John wants to build a corral next to his barn. He has 300 feet of fencing to enclose three sides of his rectangular yard.
a. What is the largest area that can be enclosed?
b. What dimensions will result in the largest yard?

Answers

Answer 1
Let's first define the variables:
 x = width
 300 - 2x = long
 The area will be:
 A = (x) * (300 - 2x)
 A = 300x - 2x²
 We look for the maximum area, for this, we derive:
 A '= 300 - 4x
 We match zero:
 0 = 300 - 4x
 x = 300/4 = 75
 Therefore, the width is:
 x = 75 feet
 The length is:
 300 - 2x = 300 - 2 (75) = 300-150
 150 feet
 Answer:
 Part A:
 
The maximum area will be:
 
A = (150) * (75) = 11250 square feet
 
Part B:
 
The dimensions are:
 
Length = 150 feet
 width = 75 feet

Related Questions

The length of a rectangular garden is 7 feet longer than its width. if the garden's perimeter is 182 feet, what is the area of the garden in square feet?

Answers

182 - 14=168
168/2
=84
84+7=91
91x84 = 7644 square feet
7644 square feet :))))))))

The explicit rule for a sequence is an=14-9n
What is the recursive rule for the sequence?

Answers

you have to add it then divide it 

The explicit rule for the sequence is [tex] a_{n}=14-9n [/tex]

Let us put n=1, we get

[tex] a_{1}=14-(9 \times 1)=5 [/tex]

Now let n=2,

[tex] a_{2}=14-(9 \times 2)=-4 [/tex]

Let n=3,

[tex] a_{3}=14-(9 \times 3)=-13 [/tex]

Similarly, in this manner we obtain a sequence as

5, -4, -13, -22,.....

Since we can clearly observe that the first term is '5' and common difference is '-9'.

So, we get recursive rule for the sequence as:

[tex] a_{n}=a_{n-1}-9 [/tex] , where [tex] a_{1}=5 [/tex].

Which ordered pair is the best estimate for the solution of the system of equations?

y=−34x−2y=x+6




(−4.25,1.5)

(−4.75,1.75)

(−4.5,1.5)

(−4.5,1.75)

Answers

Final answer:

The best estimate for the solution of the system of equations is (-4.5, 1.5).

Explanation:

The system of equations given is:

y = -34x - 2

y = x + 6

To find the best estimate for the solution, we can substitute the x-coordinate from each ordered pair into the second equation and solve for y.

Let's check each option:

For (-4.25, 1.5):

1.5 = -4.25 + 6

1.5 = 1.75 (not equal)

This is not a solution for the system.

For (-4.75, 1.75):

1.75 = -4.75 + 6

1.75 = 1.25 (not equal)

This is not a solution for the system.

For (-4.5, 1.5):

1.5 = -4.5 + 6

1.5 = 1.5 (equal)

This is a solution for the system.

For (-4.5, 1.75):

1.75 = -4.5 + 6

1.75 = 1.5 (not equal)

This is not a solution for the system.

Therefore, the best estimate for the solution of the system of equations is (-4.5, 1.5).

Point A is located at (0, 4) and point B is located at (−2, −3). Find the x value for the point that is 1/4 the distance from point A to point B.

−1

−0.75

−0.5

−0.25,

Answers

- First thing, find the distance between A and B:
 
AB =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex] =
      =[tex] \sqrt{(0-(-2))^{2} + (4-(-3))^{2} } [/tex] =
      = [tex] \sqrt{4+49} [/tex] =
      = √53

- Hence, we know that the distance between point A and the point C to be found is: 
AC = √53 / 4

- The only other thing we know about point C is that it lays on the line that connects A and B. Let's use the point-slope formula to find the equation of this line:

y - y₂ = [tex] \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] (x - x₂)
y - (-3) = (7/2)(x - (-2))
y + 3 = (7/2)(x + 2)
y = (7/2)x + 7 - 3
y = (7/2)x + 4

This is the equation that ties the coordinates of every point laying on it, therefore it is vaid for A, B and, above all, C which will be:
C (x , (7/2)x + 4)

- Now let's find the distnce between A and C:
AC =[tex] \sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]=
      =[tex] \sqrt{(x-0)^{2} + ((7/2)x+4-4)^{2} } [/tex] =
      =[tex]\sqrt{x^{2} + (49/4)x^{2} }[/tex] =
      =[tex] \sqrt{(53/4) x^{2} } [/tex] =
      =+/-(√53/2)x 
- Lastly, we know this distance must be equal to √53 / 4, therefore you need to set and solve the equation:
+/-(√53/2)x = √53 / 4
(1/2)x = +/-(1/4)
x = +/-(1/2)

Since point C is towards point B, we have to take the negative answer: 
x = -(1/2)

- Therefore the correct answer is C: -0.5

Rico is making 4 batches of salsa.EAxh batch needs 2/3 cup of corn.He only had a 1/3 cup measure.How many times must rico measure 1/3 cup of corn to have enough for all of the salsa

Answers

He would need to measure the  1/3 cup of corn 2 times

What context clue in the paragraph best helps in understanding the meaning of the word native?

Question 2 options:

"much in America"


"lived in Nantes, France"


"first in France"


"born in Louisiana"

Answers

What was the Answer?


Shannon collects charms for her charm bracelet. her charm bracelet had 4 charms when she bought it. each year on her vacation she buys 2 more charms to add to her bracelet. assume that shannon continues to buy the same number of charms each year. write an equation that can be used to find how many charms shannon will have on her bracelet after 5 years.

Answers

I think it should be y=4+2*5
2x + 4 = the number of charms that Shannon has

x = the number of years that Shannon has had the bracelet 

Replace x with 5 to find the total number of charms after 5 years

2*5 + 4 = 14 charms after 5 years. 

Solve for z. 7-~-3z+2=4 What is the root? If there is no root, choose none.

Answers

Desmos is Function Calculator is a great tool for this, the correct answer is z= 7/3


7/3= 2.333~ and so √(3*2.333~) + 2= 2.9999999833333~

Now 7- 2.9999999833333~= 4.0000000166667~ but I don't know the true infinate sign for this so thats why my numbers look a little werid, just plug (7/3) in for z and you will get 4, trust me


The root of the given equation 7-[tex]\sqrt{3z+2}[/tex] = 4 is z = 7/3

What is an equation?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, an equation 7-[tex]\sqrt{3z+2}[/tex] = 4

Solving for z,

7-[tex]\sqrt{3z+2}[/tex] = 4

[tex]\sqrt{3z+2}[/tex] = 3

Squaring both sides,

3z + 2 = 9

3z = 9-2

3z = 7

z = 7/3

Hence, the root of the given equation 7-[tex]\sqrt{3z+2}[/tex] = 4 is z = 7/3

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Please help!


Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are spades? Are these events independent?


A. 1/17: no, they are dependent events

B. 1/16: yes, they are independent events

C. 25/52: yes, they are independent events

D. 3/52: no, they are dependent events

Answers

Answer: 
Choice A
1/17; no, they are dependent events

============================================

Explanation:

There are 13 spades and 52 cards total. So 13/52 = 1/4 is the probability of drawing one spade

If we do not replace the card we pull out, then the probability of another spade is 12/51 since there are 12 spades left out of 51 total. 

Multiply the fractions 1/4 and 12/51 to get
(1/4)*(12/51) = (1*12)/(4*51) = 12/204 = 1/17

The two events are not independent because the second event (pulling out a second spade) depends entirely on what happens in the first event (pulling out a first spade). The fact that the probability is altered indicates we have dependent events.

If the state sales tax is 6% and a city adds an additional 1 1/4% tax,
What will the tax be on a purchase of $146.00? (Round the answer to the nearest cent.)

A. $10.59
B. $8.76
C. $10.80
D. $18.25

Answers

Your answer is A. 10.59 is the tax. 

draw a number line from 0 to 2 write 3\8 1 and 3\4 and 1.25 on the number line,

Answers

To solve this exercise you must apply the proccedure shown below:
 1- You have the following numbers given in the problem above:
 3/81, 3/4 and 1.25
 2- Therefore, you have that 3/81 in decimal form, is: 
 3/81=0.03
 3- 3/4 in decimal form is:
 3/4=0.75
 3- Keeping this on mind,  you can draw the number line from 0 to 2 and write the numbers given above, as you can see in the figure attached.
The graph of the number line from 0 to 2 is shown in Figure 1. We start this graph by setting the number zero to the left of the number 2, that is, the numbers increases from left to right. Next, we have the following points to be marked in the number line:

 [tex]\frac{3}{8} \\ \\ 1 \\ \\ \frac{3}{4} \\ \\ 1.25[/tex]

But we can rewrite these numbers as decimals:

[tex]\frac{3}{8}=0.375 \\ \\ 1 \\ \\ \frac{3}{4}=0.75 \\ \\ 1.25[/tex]

So Figure 2 shows each point marked on the number line. The way we choose is to set each point on the number line analyzing in which position it must lay. For instance, [tex]\frac{3}{8}[/tex] is less than [tex]\frac{3}{4}[/tex] but greater than zero. So its position is as indicated in Figure 2.

What is the number of pi?

Answers

It is irrational and cant be expressed as a dividion of two intergers. It is somewhat accurately described as 3.14159 or 22/7 .

Pi is a very special number in math and it’s so special that it even gets its own symbol. Mathematicians found out that when you try to write down what pi is, the decimal points keep going and going. This means that it’s impossible to find all the digits of pi.

I will only write down some digits.

π = 3.1415926535897932384626

In the triangle below, 4/5 represents which ratio?

Answers

Answer:
sin (C)

Explanation:
In a right-angled triangle, special trig functions can be applied. These functions are as follows:
sin (theta) = [tex] \frac{opposite}{hypotenuse} [/tex]

cos (theta) = [tex] \frac{adjacent}{hypotenuse} [/tex]

tan (theta) = [tex] \frac{opposite}{adjacent} [/tex]

Now, let's check the triangle we have:
We have two options:
First option:
5 is the hypotenuse of the triangle
4 is the side adjacent to angle B
Therefore, we can apply the cos function:
cos (B) = [tex] \frac{4}{5} [/tex]

Second option:
5 is the hypotenuse of the triangle
4 is the side opposite to angle C
Therefore, we can apply the sin function:
sin (C) = [tex] \frac{4}{5} [/tex]

Among the two options, the second one is the one found in the choices. Therefore, it will be the correct one.

Hope this helps :)

A lab is conducting a test to see if people prefer chocolate A or chocolate B. The steps in the test are outlined below: Step 1. Recruit one hundred volunteers and tell them the purpose of the study. Step 2. Give them chocolate A and ask them to rate the flavor. Step 3. Give them chocolate B and ask them to tell how delicious it is. Step 4. Reveal which chocolate they preferred. Which step could lead to biased results?

Answers

I'd say step 3 because it's asking how "delicious" it was while step 2 said "rate the flavor." People could give it a 1 in delicious and a 5 in flavor. This leads to unfair results. *Also add about them having a constant and variable.*

Hope that helped! <3

Answer:

Step 3

Step-by-step explanation:

By asking the participants how delicious chocolate B is, you can possibly create bias in the test.  It is a leading question; these should not be asked to avoid creating bias.

Solve the equation 2cos^2x = sin2x , giving your answer in terms of π. 0

Answers

2cos^2x = sin2x 2cos^2x = 2sin x cos x (2sin x cos x) / (2cos^2x) = 1 sin x / cos x = 1 tan x = 1 x = π/4

Given is [tex] 2*cos^{2} (x)=sin(2x) [/tex]

We can use following formulas to solve this problem :-

1. [tex] \frac{sin\;\theta}{cos\;\theta} = tan\;\theta [/tex]

2. sin(2∅) = 2·sin(∅)·cos(∅)


Solving the given equation :-

[tex] 2*cos^{2} (x)=sin(2x) \\\\2*cos^{2} (x)=2*sin(x)*cos(x) \\\\2*cos^{2} (x)-2*sin(x)*cos(x)=0 \\\\2*cos^{2}(x)*(1-\frac{sin(x)}{cos(x)}) =0 \\\\2*cos^{2}(x)*(1-tan(x)) =0 \\\\cos^{2}(x) = 0 \;or\; (1-tan(x)) =0 \\\\cos(x) = 0 \;or\; tan(x) =1 \\\\x = cos^{-1}(0) \;or\; x=tan^{-1}(1) \\\\x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex]

Hence, final answer is [tex] x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex].

Please explain it and tell me how u got the answer
Thx

Answers

The y-intercept of a function is that function's value when x=0.
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.

If you want them to differ by zero (be the same), you have to move them to the same point.

Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.

Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.

Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.

Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.

___
The appropriate choice is the 1st one.
&nbsp; f(x) - 3 and
&nbsp; g(x) + 1

Overdraft protection means the bank will loan you the money needed to cover the check that cannot be covered by funds in the account. True or false ASAP HELP PLEASE

Answers

yep i agree its true.


True. Overdraft protection is a service offered by banks to their customers. When your account does not have enough money to cover a transaction, overdraft protection allows the bank to loan you the necessary funds to complete the transaction.

If you make a purchase or withdrawal that exceeds your account balance, the bank will cover the shortfall by lending you the needed amount. This ensures the transaction goes through, but typically comes with fees or interest. While convenient, it can lead to extra costs if used frequently.

Overdraft protection may apply to debit card purchases, checks, or automatic bill payments, depending on the account settings. Some banks offer this service automatically, while others require customers to opt in. It's a useful safety net but should be used responsibly to avoid accumulating unnecessary charges.

Which point lies in the plane represented by the equation 2x + 7y + 3z = -25?

(–3, 3, –2)
(–6, –4, 5)
(6, 1, –3)
(6, 1, 2)

Answers

the second one is true
[tex]2 \times - 6 + 7 \times - 4 + 3 \times 5 \\ = - 12 + - 28 + 15 \\ = - 40 + 15 = - 25[/tex]
hope this helps

The point which satisfy the equation 2x + 7y + 3z = -25 will be (–6, –4, 5). The correct option is C.

What is an equation of plane?

The equation of the plane is defined as the plane has three variables. Having the coordinates in all three dimensions. The general form of the equation of the plane is ax + by + cz = d.

The given equation of plane is 2x + 7y + 3z = -25.

Check the point which satisfies the equation of the plane. Take the point ( -6,-4,5).

2x + 7y + 3z = -25.

2 ( -6 ) + 7(-4) + 3(5) = -25

-12 - 28 + 15 = -25

-40 + 15 = -25

-25 = -25

Therefore,  the point which satisfy the equation 2x + 7y + 3z = -25 will be (–6, –4, 5). The correct option is C.

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BRAINLIEST ANSWER RN!!!!!!! HELP ME PLZZ!!!!!

A cylinder tube with caps on both ends is used to safely carry a rolled up poster. The tube is 42 inches tall with a radius of 1.5 inches. If one mini can of spray paint covers 150 square inches, how many mini spray cans of red paint would be needed to cover the entire tube?

A. 3
B. 2
C. 1
D. 4

Answers

find surface area
SA=2pir^2+2hpir

h=42
r=1.5

SA=2pi1.5^2+2(42)pi1.5
SA=4.5pi+126pi
SA=130.5pi square inches


area/areacoverdperspray≤numberofsprays
130.5pi/150
2.73
so buy 3 cans because you can't get 0.73 cans

A

10 points!
Which graph represents the solution to the system of inequalities?
2x – y ≥ 3
x + 2y < 4

Answers

Graph C is the answer. 

2x – y ≥ 3x + 2y < 4
=y is less than or equal to 2x-3
y is less than -x/2+2



Answer:

graph c is the correct answer hope this helps you get an A.

How to find x in this math problem?

Answers

In a triangle, the three interior angles always add to 180°  ⇒
The third interior angle of the triangle = 180 - (30+20) = 130°

Vertical angles are equal ⇒  x = 130°

The answer is 130°

what is y−4=−2(x+7) written in standard form?

Answers

y=2x+18

Hope that helps!
The standard form of a linear equation is [tex]ax+by=c[/tex], where a, b, and c are numbers.

You are given [tex]y-4=-2(x+7)[/tex]. We need to start by expanding and simplifying.

 [tex]y-4=-2x-14\\y=-2x-14+4\\2x+y=-10[/tex]

Some teachers, including mine when I took Algebra 1, require that you find integers (whole numbers) for a, b, and c, and that a be positive. Here, we are fine.

How do you decide which variable to isolate in order to use the substitution method to solve a system of linear equations?

Answers

Find a variable with no coefficient.If there is more than one variable with no coefficient,it dose not matter which one you isolate.Isolate the variable and then use substitution to solve the system of equations.

The way to decide which variable to isolate in order to use the substitution method to solve a system of linear equations is;

to look for the variable with no coefficient or least coefficient and then isolate it and use substitution to solve the simultaneous equation.

       A system of linear equations can be solved by three major methods which are;

- Elimination method

- Substitution method

- Graph method

     Now, in this question we want to know how substitution method is done.

Let us say we have two simultaneous equations which are;

2x + 3y = 8   ----(eq 1)

x + 5y = 11     ----(eq 2)

      Now, in this method, we need to first isolate a variable in one of the equations by making it the subject of formula there. Usually, we go with the variable that has no coefficient first.

In this case, it is x that has no coefficient in eq 2 and as such, we will isolate it to get;

x = 11 - 5y

    In conclusion, the way we decide which variable to isolate in substitution method of simultaneous equations is to look for the variable with no coefficient or least coefficient.

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what is the missing number in the synthetic division problem below?
(everything in picture)

Answers

The answer is C, 10.

When performing synthetic division, we bring down the first number in the box.  We then multiply this number by the number outside the box, and place that result under the second number in the box.  We add these two numbers and bring that sum down.

We then continue this process by multiplying this second number by the number outside the box, and place the result under the third number in the box.  We then add the two numbers in the third column and bring the sum down.  The missing number is under this column; that means it is found by adding 2+8, so it is 10.

In the given problem , missing number in the synthetic division is equal to [tex]10[/tex].

What is synthetic division?

" Synthetic division is defined as simplified way of dividing a polynomial by another polynomial of first degree by writing its coefficient and changing usual subtraction into addition."

According to the question,

As shown in the given synthetic division,

[tex]4 + 20 = 24\\\\-2 + 6 = 4[/tex]

Therefore,

Missing number in the given synthetic division [tex]= 2+ 8[/tex]

                                                                                [tex]=10[/tex]

Hence, Option (C) is the correct answer.

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Suppose an investment of $2,300 doubles in value every decade. The function gives the value of the investment after x decades. f(x)=2300*2^x How much is the investment worth after 2 decades?
(1 point)$2,355,200
$92,000
$46,000
$9,200

Answers

Final answer:

The investment is worth $9,200 after 2 decades.

Explanation:

To find the value of the investment after 2 decades, we can substitute x = 2 into the function f(x) = 2300 * 2^x.

So, f(2) = 2300 * 2^2 = 2300 * 4 = 9200.

Therefore, the investment is worth $9,200 after 2 decades.

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Find an angle between 0 and 2π that is coterminal with 27 pi/10

Answers

27pi/10 *180/pi= 486, but since we want a coterminal angle between 0 and 2pi we substract 360, 486-360= 126 (this is the answer in degree form), =126* pi/180= 7pi/10
to make sure this is the right answer we have to check if the reference angles are the same, which is this case they are. (180-126= 54) (540-486=54)

Please answer this and thank you

If DE=4x+10, EF=2-1, and DF=9x-15, find DF.

Answers

I hope that 2-1 means 21.

DE + EF = DF
4x + 10 + 21 = 9x - 15
4x + 31 = 9x - 15
31 = 9x - 4x - 15
31 = 5x - 15
46 = 5x
x = 9 1/5 = 9.2

You want 9x - 15
9*9.2 - 15
82.8 - 15
67.8 <<<<< answer. 
If I have given the wrong meaning to 2-1 (which could mean 1) leave another note and I will correct my work. 

Will mark brainliest ⭐️⭐️⭐️⭐️⭐️

Answers

is a hope this helped

Answer:

answer is d

Step-by-step explanation:

Please help me on this....

Answers

8x + 4y = 16
x + 7y = 15
multiply second equation by (-8)
-8x - 56y = -120
so now
 8x + 4y = 16
-8x - 56y = -120
-----------------add
-52y = -104
y = 2


7(2) = 15 - x
14 = 15 - x
x = 1

answer is C. 
(1, 2)

What is the best first step in solving the equation 3 +3 square root 6x = 5? A.)Subtract 3 from both sides.
B.)Find the cube of 3 square root 6x .
C.)Cube both sides of the equation.
D.) Subtract 5 from both sides.

Answers

Final answer:

The best initial step in solving the equation 3 + 3√(6x) = 5 is to subtract 3 from both sides, simplifying the equation to 3√(6x) = 2, which lays a clear path towards isolating and solving for x.So,option A.)Subtract 3 from both sides. is correct.

Explanation:

The best first step in solving the equation 3 + 3√(6x) = 5 is to simplify the equation by isolating the square root term. This can be done by following option A: Subtract 3 from both sides of the equation. This action makes the equation easier to manage step-by-step as you move toward isolating x, which is the ultimate goal of solving for x. The resulting equation after subtracting 3 from both sides is 3√(6x) = 2. This simplified equation can then be further manipulated to solve for x, primarily by squaring both sides to eliminate the square root, and then solving the resulting simple algebraic equation.

Other Questions
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