A farmer has 324 feet of fencing to make three identical adjacent rectangular pens, as shown in the picture. What dimensions of each pen will maximize the total enclosed area?

[tex]\\ \rm\Rrightarrow g(f(2))[/tex]

[tex]\\ \rm\Rrightarrow g(3(2)²-4)[/tex]

[tex]\\ \rm\Rrightarrow g(12-4)[/tex]

[tex]\\ \rm\Rrightarrow g(8)[/tex]

[tex]\\ \rm\Rrightarrow 2(8)-6[/tex]

[tex]\\ \rm\Rrightarrow 16-6[/tex]

[tex]\\ \rm\Rrightarrow 10[/tex]

Answer:

[tex]g[f(2)] = 10[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=3x^2-4\\g(x)=2x-6\end{cases}[/tex]

Find f(2) by substituting [tex]x = 2[/tex] into function f(x):

[tex]\begin{aligned}\implies f(2)& =3(2)^2-4\\& = 3(4)-4\\& = 12-4\\& = 8\end{aligned}[/tex]

Now substitute the found value of f(2) into function g(x):

[tex]\begin{aligned}g[f(2)] & = 2[f(2)]-6\\\implies g[f(2)] & =2(8)-6\\& = 16-6\\& = 10\end{aligned}[/tex]

Answer:

What is Parabola:

a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

What is the transformation of parabolas?

The function y=x2+b has a graph which simply looks like the standard parabola with the vertex shifted b units along the y-axis. Thus the vertex is located at (0,b). If b is positive, then the parabola moves upwards and, if b is negative, it moves downwards. Similarly, we can translate the parabola horizontally

Step-by-step explanation:

Step-by-step explanation:

that is a large gift. wow ! you have a lucky teacher ...

the surface of a block consists of 6 (3 pairs of) areas :

front and back

left and right

top and bottom

you know that the area of a rectangle is length × width ?

so,

front and back are

2× 9×13.5 = 18×13.5 = 243 m²

let and right are also

2× 9×13.5 = 243 m²

top and bottom are

2× 9×9 = 2 × 81 = 162 m²

so, for the whole package you need

243 + 243 + 162 = 648 m²

the money for that amount of wrapping paper alone would be way more than I ever spent on a teacher in my life ...

The option (B) 2,-2 is correct because the number satisfy the provided expression.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a number bank shown in the picture.

The problem given:

7 - __ =  7 +  __

A. 3,-4

Checking for the above option:

7 - 3 = 7 - 4

4 = 3 (false)

B. 2,-2

Checking for the above option:

7 - 2 = 7 - 2

5 = 5 (true)

O C. 1;-4

Checking for the above option:

7 - 1 = 7 - 4

6 = 3 (false)

D. 2; 3

Checking for the above option:

7 - 2 = 7 + 3

5 = 10 (false)

Thus, the option (B) 2,-2 is correct because the number satisfy the provided expression.

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ1

Using it's concept, it is found that the desired probability is given by:

P(Take the bus | Junior) = 0.5714 = 57.14%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that out of the 13 + 20 + 2 = 35 Junior students, 20 take the bus, hence the probability is given by:

P(Take the bus | Junior) = 20/35 = 0.5714 = 57.14%.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

  (a)  3.8

Step-by-step explanation:

The Law of Sines can be used to find a missing side length in a triangle where the angles are known and at least one side is given. It tells you the ratio of side lengths is equal to the ratio of the sines of their opposite angles. In effect, longer sides are opposite larger angles.

__

The given side length (DE=3) is opposite given angle F=50°. The unknown side length EF is opposite larger angle D=75°.

Since the unknown side is opposite a larger angle than the other angle given, the length of the unknown side will be longer than the side given.

  EF > DE

  EF > 3

Only one answer choice satisfies this inequality.

  EF = 3.8

__

Additional comment

If you want to do the actual computation, we have ...

  EF/sin(D) = DE/sin(F)

  EF = DE·sin(D)/sin(F) = 3·sin(75°)/sin(50°) ≈ 3.7828

  EF ≈ 3.8

The standard deviation from the mean of the data with a variance of 36 is: B. 6.

Standard deviation can be described as the average of the distance each of the value lies from the mean of the data.

The standard deviation is the square root of the variance.

Variance of the data is given already as 36.

Standard deviation = √36 = 6.

The answer is B. 6.

Learn more about the standard deviation on:

https://brainly.com/question/12402189

#SPJ1

Answer:If your in FLVS i don't really know because this give really hard things. Wish you luck

Step-by-step explanation:

Answer + Step-by-step explanation:

» ABC ≅ DBE

» DE // AC  

(properties of the mid-segment of a triangle)

» Length of DE = 1/2 length of AC  

(properties of the mid-segment of a triangle)

» ∠BDE = ∠DAC

(Corresponding angles)

The number that could be divided up either into bags of 18 marbles or into bags of 42 marbles is 126.

The number that could be divided up either into bags of 18 marbles or into bags of 42 marbles, with no marbles left over in each case, is the lowest common multiple between these two numbers.

By decomposing these numbers as a product of primes, we get:

18 = 2*3*3

42 = 2*3*7

Notice that the first two prime factors are the same, but the third one changes. To get the first common multiple, we need to multiply both numbers by the third factor (the different one) of the other.

We will get:

18*7 = 126

42*3 = 126

Then 126 is the smallest number that can be divided by 18 and 42.

If you want to learn more about lowest common multiple:

https://brainly.com/question/10749076

#SPJ2

Answer:

2^1

Step-by-step explanation:

a^m/a^n = a^(m-n)

so, 2^8/2^7 = 2^(8-7) = 2^1

hope this helps :)

282.5 of 10 tickets were sold in the rock concert by the promoter

To do this, we make use of the following representations:

The 475 tickets that were sold means that:

x + y + z = 475

The income means that:

10x + 15y + 20z = 6300

Also, we have:

10y = 4z

Divide both sides by 10

y = 0.4z

Substitute y = 0.4z in 10x + 15y + 20z = 6300

10x + 15*0.4z + 20z = 6300

10x + 6z + 20z = 6300

Evaluate the like terms

10x + 26z = 6300

Substitute y = 0.4z in x + y + z = 475

x + 0.4z + z = 475

Evaluate the like terms

x + 1.4z = 475

Make x the subject

x = 475 - 1.4z

Substitute x = 475 - 1.4z in 10x + 26z = 6300

10(475 - 1.4z) + 26z = 6300

Expand

4750 - 14z + 26z = 6400

Evaluate the like terms

12z = 1650

Divide both sides by 12

z = 137.5

Substitute z = 137.5 in x = 475 - 1.4z

x = 475 - 1.4 * 137.5

Evaluate

x = 282.5

Hence, 282.5 of 10 tickets were sold

Read more about system of equations at:

https://brainly.com/question/14323743

#SPJ1

The end behavior is that as x approaches positive infinity, f(x) approaches positive infinity and as x approaches negative infinity, f(x) approaches negative infinity

The function is given as:

f(x) = 8x+8

The above function is a linear function.

A linear function is represented as:

f(x) = mx + b

This means that the slope of f(x) is 8 (a positive number)

For a linear function with a positive slope, the end behavior is that:

As x approaches positive infinity, f(x) approaches positive infinity and as x approaches negative infinity, f(x) approaches negative infinity

Read more about end behavior at:

https://brainly.com/question/1365136

#SPJ1

Answer:

x= -y+8

Step-by-step explanation:

hope it's helpful

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to solve the equation [tex]\pmb{2x+3=-1}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

First, subtract 3 from both sides of the equal sign:

[tex]\mathrm{2x=-1-3}[/tex]

[tex]\mathrm{2x=-4}[/tex]

Now, divide both sides by 2:

[tex]\mathrm{x=-2}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

It's A

Step-by-step explanation:

Thx to the guy in the comments above

Answer:

It's A

Step-by-step explanation:

It's right

[tex] \huge \qquad \sf \: Answer[/tex]

Here we go ~

1. A circle can be named by their Centre, so here in the diagram it's :

2. Name 4 radii :

Radii are the line segments that joins the centre and boundary of circle.

They are :

3. 2 Major arcs :

considering two points on a circle, and joining them forms a curve ( you can say part of circumference )

When we consider two points two arcs are formed and the arc with more length is known as Major Arc

That is :

4. A Semicircle :

Semicircle is special arc which is formed when two arcs formed by the points are equals to one another... it's also half the Perimeter of circle.

that is :

5. 3 minor arcs :

The arc formed by two points having lesser length is known as minor arc.

that is :

6. 3 Central angles :

Central angles are angles formed by arcs on centre of the circle ~

that is :

7. A diameter :

Diameter is a chord that passes through centre of the circle.

8. Congruent Angles :

In the given figure, there are two equal/congruent angles that are ~

9. Adjacent arcs :

The arcs that have one common end point are known as Adjacent arcs ~

that are :

Answer:

A circle is named by its center.  The center of the given circle is A, therefore:

Name of the circle:  A

The radius is any line segment from the center of the circle to the perimeter.

Name 4 radii:  [tex]\sf AC, \quad AB, \quad AG, \quad A\,F[/tex]

A major arc is an arc whose measure is greater than 180°.

When naming a major arc, the first point and last point are the endpoints, and we also need include the name of any point between those two endpoints.

2 major arcs:  [tex]\sf \widehat{CEG},\quad \widehat{BCF}[/tex]

A semi-circle is half a circle with an arc that measures 180°.

Its endpoints lie on the diameter of the circle.  We need three points to name a semicircle (the endpoints and a point between the endpoints).

A semi-circle:  CEF

A minor arc is an arc whose measure is less than 180°.

3 minor arcs:  [tex]\sf \widehat{FG}, \quad \widehat{GB}, \quad \widehat{BC}[/tex]

A central angle has its vertex at the center of the circle, and is formed by 2 radii.  When naming the central angle, the middle letter is the center of the circle.

3 central angles:  [tex]\sf \angle F\,AG, \quad \angle GAB, \quad \angle BAC[/tex]

The diameter is the widest part of the circle.  It is a straight line segment that passes through the center of the circle.

A diameter:  CF

Congruent angles are angles with the same measure.
On the diagram, the same angle measures are indicated by the addition of the same number of dashes on the angle sign.

Congruent angles:  [tex]\sf \angle F\,AG, \quad \angle GAB[/tex]

Adjacent arcs are arcs that have one point in common.

Adjacent arcs:  [tex]\sf \widehat{GB}[/tex] and [tex]\sf \widehat{BC}[/tex]  (they share point B)

Answer:

(x+5) (x+5)

Step-by-step explanation:

it's just (x+5)^2 twice

Real life scenarios of acute angles are:

As a general rule, an acute angle, x is represented as: x < 90

This means that acute angles are less than 90 degrees.

The real life scenarios that involve acute angles are scenarios that whose measure of angle is less than 90 degrees.

Sample of the real life scenarios that satisfy the above definition are:

Read more about acute angles at:

brainly.com/question/3217512

#SPJ1

Answer:

-11

Step-by-step explanation:

I don't know how to type Numerical using a cellphone

Answer:

58.5 ft

Step-by-step explanation:

sin 70=55/length

length=58.5 ft

Answer:

1&32 2&16 4&8

Step-by-step explanation:

Factor Pair Pair Factorization

1 and 32       1 x 32 = 32

2 and 16         2 x 16 = 32

4 and 8      4 x 8 = 32

Answer:

_4

Step-by-step explanation:

x+19/5=3 cross multiply

x+19=3*5

x+19=15

x=15-19

x=-4

The remainder when (x + 19) is divided by 5 is 2.

If the positive integer x has a remainder of 3 when divided by 5, it can be represented as:

x = 5a + 3, where "a" is a non-negative integer.

Now, let's consider the expression (x + 19) and determine the remainder when it is divided by 5:

x + 19 = (5a + 3) + 19

       = 5a + 22

When we divide 5a + 22 by 5, we find:

(5a + 22) = 5(a + 4) + 2

Therefore, the remainder when (x + 19) is divided by 5 is 2.

Learn more about remainders here:

https://brainly.com/question/29019179?

#SPJ2

Answer:

x = 115° , y = 65° , z = 115°

Step-by-step explanation:

x and 65° are a linear pair and sum to 180°

x + 65° = 180° ( subtract 65° from both sides )

x = 115°

y and 65° are vertically opposite angles and are congruent , then

y = 65°

x and z are vertically opposite angles and are congruent , then

z = x = 115°

CPA is parallel to BPD and so it is also equal to 65 degrees

And all you have to do to find CPB is 180-65=115 and CPB is Parallel to APD thus, its equal to 115 too!

CPA= 65 degrees

BPD=65 degrees

APD= 115 degrees

CPB=115 degrees

Hope i helped

TheOneAndOnlyLara~

The combined total of their contracts is $1,296,250

The values of the contracts are given as:

The combined total is represented as:

Total = Exxon Mobil + Aerospace

Substitute known values

Total = $756,733 + $539,517

Evaluate the sum

Total = $1,296,250

Hence, the combined total of their contracts is $1,296,250

Read more about sum and total at:

https://brainly.com/question/4916384

#SPJ1

Answer:

should be 63

Step-by-step explanation:

Answer:

40 units.

Step-by-step explanation:

Consider ∆ADC

Perimeter = 26cm (Given)

★ Perimeter of a triangle is the sum of its three sides.

=> AD + DC + AC = 26

Now, from the figure we can see that side AD = DC

Hence we can also write

=> AD + AD + AC = 26

=> 2AD + AC = 26

=> AC = 26 - 2AD ——— ‘1’

Consider ∆ ABC,

Let us consider it's perimeter to be ‘x’.

=> AB + AC + BC = x

Here also we can make out from the figure that side AB = BC

=> AB + AB + AC = x

=> 2AB + AC = x

From ‘1’ substituting AC value, we get

=> 2AB + ( 26 - 2AD ) = x

=> 2AB - 2AD + 26 = x

=> 2( AB - AD ) + 26 = x

=> 2 (7) + 26 = x ( Given )

Therefore perimeter of the ∆ABC (x) = 40

Answer:

[tex]f^{-1}(x) = 9x -18.[/tex]

Step-by-step explanation:

[tex]y=f(x)=\dfrac 19 x +2\\\\\text{Replace x with y and then solve for y,}\\\\~~~~~~~x = \dfrac 19 y+2\\\\\implies 9x =y + 18~~~~~~~~~~~~~~~;[\text{Multiply both sides by 9}]\\ \\\implies y = 9x -18\\\\\implies f^{-1}(x) = 9x -18\\\\\text{Hence, the inverse of the given function is}~ f^{-1}(x) = 9x -18.[/tex]