Answer:
The farmer can achieve a maximum area of 50 square yards with 20 yards of fencing.
Step-by-step explanation:
Given that farmer shall construct a rectangular fenced-in area and a side of the barn is one side of such area, the needed length of fencing is represent by the following perimeter equation ([tex]p[/tex]), measured in square yards:
[tex]p = 2\cdot l + w[/tex]
Where:
[tex]l[/tex] - Length of the rectangle, measured in yards.
[tex]w[/tex] - Width of the rectangule (side of the barn), measured in yards.
In addition, the equation of the fenced-in area ([tex]A[/tex]) is:
[tex]A = w\cdot l[/tex]
If [tex]p = 20\,yd[/tex], equation of area is now simplified as follows:
[tex]A = (20\,yd - 2\cdot l)\cdot l[/tex]
[tex]A = 20\cdot l - 2\cdot l^{2}[/tex]
The value of [tex]l[/tex] associated with the maximum area is obtained with the help of First and Second Derivative Tests. Firstly, first and second derivatives of the area function are determined:
[tex]A' = 20 - 4\cdot l[/tex]
[tex]A'' = -4[/tex]
Let equalize first equation to zero, second derivative indicates that critical value follows to an absolute maximum. Hence:
[tex]20-4\cdot l = 0[/tex]
[tex]l = 5\,yd[/tex]
The width of the rectangle is: ([tex]p = 20\,yd[/tex] and [tex]l = 5\,yd[/tex])
[tex]w = p - 2\cdot l[/tex]
[tex]w = 20\,yd - 2\cdot (5\,yd)[/tex]
[tex]w = 10\,yd[/tex]
And finally, the maximum area she can achieve is:
[tex]A = (5\,yd)\cdot (10\,yd)[/tex]
[tex]A = 50\,yd^{2}[/tex]
The farmer can achieve a maximum area of 50 square yards with 20 yards of fencing.
A circle has a radius of 6. An arc in this circle has a central angle of 48 degress. What is the length of the arc?
Answer: [tex]1.6\pi[/tex]
Step-by-step explanation:
If a circle has a radius of 6, then the perimeter of the circle is 12pi, or about 37.68. A circle has 360 degrees. Thus, the arc takes up 48/360 of the circle. Thus, simply multiply [tex]\frac{48}{360} * 12\pi[/tex] to get 5.024 or 1.6pi.
Hope it helps <3
A rectangular rug is 12.5 feet long and 10 feet wide. The rug needs to be reduced by a factor of One-fifth to be placed near a door. What is the area of the reduced rug, in square feet? 5 25 50 100
Answer:
5 Feet-
Step-by-step explanation:
I did the test-
What is X^2-9=0 I really need the answers
Answer:
X^2-9=0 is x2 = 9
Step-by-step explanation:
set these 2 distances to equal each other
Which of the following best describes how muckrakers brought about reform in the Progressive Era?
Muckrakers presented Americans with facts about corruption in government and industry and encouraged them to investigate further.
Muckrakers presented Americans with facts about corruption in industry and government that prompted them to demand change.
Muckrakers presented government officials with different ways to reform existing legislation.
Muckrakers presented government officials with facts about different industries and demanded change.
Answer:
B
Step-by-step explanation:
Both A and B are similar but the difference is that muckrakers did not present facts to encourage more investigation, they presented facts to make a change. There are many examples but one major one is Upton Sinclair and his book "The Jungle". It exposed the meat industry and how corrupted it was. This led to many changes such as new food safety laws.
Answer:
B edg
Step-by-step explanation:
what is the answer of it
Answer:
Option A
Step-by-step explanation:
E = 1 - x/p = 1 - 293/473 = ~0.38
=> The number of joules of montion energy that the engine can obtain from 40,000,000 joules of fuel energy:
N = 0.38 x 40000000 = 15,200,000 (J)
Hurry I WILL MARK YOU AS BRAINLIEST
Answer:
Third choice is correct
Step-by-step explanation:
-2x-y=-2
-y=2x-2
y=-2x+2
3x-y=-2
-y=-3x-2
y=3x+2
These two lines intersect at (0, 2)
Solve the following systems of linear equations graphically: 3x + 2y = 6 and
X = 2y + 4. You may use one of the following strategies: a) table of values,
b) x and y intercepts, or c) y = mx + b. In your response, be sure to specify
which strategy you are using. You do not need to submit a graph.
Vanswer
Answer:
The solution set is where the 2 lines intersect.
Step-by-step explanation:
Answer:
2.5 and -0.75
Step-by-step explanation:
i think i could be wrong x
Rick asked a random sample of 160 students from his school what they did for lunch. The table shows the results of Rick’s survey. Work out the relative frequency of eating school lunch. Input note: give your answer as a fraction.
Answer:
43/160
Step-by-step explanation:
To find the relative frequency,
We just have to know things:
1. The data for asked event
2. Total number of data.
With these 2 points, we can create a fraction that is formed like this:
Data of event / Total data
In this case it is:
43/160
Hope this helps
Which of the following explains why cos 60º = sin 30° using the unit circle?
simplify (2) - (x2-x3+2x-1)
Answer:
-x + 3
Step-by-step explains:
Um... You can do it on a computer...
Consider the function. Which statement correctly describes the function’s behavior around its vertical asymptote?
A) As x → –2–, f(x) → ∞ and as x → –2+, f(x) → ∞.
B) As x → –2–, f(x) → –∞ and as x → –2+, f(x) → ∞.
C) As x → –2–, f(x) → –∞ and as x → –2+, f(x) → –∞.
D) As x → –2–, f(x) → ∞ and as x → –2+, f(x) → –∞.
Answer:
B) As x → –2–, f(x) → –∞ and as x → –2+, f(x) → ∞.
Step-by-step explanation:
2020 edg.
A function assigns the values. The correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The statement that correctly describes the function's behavior around its vertical asymptote is As x → –2–, f(x) → –∞ and as x → –2+, f(x) → ∞. Thus, the correct option is B.
Learn more about Function:
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Al aplicar el teorema de Pitágoras en alguno de los triángulos que aparecen en la figura, solo un planteamiento es el correcto, ¿cuál es?
Seleccione una:
a. h2 + b2 = c2
b. c2 + b2 = a2
c. Ningún planteamiento es correcto
d. a2 + m2 = b2
Question:
Found a picture which relates to the question asked. It can be found in the attachment below.
Answer:
b. c2 + b2 = a2
Step-by-step explanation:
According to Pythagoras rule :
The longest side of the triangle is the hypotenus
The opposite and adjacent sides depends on the particular angle provided or one which is to be calculated.
The opposite side is one drawn across a given angle, while the side next to the Given angle is called the adjacent side.
FROM △ABC ;
THE longest side is 'a' = hypotenus
Opposite side = c
Adjacent = b
From Pythagoras :
(Hypotenus)^2 = (Opposite)^2 + (adjacent)^2
Hence,
a^2 = c^2 + b^2
Write the formula to find the profit %, if selling price and cost price both are given.
Answer:
[tex]profit \: percent = \frac{sp - cp}{cp} \times 100 \: percent[/tex]
where,
SP=Selling price
CP=Cost price
For example:Given,
Selling price(SP)= 1000
Cost price(CP)=800
Now,
[tex]profit \: percent = \frac{sp - cp}{cp} \times 100 \: percent \\ = \frac{1000 - 800}{800} \times 100 \\ = \frac{200}{800} \times 100 \\ = 25 \: percent[/tex]
Hope this helps...
Good luck on your assignment..
Find the degree of the polynomial: [tex]2x^{2} y-4x^{5} +6xy^{3}[/tex]
Answer:
5Explanation:
sum of the power of 2x^2y=2+1=3
sum of the power of 4x^5=5
sum of the power of 6xy^3=1+3=4
Highest power=5
Therefore, The degree of given polynomial is 5.
Hope this helps...
Good luck on your assignment..
translate into an algebraic expression: b is decreased by 40% and decreased again by 40% . What is the result ?
Answer:
The result is 0.36b
Step-by-step explanation:
Here. we want to translate the wordings into an expression of algebra.
Firstly, we decrease b by 40%
40% is same as 40/100 = 0.4
So decreasing b by 40% = b-0.4(b) = b-0.4b = 0.6b
Now we want to decrease 0.6b by another 40%
= 0.6b -0.4(0.6b)
= 0.6b - 0.24b
= 0.36b
There are ten meerkats in a colony. Every night, two meerkats stand guard while the others sleep. During a certain period of nights, every meerkat stands guard with every other meerkat exactly once. During that period, how many nights of sleep does each meerkat get?
Answer:
Each gets 36 nights of sleep every 45 nights.
Step-by-step explanation:
This is called the handshake problem, which is the same problem as n guests (including host) attend a party. At the end, everyone shakes hands with everyone else. The number of handshakes is each person shakes hands with (n-1) other persons to give n(n-1) handshakes. However, this counts each handshake twice (A with B and B with A), so the actual number of handshakes is n(n-1)/2
For n=10, then number of "teams" of two meerkats is 10(10-1)/2 = 45.
So each meerkat gets to be on duty 9 nights out of 45, or gets 36 nights of sleep every 45 nights.
Which inequality matches the graph? (2 points)
A) −2x + 3y > 7
B) 2x − 3y < 7
C) −3x + 2y > 7
D) 3x − 2y < 7
Answer:
D) 3x − 2y < 7
Step-by-step explanation:
We note that the x- and y-intercepts are about 2.3 and -3.5, respectively.
In "intercept form," the equation of the line can be written ...
x/x-intercept +y/y-intercept = 1
Using the given intercepts, this is ...
x/2.3 +y/(-3.5) = 1
The answer choices suggest that we should multiply this by 7. When we do, we get ...
3x -2y = 7 . . . . the equation of the boundary line
__
The next trick is to figure the comparison symbol. We note that x-values are less than those on the line, and y-values are greater than those on the line. It is convenient to consider the term with a positive coefficient, so we don't get confused with minus signs and reversed comparisons.
As we said, x-values are less than those on the line, so the shaded area is ...
3x -2y < 7 . . . . matches choice D
Answer:
D) 3x − 2y < 7
Step-by-step explanation:
Took the test and got it right :)
A line passes through (2,-1) and (4,5). Which answer is the equation of the line?
Answer:
C.
Step-by-step explanation:
Slope = m = (y2 - y1)/(x2 - x1) = (5-(-1))/(4 - 2) = 6/2 = 3
Slope - point form:
y - y1 = m(x -x1)
y - 5 = 3(x - 4)
y - 5 = 3x - 12
- 3x + y = - 12 + 5
- 3x + y = - 7
Answer:
[tex] - 3x + y = - 7[/tex]Option C is the correct option.
Step-by-step explanation:
A line passes through ( 2 , -1 ) and ( 4 , 5 )
The equation of line:
[tex] \frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1} [/tex]
Plug the values
[tex] \frac{ y - ( - 1)}{x - 2} = \frac{5 - ( - 1)}{4 - 2} [/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
[tex] \frac{y + 1}{x - 2} = \frac{5 + 1}{4 - 2} [/tex]
Add the numbers
[tex] \frac{y + 1}{x - 2} = \frac{6}{4 - 2} [/tex]
Subtract the numbers
[tex] \frac{y + 1}{x - 2} = \frac{6}{2} [/tex]
Reduce the numbers with 2
[tex] \frac{y + 1}{x - 2} = 3[/tex]
Apply cross product property
[tex]3x - 6 = y + 1[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex]3x - y = 1 + 6[/tex]
Add the numbers
[tex]3x - y = 7[/tex]
[tex] - 3x + y = - 7[/tex]
Hope this helps...
Best regards!
There are 1,000 cubic centimeters in 1 liter, 1,000 cubic millimeters in 1 milliliter, and 1,000 milliliters in 1 liter. How many cubic millimeters are there in 200 cubic centimeters?
Answer:
200,000 cubic milliliters
Step-by-step explanation:
PLEASE MARK BRAINLIEST
please solve this
Find H.C.F
m^3 - 1, m^4 + m^2 + 1, m^2+ m + 1
Answer:
m^2+m+1
Step-by-step explanation:
m^3 - 1= (m-1)(m^2+m+1) m^4 + m^2 + 1= m^4+2m^2+1 - m^2= (m^2+1)^2 -m^2= (m^2+m+1)(m^2-m+1)m^2+ m + 1HCF= m^2+m+1 which is the factor of all three polynomials
Find the solution to the problem and show your steps. -7x+9=3x+49
Answer:
x=-4 is the answer
Step-by-step explanation:
-7x+9=3x+49
Subtracting 3x on both sides
-7x-3x+9=49
Subtracting 9 on both sides
-10x=49-9
-10x=40
x=-4
I hope this will help you :)
PLZ HELP I NEED BIG BRAINERZ HERE Evaluate the expression below and write the answer in standard exponent form. What is the power of the answer? 6.07288 × 10^14÷7÷37 × 10^4
Answer:
The solution would be 75911*10^10/462500 or 1.64132 x 10^9
Step-by-step explanation:
Can any one please help me I really need help please help me thank you
Step-by-step explanation:
Plug in -2 whenever u see x
3(-2) -7= 5(-2-1)
-6-7= -10-1
-13 = -11
Therefore, x is not equal to -2.
Simplify the polynomial (3a^2+4a+25) - (2a^2+4a-5)
Answer:
The polynomial simplified would be a^2 + 30
I hope this helps you:))
P.S. Might I recommend a good online calculator for these types of problems. It's called Symbolab. I use it every day and it's a lifesaver. It shows the step-by-step and has a plethora of different actions like simplifying, inverse, and line.
I NEED HELP PLEASE HURRY, THANKS! :)
Answer:
B
using SOHCAHTOA
COS THETA WILL BE EQUALS TO ROOT 5/3 AND TAN THETA WILL BE EQUALS TO 2ROOT 5/3
Answer:
B.
Step-by-step explanation:
First, note that since [tex]sin(\theta)=2/3[/tex], this means that the opposite side is 2, the hypotenuse is 3, and the last, adjacent side is [tex]\sqrt{5\\[/tex].
Also note that we are told that [tex]sec(\theta)<0[/tex]. This means that [tex]\theta[/tex] cannot be in quadrants 1 nor 4 because (remember All Students Take Calculus?) in those quadrants cosine and secant are positive. Also, we know that sine is positive so we can conclude that [tex]\theta[/tex] is in the second quadrant.
In the second quadrant, sine is positive, cosine is negative, and tangent is negative. Now we can answer the question. We already know the side lengths: opposite=2, adjacent=[tex]-\sqrt{5}[/tex] (because it's in Quadrant II), and hypotenuse=3.
Therefore...
[tex]cos(\theta)=-\sqrt{5} /3[/tex]
[tex]tan(\theta)=2/(-\sqrt{5})=-(2\sqrt{5}/5)[/tex]
13. Gayle is getting ready for her first day of school. She has 7 new dresses to choose from and 4
new pairs of shoes. How many different outcomes are possible for Gayle to wear one dress and
one pair of shoes?
Answer:
49
Step-by-step explanation:
7 times 4 equals 49.
Question 3(Multiple Choice Worth 3 points)
(6.03)
What is the coefficient of the variable in the expression 2 - 5x - 4 + 8?
1. -5
2. O-4
3. 02
4. 08
Answer:
-5
Step-by-step explanation:
The coefficient is the number that goes in front of the variable
The only variable is x and the number in front is -5
The coefficient is -5
Answer:
-5 i did the test
Step-by-step explanation:
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which is a true statement about the diagram?
m∠5 + m∠6 = m∠1
m∠3 + m∠4 + m∠5 = 180°
m∠1 + m∠2 = 180°
m∠2 + m∠3 = m∠5
Answer:
m∠1 + m∠2 = 180°
Step-by-step explanation:
An interior angle and its exterior angle are supplementary (they add up to 180°).
I would really appreciate it if you would mark me brainliest!
Have a blessed day!
Answer:
c
Step-by-step explanation:
How many coordinates can you find along this function? When graphed F(x)=mx+b when m=2 and b=1.
Answer:
assuming the graph is a 10 by 10 there would be 10 diffrent whole number coordinates.