boxes filled by B) = 100

Now, let's use their rates of work to form two more equations:

Rate of work of A = 1 box every 6 minutes

Rate of work of B = 1 box every 9 minutes

Since work = rate × time, we can write two equations:

x (boxes filled by A) = (1/6) * t (time in minutes)

y (boxes filled by B) = (1/9) * t (time in minutes)

Since they both worked for the same time, we can set the time for both machines as equal:

t = t

Now, we have a system of equations:

x + y = 100

x/6 = y/9

t = t

Let's solve the system of equations. We can start by substituting the value of y from the second equation into the first equation:

x + (x/6)*3 = 100

x + (x/2) = 100

Multiply both sides by 2 to eliminate the fraction:

2x + x = 200

3x = 200

x = 200/3

Now, let's find the value of y using the second equation:

y = (x/6)*3

y = (200/3)/6 * 3

y = 200/3

So, machine A filled 200/3 boxes of nails, which is approximately 66.67 boxes.

Machine B filled 200/3 boxes of nails, which is also approximately 66.67 boxes.

Since they cannot fill a fraction of a box, we can distribute the remaining 2/3 box between machine A and machine B, giving one extra box to each.

In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.

To know more about machine:

https://brainly.com/question/31535149

#SPJ2

Answer:

Area: [tex]50\pi -100[/tex]

Perimeter: 20[tex]\pi[/tex]

Step-by-step explanation:

If we take half of one of these "pedals" we can see that it is simply 1/4 of a circle with radius 5, subtracted by a triangle. Let's calculate this half-pedal.

[tex]1/4(25 \pi) - 1/2(5* 5)[/tex]

That means 4 pedals is equal to:

[tex]8(1/4(25\pi) - 1/2 (25))[/tex]

[tex]50\pi - 100[/tex]

So.. The area of the shaded region is [tex]50\pi -100[/tex]

Perimeter is even simpler. the half-pedal is just 1/4 of the circumference of the circle. The circumference is just [tex]10\pi[/tex], which means our half pedal is:

[tex]1/4(10\pi )[/tex]

Multiplying by 8, our perimeter is just 20[tex]\pi[/tex].