Answer: the awser is 2 not 6
Step-by-step explanation:
a farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. if the fencing costs per linear foot to install and the farmer is not willing to spend more than , find the dimensions for the plot that would enclose the most area.
The constraint for the maximum enclosed area is the amount the farmer is
willing to spend on fencing.
The width of the plot that will give the most area, y = 83.[tex]\underline{\overline 3}[/tex] feet
The length of the plot that will give the most area, y = 125 feet
Reasons:
The given parameters are;
The cost of fencing per foot = $20
The maximum amount the farmer is willing to spend = $5000
Number of sides of fencing = 3 sides
Cost of the west side of the = Split with neighbor
Solution:
Let, y, represent the length of the fence, and let x represent the width of
the fence, we have;
Length of fence required = y + 2·x
Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x
Therefore;
Maximum amount to be spent on the fence, 5000 = 20·y + 30·x
[tex]\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x[/tex]
[tex]y = \mathbf{250 - \dfrac{3}{2} \cdot x}[/tex]
Area of a rectangle = Length × Width
The enclosed rectangular area of the fencing, A = y × x
[tex]\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2[/tex]
[tex]\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}[/tex]
The leading coefficient of the quadratic function of the area is negative,
therefore, the function only has a maximum point.
At the point of the most area, the slope, [tex]\dfrac{dA}{dx} = 0[/tex]
Finding the value of x at the maximum point, we get;
[tex]\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0[/tex]
Therefore;
[tex]\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}[/tex]
[tex]\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125[/tex]
The length of the plot that will give the most area, y = 125 feet
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Select all that are solutions to the inequality below:
3x - 15 > 3
Answer:
solutions are all values greater than 6
Step-by-step explanation:
add 15 to each side to get:
3x > 18
divide each side by 3 to get:
x > 6
solutions are all values greater than 6
what is 6/2(1+2)=?give with expiation
Step-by-step explanation:
6/2 (1+2) = 3(3) = 9.
hope this helps you.
Answer:
9
Step-by-step explanation:
First you need to multiply 6/2 or 3 by the numbers in the ( ) 6/2 x 1 and 6/2 x 2. You will get 3 and 6. 3+6= 9
If -2 is a zero of P(x) = 2x²- 3x( 5k+4) then k = ____.
Brainly Challange for high level user.
Answer:
k = - [tex]\frac{16}{15}[/tex]
Step-by-step explanation:
Since x = - 2 is a zero , then p(- 2) = 0 , that is
2(- 2)² - 3(- 2)(5k + 4) = 0
2(4) + 6(5k + 4) = 0 ← distribute parenthesis
8 + 30k + 24 = 0
30k + 32 = 0 ( subtract 32 from both sides )
30k = - 32 ( divide both sides by 30 )
k = [tex]\frac{-32}{30}[/tex] = - [tex]\frac{16}{15}[/tex]
Given Polynomial P(x) = 2x^2-3x(5k+4)
Zero = -2
We know that
If -2 is zero of the Polynomial then it satisfies the given Polynomial
⇛P(-2) = 0
⇛ 2(-2)^2-3(-2)(5k+4)=0
⇛ 2(4)+6(5k+4) = 0
⇛ 8+30k+24 = 0
⇛ 30k+32 = 0
⇛ 30 k = -32
⇛ k = -32/30
⇛ k = -16/15
Answer:- The value of k = -16/15.
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Please solve step by step
Answer:
Hopefully this is the question: 7[tex]x^{2}[/tex] + 3x - [tex]x^{2}[/tex]
Step-by-step explanation:
7[tex]x^{2}[/tex] + 3x -[tex]x^{2}[/tex]
= 6[tex]x^{2}[/tex] + 3x
= 3x ( 2x + 1 )
Hopefully this helps.
answer this
help me with this question.
Answer:
i cant read the handwriting
Step-by-step explanation:
A jar contains 450 beans. Of all beans, 1/5 are mung beans and the rest are pinto beans. What is the ratio of mung beans to pinto beans?
PLEASE HELP ME!
=======================================================
Explanation:
1/5 of the beans are mung, so 4/5 of the beans are pinto. The two fractions add to 5/5 = 1.
Ignore the denominators and focus on the numerators for each fraction. We have 1 mung and 4 pinto. The values are read in this order to form the ratio 1:4 which is our answer. We cannot reduce this ratio any further.
The order is important because saying 4:1 would mean that we have 4 mung beans and 1 pinto, when it's the other way around.
Side note: The value 450 isn't needed. We could easily change it to any other multiple of 5 and get the same exact answer.
its urgent please. my assignment is due in like 30 minutes
Answer:
( iii)
a-x/a+x =b
a-x=b(a+x)
a-x=ab+ax
a-ab=ax+x
a-ab=x(a+1)
a-ab/a+1=x(a+1)/a+1
x=a-ab/a+1
x=a(1-b)/a+1
please help me in questions 16 and 17 only and i’ll mark you as brainliest i promise
Answer:
16. Domain: [-3,5] and range : [-5,3]
17. Domain: [0,4] and range: [0,4]
Mallika and Kishore have the same numbser o marbles. To have 100 marbles they must pool their marbles together and then gset 30 more. " which equation represents the above relationship?
Number of marbles with Mallika = x
Number of marbles with Kishore = x (same number of marbles)
To get 100 marbles = x + x + 30
=》x + x + 30 = 100
2x + 30 = 100
2x = 100 - 30
2x = 70
x = 70/2
x = 35
■ Final answer =》Mallika & Kishore both have 35 marbles each.
■ Equation =》2x + 30 = 100
■ Equation type =》Linear equation in 1 variable
______
Hope it helps ⚜
The equation for the given situation will be;
⇒ 2x + 30 = 100
Where, 'x' is represent the number of marbles.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Mallika and Kishore have the same number of marbles.
And, To have 100 marbles they must pool their marbles together and then get 30 more.
Now,
Since, Mallika and Kishore have the same number of marbles.
Hence, Let the number of marbles = x
So, We can formulate;
⇒ x + x + 30 = 100
⇒ 2x + 30 = 100
⇒ 2x = 100 - 30
⇒ 2x = 70
⇒ x = 35
Thus, Number of marbles each have = 35
And, The equation for the given situation will be;
⇒ 2x + 30 = 100
Where, 'x' is represent the number of marbles.
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7,200 divided by 10 to the power of 2
Answer:
51840
[tex] 51840[/tex]
Answer:
518400
Step-by-step explanation:
7200 ÷ 10 is just the zero less:
= 720
Then
720 × 720 =
+1440
+5040
=518400
Harry has a balance of $-60.00. He buys 4 bags of apples at the store. 1 bag of apples costs $3. What is his balance now? Explain whether he is making a good financial decision.
Answer:
I may not know his balance but I think he's not making a good financial decision because he already has - $60 in his account and he's spending more making him more liable to burn money and it's not advisable
BRAINLIEST
please help me ty
You can just do two questions or even just one but I would appreciate all
Answer:
Some answers for #4 I think!
a = 36
b = 90
c = 36
d = 90
e = 54
Sorry if they are wrong I tried my bestest!
solve pls brainliest
Answer:
76%
Step-by-step explanation:
to make this a percentage we need to make the denominator 100. luckily 25*4=100, so multiply 19/25 by 4/4 to get 76/100. so our percentage is 76
Answer:
76%
Step-by-step explanation:
percent is out of 100, so 19*4/25*4=76/100=76%
Given that E is the midpoint of AD and BC, which of the following proves that AB∥CD?
HELP ASAP!
The proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
The given figure showing ΔABE ≅ ΔDCE is in the image attached below.
We know that:
E is the midpoint of AD. Therefore, AE ≅ ED by the definition of midpoint.
E is the midpoint of BC. Therefore, BE ≅ EC by the definition of midpoint.
∠AEB and ∠CED are vertical angles, therefore, ∠AEB ≅ ∠CED by the vertical angles theorem.
This means that ΔAEB and ΔDEC have:
two pairs of congruent sides - AE ≅ ED and BE ≅ EC
one pair of congruent included side - ∠AEB ≅ ∠CED
Hence, ΔABE ≅ ΔDCE by the SAS Congruence Theorem.
If both triangles are congruent, it implies that all corresponding sides and angles of ΔAEB will be congruent to that of ΔDEC.
Therefore, AB∥CD by the CPCTC Theorem.
Thus, the proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
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Juan alquiló un auto por un día. La tarifa mínima es $490.00, con un cargo adicional de $9.70 por cada kilómetro que maneje. Juan pagó $2847.10 cuando entregó el auto. ¿Qué cantidad de kilómetros manejó? kilómetros Х $ ?
Answer:
243 km
precio de los kilómetros: $2357.10
Step-by-step explanation:
precio total = tarifa mínima + precio de los kilómetros
Para x kilómetros,
P = 490 + 9.7x
P = 2847.1
490 + 9.7x = 2847.1
9.7x = 2357.1
x = 243
precio de los kilómetros: 243 × $9.70/km = $2357.10
Respuesta: 243 km
precio de los kilómetros: $2357.10
please help me 8x-3+4x+3
Answer:
12xStep-by-step explanation:
please help me 8x-3+4x+3
8x - 3 + 4x + 3 =
8x + 4x - 3 + 3 =
12x
Answer:
12x
Step-by-step explanation:
1. To simplify this expression, we must group like terms.
[tex](8x + 4x) + (-3 + 3)[/tex] [tex]12x + (-3+3)[/tex] [tex]12x[/tex]Therefore, the answer is 12x.
Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?
(A) A sample of size 25 will produce more variability of the estimator than a sample of size 50.
(B) A sample of size 25 will produce less variability of the estimator than a sample of size 50.
(C) A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.
(D) A sample of size 25 will produce a more biased estimator than a sample of size 50.
(E) A sample of size 25 will produce a less biased estimator than a sample of size 50.
Using the Central Limit Theorem, it is found that the correct option is:
(A) A sample of size 25 will produce more variability of the estimator than a sample of size 50.
By the Central Limit Theorem, for a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], considering the sampling distribution of sample means of size n, the measure of variability is the standard error, which is given by:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Hence, the higher the sample size, the lower the variability, and option A is correct.A similar problem is given at https://brainly.com/question/24663213
Which of the following are cube numbers. select all that apply
8/9
27
30
8/27
1/27
27/64
64
1/9
Answer:
Step-by-step explanation:
8/9 8 is a cube but 9 is not. 8/9 is not a cube
27 27 = 3^3, a perfect cube
30 Not a cube
8/27 Both 8 and 27 are perfect cubes, and so 8/27 is one also.
1/27 This is equivalent to 1^3 / 3^3 and is a perfect cube.
27/64 Both 27 and 64 are perfect cubes, so 27/64 is one also
64 64 = 4^3, a perfect cube
1/9 9 is not a cube, so 1/9 is not one either.
Help me pls
Find angle fgh
Answer:
116
Step-by-step explanation:
Fast and loose: The two triangles are congruent by SSS (they are both right triangles, the hypotenuse is in common, one of the sides is congruent as a given, the second has to be because of pythagorean theorem). The two angles are thus congruent, and their measure is the same:
[tex]2x+20 = 5x-37 \rightarrow 3x=57 \rightarrow x=19[/tex]
Found x, we can find the measure of the larger angle which is [tex](2\times 19 + 20 )\times 2 = 58 \times 2 = 116[/tex]
Answer:
Angle fgh=116
Step-by-step explanation:
Since segments FI and HI are congruent and angles H and F are congruent we can safely assume that angles FGI and HGI are congruent too. Since they are congruent we're going to set up our equation like so:
(2x+20)=(5x-37)
Now we set the equations equal to each other to solve for x
-3x=-57
Divide the -3 by both sides
x=19
Now we have to plug the x into the equations
2(19)+20 and 5(19)-37
Our answer is 58 for both equations
Now we have to add 58+58 because we're solving for FGH not just FGI or HGI.
SO our final answer is 116
(Hope this helps! If I did this wrong someone please correct me and respond to this answer so that I can delete it. Have a great day!)
Is the point (3,2) a solution of the equation?
Step-by-step explanation:
no cause 3/2 can't be changed
$6.00 for 3 chocolate bars how many did he pay per bar
Answer:
$2.00
Step-by-step explanation
To solve this problem, divide $6 by 3 bars which is $2 a bar
Answer:
One bar= $2
Step-by-step explanation:
6 is the amount paid, 3 is the amount of bars he got. so to find the amount for one bar you divide, 6÷3= 2
auestion is in the picture, 10 points!
Answer:
y = K/(16z)
Step-by-step explanation:
[tex]K=16yz\qquad\text{given}\\\\\boxed{y=\dfrac{K}{16z}}\qquad\text{divide by the coefficient of y}[/tex]
Make x the subject of the equation x2+3=h
Answer:
x2\2+3\2=h/2 therefore x= -3\2+h\2
the 120 grams powdered milk make 12 cups of milk. how many kilograms of powdered milk can produce 60 cups of milk. how many liters is 60 cups of milk?
Answer: 0.6 Liters of powdered milk can produce 60 cups of milk.
Explanation: 120 grams of powdered milk makes 12 cups of milk. 120 divided by 12 is 10. 60 times 10 is 600. So 600 grams of powdered milk to make 60 cups of milk. That is equal to 0.6 kilograms and that is equal to 0.6 liters.
Factor completely by finding the greatest common factor:
12xy^4 − 21x^2y^5z + 36xy^3
Answer:
the coomon factor is 3xy³
by factoring we get
3xy³(4y-7xy²z+12)
Javad had a mix of yellow and red jelly beans are shown on the graph if there are 42 jelly beans in his bag how many are red?
Answer:
there is no graph though
I'm stuck on question 6 + (-20.5)
Answer:
Step-by-step explanation:
First you put the negative sign away for the end and then you switch the problem to 20.5 - 6. Then you put the 0.5 away for later too. 20 - 6 is equal to 14. Then you add the 0.5 back to the number. So it is equal 14.5 and the you put the negative sign back on to get the final answer of -14.5.
write down, all the multiples of 8 less than 80
Answer:
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, and 72.
Answer:
8, 16, 24, 32, 40, 48, 56, 64, 72
Step-by-step explanation:
8, 16, 24, 32, 40, 48, 56, 64, 72
i need help on this pls
Answer:
the answer is 15 bc 30-15=15
Step-by-step explanation:
Answer:11?
Step-by-step explanation:30 buldogs
pirates 10 plus star 9 19 in 30 wwhats left