Six equilateral triangles are connected to create a regular hexagon. The area of the hexagon is 24a2 – 18 square units. Which is an equivalent expression for the area of the hexagon based on the area of a triangle?

6(4a2 – 3)
6(8a2 – 9)
6a(12a – 9)
6a(18a – 12)

Option A)

Yes, Fraction 37/8 is a rational number because the decimal form of the number is terminal.

.

A Rational Number is any number that can be expressed as a fraction or ratio of two integers.

For example, 3/4, 8.75, 2, and -6 are all considered rational numbers.

Note that integers, or "whole numbers", are rational numbers. This is because they can be expressed as fractions.

For example, 2 can be rewritten as 2/1, or 200/100. -6 can be rewritten as -6/1, 6/-1, or -12/2.

Many non-integer, or decimal numbers, are also rational numbers.

For instance, 8.75 can be rewritten as 8 3/4, 875/100, or 1750/200. This also includes repeating decimal numbers like 0.3333333..., which can be rewritten as 1/3.

Fraction = 37 /8

Numerator = 37

Denominator = 8

Both are integer

The fraction of 37 divided by 8  = 37/8 is a Rational Number because both the numerator and denominator are integers.

Learn more about Rational Numbers: brainly.com/question/24398433

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Answer:

1) -0.016 pounds per square inch per cubic inch.

2) [tex]\displaystyle V'(P)=-\frac{800}{P^2}[/tex]

Step-by-step explanation:

We are given the equation [tex]PV=800[/tex].

Part A)

We want to determine the average rate of change of P as V increases from 200 cubic inches to 250 cubic inches.

To find the average rate of change between two points, we find the slope between them.

Rewrite the given equation as a function of V:

[tex]\displaystyle P(V)=\frac{800}{V}[/tex]

Hence, the average rate of change for V = 200 and V = 250 is:

[tex]\displaystyle \begin{aligned} m &= \frac{P(250) - P(200)}{250 - 200} \\ \\ & = \frac{3.2 - 4}{250 - 200} \\ \\ & = -0.016\end{aligned}[/tex]

Therefore, the average rate of change is -0.016 pounds per square inch per cubic inch.

Part B)

We want to express V as a function of P. This can be done through simple division:

[tex]\displaystyle V(P)=\frac{800}{P}[/tex]

We want to show that the instantaneous change of V with respect to P is inversely proportional to the square of P. So, let's take the derivative of both sides with respect to P:  

[tex]\displaystyle \frac{d}{dP}\left[V(P)\right]=\frac{d}{dP}\left[\frac{800}{P}\right][/tex]

Differentiate. Note that 1/P is equivalent to P⁻¹. This allows for a simple Power Rule:

[tex]\displaystyle \begin{aligned} V'(P) & = 800\frac{d}{dP}\left[ P^{-1}\right] \\ \\ & = -800(P^{-2}) \\ \\ & = -\frac{800}{P^2}\end{aligned}[/tex]

Therefore, the instantaneous change of V is indeed inversely proportional to the square of P.

Answer:

3x^2+2x+15

Step-by-step explanation:

3x^2+2x+2+(4x2)+5

use pemdas

Answer:

smhhh

Step-by-step explanation:

By inspection, we can see that x = ±√2, since (±√2)⁴ = 2² = 4.

In particular, if [tex]x^n=n[/tex], which means [tex]x=n^{\frac1n}[/tex], then [tex]x^{x^n}=x^n=n[/tex].

Let x = √2. Then

[tex]x^{x^2}+x^{x^8}=(\sqrt2)^{(\sqrt2)^2}+(\sqrt2)^{(\sqrt2)^8}[/tex]

[tex]x^{x^2}+x^{x^8}=(\sqrt2)^2+(\sqrt2)^{16}[/tex]

[tex]x^{x^2}+x^{x^8}=2+256[/tex]

[tex]x^{x^2}+x^{x^8}=\boxed{258}[/tex]

Answer:

27

Step-by-step explanation:

Answer:

yaa , when X=15, y = 3;

here the value of X is five times the value of y

so when X= 10

then. y =X/5 = 10/5= 2

so the value of y will be 2

hope you like the answer

1 yard = 3 feet.

100 yards x 3 = 300 feet.

300 feet x 3/4 = 225 feet.

The answer is 225 feet.

Answer:

225 ft hope it helps

Answer:

D. 1.061 + 4.899

Step-by-step explanation:

1061 + 4899     149              149

———————————  =  ———

   1000         25                     25

149          

——— = 5.96000

 25            

If this helps please mark brainliest. Have a great day!

Answer:

a=2s-b-c

Step-by-step explanation:

2s=a+b+c

a=2s-b-c

Answer:

2s-c-b =a

Step-by-step explanation:

s = ( a+b+c)/2

Multiply each side by 2

2s = ( a+b+c)/2 *2

2s = a+b+c

Subtract c from each side

2s -c = a+b+c-c

2s -c = a+b

Subtract b from each side

2s-c-b = a+b-b

2s-c-b =a

Answer

The answer is A

Answer:

It is A. my friend

Step-by-step explanation:

Answer :pink i think

Step-by-step explanation:

Im guessing the ratio for a cirlce could be 1/2 or more

uplod the pic so i can solve the problem

Answer:

[tex]A(k) = 55k[/tex]

Step-by-step explanation:

Given

[tex]1kg = P55[/tex]

Required

Determine the cost of k kilogram

[tex]1kg = P55[/tex]

Multiply both sides by k

[tex]k * 1kg = P55 * k[/tex]

[tex]k\ kg = 55 k[/tex]

Representing this as a function:

[tex]A(k) = 55k[/tex]

It's not clear what the pattern is supposed to be for the digits in the givne number. It looks like the repeating block should be 846, but it could just as easily be 84684.

Assume the first case, and let x = 7.846846846... . Then

1000x = 7846.846846846...

Subtract x from this to cancel the repeating decimal part, then solve for x :

999x = 7846 - 7 = 7839

x = 7839/999 = 871/111

If instead you meant the second case, let x = 7.846848468484684... . Then

10⁵ x = 784,684.846848468484684...

Solve for x :

99,999 x = 784,684 - 7 = 784,677

x = 784,677/99,999 = 261,559/33,333

Maybe you meant something else altogether?

Answer:

x=17

Step-by-step explanation:

These are corresponding angles, meaning they have the same measure. We must set them equal to each other.

Hope this helps :-)

Answer:f(x, y) = e

−xy. For the interior of the region, we find the critical points:

fx = −ye−xy

, fy = −xe−xy, so the only critical point is (0, 0), and f(0, 0) = 1.

For the boundary, we use Lagrange multipliers.

g(x, y) = x

2 + 4y

2 = 1 ⇒ λ∇g = h2λx, 8λyi, so setting ∇f = λ∇g we get

−ye−xy = 2λx and −xe−xy = 8λy. The first of these gives e

−xy = −2λx/y,

and then the second gives −x(−2λx/y) = 8λy ⇒ x

2 = 4y

2

. Solving this

last equation with the constraint x

2 + 4y

2 = 1 gives x = ± √

1

2

and y = ±

1

2

√

2

.

Now f

± √

1

2

, ∓

1

2

√

2

= e

1/4 ≈ 1.284 and f

± √

1

2

, ±

1

2

√

2

= e

−1/4 ≈ 0.779.

The former are the maxima on the region and the latter are the minima.

Step-by-step explanation:

Answer:

There were 7 small boxes and 14 large boxes shipped.

Step-by-step explanation:

This problem may be solved by a system of equations:

I am going to say that:

x is the number of small boxes used

y is the number of large boxes used

There were twice as many large boxes shipped as small boxes shipped

This means that y = 2x

Each small box of paper weighs 45 pounds and each large box of paper weighs 80 pounds. The total weight of all boxes was 1435 pounds.

This means that 45x + 80y =1435

So we have to solve the following system:

y=2x

45x + 80y =1435

45x + 80 (2x) = 1435

205x = 1435

x= 1435/205

x=7

y=2x= 2(7) = 14

There were 7 small boxes and 14 large boxes shipped.

Answer: x ≤ 15

Step-by-step explanation: All we need to do is divide both sides by 1/3, so1/3x / 1/3 and 5/ 1/3 = 15. So x  ≤ 15.

Hope this helps!

Answer:

50

Step-by-step explanation:

62+(3·4)−24

62+12-24

Final Answer: 50

Answer:

50

Step-by-step explanation: :D

Answer:

Use the drop-down menus to complete each statement.

The amplitude of the function is  

✔ 48

.

The period of the function is  

✔ 28

.

The graph has a vertical shift of  

✔ 48

units.

Step-by-step explanation:

i got the question wrong for you homies, these were the correct ones on edge2020

Answer:

Y=1/4x-3/4

Step-by-step explanation:

I got this answer right on my questions

Answer:

Step-by-step explanation:

yes!

Answer:

<A=<C=45°

Step-by-step explanation:

you can see in the picture above

Answer:

1,289 divided by 22 is 58 r13

Step-by-step explanation:

Answer:

Y= 43, x=137, z=137 total is 360