Peter's farm has 160 meters of fencing, and he wants to fence a rectangular field thatborders a straight river. He needs no fence along the river side. Find the largest areaof Peter's farm that can be fenced.
Answers
ANSWER
3200 m²
EXPLANATION
Peter wants to build a fence around a rectangular field, except for one side because the river is there,
So, the total perimeter of the fence is,
[tex]P=W+W+L=2W+L[/tex]And this is equal to 160 m. Solving for L,
[tex]160=2W+L\text{ }\Rightarrow\text{ }L=160-2W[/tex]The area of this field is,
[tex]A=WL[/tex]Replace L with the expression we found from the perimeter,
[tex]A=W(160-2W)=160W-2W^2[/tex]The area is given by a quadratic function whose leading coefficient is negative, which means that the graph is a downward parabola and, therefore, the vertex is the maximum value of the area.
The x-coordinate of the vertex is given by,
[tex]f(x)=ax^2+bx+c\text{ }\Rightarrow\text{ }x_{vertex}=\frac{-b}{2a}[/tex]In this case, x is W, a = -2, and b = 160, so the width of the field for the maximum area is,
[tex]W_{vertex}=\frac{-160}{2(-2)}=\frac{160}{4}=40m[/tex]And the length when W = 40 is,
[tex]L=160-2W=160-2\cdot40=160-80=80m[/tex]And the area is,
[tex]A=WL=40m\cdot80m=3200m^2[/tex]Hence, the largest area of Peter's farm that can be fenced is 3200 square meters.
Related Questions
A backpack weighs 10 N. What is the mass of the backpack?
Answers
The mass of the backpack is 1.02 kilograms.
What is the mass of the backpack?On earth, the weight of an object of mass M is given by:
W = M*g
Where g is the gravitational acceleration:
g = 9.8m/s^2
In this case, the weight is 10N, then we can write:
10N = M*9.8m/s^2
Solving this for M we get:
10N/(9.8m/s^2) = M = 1.02 kg
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find 5 consecutive odd integers who's sum is -45(solve algebraically)
Answers
let the consecutive odd integers be
x, x+ 1, x+ 2, x + 3, x + 4
Average = sum / total number
Average = -45
Total number = 5
-45 = x + x + 1 + x + 2 + x + 3 + x + 4 / 5
Introduce cross multiplication
-45 x 5 = x + x + 1 + x + 2 + x + 3 + x + 4
-225 = x + x + x + x + x + 1 + 3 + 4 + 5
-225 = 5x + 16
Solve for m.m- 15 = 20
Answers
Answer:
m=35
Explanation:
Given the equation:
[tex]m-15=20[/tex]We solve for the value of m by adding 15 to both sides.
[tex]\begin{gathered} m-15+15=20+15 \\ m+0=35 \\ m=35 \end{gathered}[/tex]The value of m is 35.
The result will be m=35
Select the correct answer. Jonathan has 30 chocolates. He gives some chocolates to his friend David. He then gives Sarah half the number of chocolates that he gave David and gives Lily two-thirds of what he gave David. After giving away the chocolates, Jonathan has 4 chocolates left. If the number of chocolates Jonathan gives David is x, which equation represents the situation? How many solutions does this equation have? A. x + 1 2 x + 2 3 x = 30 − 4 , which has no solution B. x + 1 2 x + 2 3 x = 30 , which has infinitely many solutions C. x + 1 3 x + 2 3 x − 4 = 30 , which has one solution D. x + 1 2 x + 2 3 x + 4 = 30 , which has one solution E. 1 2 x + 2 3 x = x − 4 , which has no solution
Answers
The solution to equation x+ 1/2x+2/3x+4= 30 and has one solution x = 12 which is the correct answer would be an option (D).
The no. of chocolates given to Sarah = 1/2 of x = x/2
Then Lily has two-thirds of what he has given David. Following the distribution of the chocolates,
The number of chocolates provided to Lily is equal to two-thirds of the number of chocolates given to David.
The number of chocolates given to Lily Equals 2/3 of x = 2x/3
Now, the total number of chocolates delivered to David, Sarah, and Lily
= x+x/2+2x/3
Here LCM of 2 and 3 is 6
The Total no. of chocolates given to David, Sarah, and lily
= (6x + 3x+ 4x)/6
The total number of chocolates distributed to David, Sarah, and Lily is 13x/6.
Jonathan had four chocolates left after giving them out.
The number of chocolates left with Jonathan equals the total number of chocolates given to David, Sarah, and Lily.
⇒ 4 = 30 - 13x/6
⇒ 4 + 13x/6 = 30
⇒ 13x/6 = 30-4 = 26
⇒ x = 26×6/13 = 2×6
⇒ x = 12
Hence, the equation which represents the given situation is 30 - 13x/6 =4
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Raina and Leila are driving separate cars to Boston. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.
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(a) Leila's car, 2 gallons
At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas.(b) 300, Raina's car
The amount of gas remaining is when the graphs intersect.Since the graph for Leila's car is higher than the graph for Raina's car before 300 miles, Raina's car will have less gas.(a) Leila's car, 2 gallons At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas.
(b) 300, Raina's car The amount of gas remaining is when the graphs intersect.
What's the graph about?(a) At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas. This can be seen by looking at the graph of the two cars' gas levels. The graph for Leila's car is higher than the graph for Raina's car at this point, so Leila's car has more gas.
(b) The amount of gas remaining is when the graphs intersect. This happens at 300 miles. Since the graph for Leila's car is higher than the graph for Raina's car before 300 miles, Raina's car will have less gas at this point.
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PLS HELP ASAP WILL GIVE BRAINLIST
Answers
The angles in the parallelogram is as follows:
a = 27°b = 55°c = 55°How to find angles in a parallelogram?A parallelogram is a quadrilateral with opposite sides equal to each other and opposite side parallel to each other.
The diagonal of a parallelogram bisect each other.
Therefore, the angles a, b and c in the parallelogram can be found as follows:
180 - 118 - 35 = a (sum of angles in a triangle)
180 - 153 = a
a = 27 degrees.
Therefore, let's find angle b.
62 + 63 + b = 180 (sum of angles in a triangle)
125 + b = 180
180 - 125 = b
b = 55 degrees
Let's find the angle c
Hence,
b = c (alternate angles)
Therefore,
c = 55 degrees.
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Please help with this problem
Answers
Answer:
The answer is I think 16
Step-by-step explanation:
You can look at the figure beside andfind this answer
Hey there Ms or Mr, could you please help me out with this problem? Just a head up, this my homework for today not a quiz. it's about Trapezoids.
Answers
We have to relate the angles of the trapezoid in order to find the measure of BAD.
Given:
[tex]\begin{gathered} AB\mleft\Vert DC\mright? \\ AD\cong BC \end{gathered}[/tex]Then
[tex]\begin{gathered} \angle BAD\cong\angle ABC \\ \angle ADC\cong\angle BCD \end{gathered}[/tex]The angles are congruent because if AD and BC are congruent, and the lines are parallel, they sides will form the same angles.
Also, as the segment AD is "cut" by two parallel lines, the angles BAD and ADC are consecutive interior angles and are, therefore, supplementary.
Then, we can write:
[tex]\begin{gathered} m\angle BAD+m\angle ADC=180\degree\text{ and }\angle ADC=\angle BCD \\ \Rightarrow m\angle BAD+m\angle BCD=180\degree \\ 2x+(3x-5)=180 \\ 5x-5=180 \\ 5x=180+5 \\ 5x=185 \\ x=\frac{185}{5} \\ x=37 \end{gathered}[/tex]Now, with the value of x, we can calculate the measure of BAD as:
[tex]m\angle BAD=2x=2\cdot37=74\degree[/tex]Answer: the measure of BAD is 74°.
#8.Verify algebraically if the function is even, odd, or neither
Answers
g(x)= x^4 √(1+x)
g(-x) = (-x)^4 √1-x
g (-x) = x^4 √1-x
Since the obtained function is not the same or the opposite it is neither.
how many 4 letter code words can be made using the letters in the word pencil
Answers
Combination is a way of selecting items from a collection where the order of selection does not matter.
The number of 4-letter code words that can be made using the letters in the word pencil is 15.
What is combination?Combination is a way of selecting items from a collection where the order of selection does not matter.
We have,
Total number of letters in the word pencil = 6
i,e P E N C I L
Combination formula:
[tex]^nC_r[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
Here,
n = 6
r = 4
The number of 4-letter code words that can be made using the letters in the word pencil:
[tex]^6C_4[/tex] = 6! / 4! 2! = (6 x 5) / 2= 15
Thus,
The number of 4-letter code words that can be made using the letters in the word pencil is 15.
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First person to help gets brainliest!!
Answers
The value of x from the equation represented by the given bar diagram is 20.
The equation is represented using the bar diagram and from the bar diagram be can observe that the equation will be the following equation mentioned below:
3.5 x + 12.5 x = 320 equation 1
The bar diagram represents 3.5 x + 12.5 x = 320 equation. Now we will simplify this equation and will find the value of x from this equation. The steps that need to be followed to simplify this equation are shown below;
3.5 x + 12.5 x = 320
16 x = 320
Divide both sides of equation by 16 , we will get
x = 320/16
x = 20
The value of x from the equation 3.5 x + 12.5 x = 320 is 20.
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I want answer. I need t’s solution.And I want explanation too.
Answers
we have the equation
[tex]log(\frac{1,000}{253.95})=12tlog(1+\frac{0.08}{12})[/tex]Solve for t
That means
Isolate the variable t
[tex]t=\frac{log(\frac{1,000}{253.95})}{12log(1+\frac{0.08}{12})}[/tex][tex]t=17.2[/tex]Suppose that Kevin's checking account shows a balance of $910.25 at the beginning of the month. During this month, he makes deposits of $175.35, $472.25, $235.40, and $450.15, and he writes checks for $307.50, $289.25, $150.30, and $327.00. Find the end-of-the-month balance in his account.
Answers
Answer:
The answer is $1,169.35
Step-by-step explanation:
Deposits is when you put money into your account, so, you'll add what he deposits. which will be $2,242.4, Next when he writes a check it means he took money out of his account so you'll subtract. You'll add up the amount of checks he wrote and subtract your answer with the deposits so, $2,243.4, - $1,074.05 = 1,169.35 and thats how you get your answer.
How many pairs of parallel edges are there this rectangular prism
Answers
Answer:
6 i think
Step-by-step explanation:
if you count the top and bottom one, thats 2, the two sides, and the front and back. add 2+2+2 which is 6.
I'll give brainliest!!
Answers
2. Y of the power of 4
3.Y of the power of 9
4.Y of the power of 6
P = 1,000 m
X =
x m
150 m width
Answers
Answer:tiny bit confused what the question is asking
length=350
Step-by-step explanation:
perimeter =(length+width )x2
perimeter/2
1000/2=(length+width )
500=(length+width)
500-150=350length
Nakeisha needs to order some new supplies for the restaurant where she works. The restaurant needs at least 566 forks. There are currently 188 forks. If each set on sale contains 8 forks, which inequality can be used to determine xx, the minimum number of sets of forks Nakeisha should buy?
Answers
The inequality that can be used to determine the minimum number of set of forks Nakeisha should buy is xx ≥ (566 - 188) / 8.
What is the minimum set of forks she should buy?The first step is to determine the appropriate inequality signs that can be used.
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is ≥.
The form of the inequality is: xx ≥ (least number of forks needed - forks they current have) / number of forks in one set
xx ≥ (566 - 188) / 8
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Answer:
566 < 188 + 8x
Step-by-step explanation:
confused on this please help!!
Answers
Answer:
12.75
Step-by-step explanation:
it is the same as the other side just like the similar triangle is.
the three sided lengths are 7,8,9 classify the triangle as an acute obtuse or right triangle
Answers
Using the law of cosines to find m∠B:
[tex]\begin{gathered} b^2=a^2+c^2-2ac\cdot\cos (B) \\ 2ac\cdot\cos (B)=a^2+c^2-b^2 \\ \cos (B)=\frac{a^2+c^2-b^2}{2ac} \\ \cos (B)=\frac{8^2+7^2-9^2}{2\cdot8\cdot7} \\ \cos (B)=\frac{32}{112} \\ B=\arccos (\frac{32}{112}) \\ B=73.4\text{ \degree} \end{gathered}[/tex]Since B is the largest angle (because it's opposite to the longer side), then angles A and C are smaller. In consequence, the three angles are smaller than 90°, which means that the triangle is acute
What is a(b(x)) if a(x) = 3x 2 and g(x) = -3x + 1?
Answers
The equivalent composite function is expressed as -9x + 5
Composite functionsComposite functions are also known as function of a function.
Given the following functions:
a(x) = 3x+2 and
b(x) = -3x + 1
Determine the value of a(b(x))
a(b(x)) = a(-3x+1)
a(b(x)) = 3(-3x+1) + 2
a(b(x)) = -9x + 3 + 2
a(b(x)) = -9x + 5
This gives the equivalent composite function.
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Can you help me find the slope, y-intercept, and the equation based off this chart?
Answers
y-interceptis As given by the question
There are given that the value of x and y.
Now,
For finding the value of the slope, choose two-point from the given table
So,
Suppose the two points are:
[tex](1,\text{ 5) and (}3,\text{ 3)}[/tex]Now,
From the formula of slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=1,y_1=5,x_2=3,y_2=3[/tex]Put all the above value into the given formula
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3_{}-5_{}}{3_{}-1_{}} \\ m=-\frac{2}{2} \\ m=-1 \end{gathered}[/tex]Hence, the value of the slope is -1.
Now,
For the equation of the line that is based on the given chart, use two supposes point and the given slope.
So,
The two poin and slope is:
[tex](1,\text{ 5) and (3, 3) and m=-1}[/tex]Then,
From the formula of two point form;
[tex](y-y_1)=m(x-x_1)[/tex]Where,
[tex]x_1=1,y_1=5,x_2=3,y_2=3,\text{ m=-1}[/tex]Then,
Put all the given value into the above formula
So,
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ (y-5_{})=-1(x-1_{}) \\ (y-5)=-x+1 \\ y-5+x-1=0 \\ y+x-6=0 \end{gathered}[/tex]Hence, the equation of the line is:
[tex]y=-x+6[/tex]Now,
To find the y-intercept, put x=0 and solve for x
So,
The y intercept of the given equation is:
[tex]\begin{gathered} y=-x+6 \\ y=-(0)+6 \\ y=6 \end{gathered}[/tex]Hence, the y-intercept is (0, 6)
Which of the following is the equation that represents the graph?
Graph of a line the passes through the points negative 3 comma 0 and 0 comma negative 2.
y equals negative two thirds times x minus 3
y equals negative three halves times x minus 2
y equals negative three halves times x minus 3
y equals negative two thirds times x minus 2
Answers
y equals negative two thirds times x minus 2 is the equation of graph.
What is slope of line?The slope of the line is the ratio of the rise to the run, or rise divided by the run.
The given two points are 3 comma 0 and 0 comma negative 2.
i.e (3,0)(0,-2)1)
The formula for slope is (y₂-y₁)/(x₂-x₁)
slope = (-2 - 0) / (0 - 3)
= -2 / -3
The negative negative are multiplied we get positive
= 2/3
The standard form of a line is y = mx + b, where m is slope of line and b is y intercept.
slope(m) = 2/3
We can use either of points (0,-2)...x = 0 and y = -2
now sub and find b, then y intercept
-2 = 2/3(0) + b
-2 = b
so equation is : y = 2/3x - 2
Hence y equals negative two thirds times x minus 2 is the equation of graph.
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negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
Answers
The Simplification of the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths is "negative 43 over 24 times j plus negative 1 over 12". option D
The expression which is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is −19.5b − 6.9. option c
Simplification of fractionnegative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
= -1/8j + 2/3 - (5/3j + 9/12)
= -1/8j + 2/3 - 5/3j - 9/12
= -1/8j - 5/3j + (2/3 - 9/12)
= (-3j-40j / 24 + (8-9) / 12
= -43/24j + (-1)/12
The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)
open parenthesis= -13.5b - 6.3 - 6b - 0.6
collect like terms= -13.5b - 6b - 6.3 - 0.6
= - 19.5b - 6.9
So therefore, the equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9
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Please help I will mark branlist
Answers
Answer: True
Step-by-step explanation:
I believe it's true since a quadratic equation can either have one real solution, two real solutions, or no real solutions. Hope this helps.
|-102.06|
Find the absolute value
Answers
Answer:
102.06
Step-by-step explanation:
Absolute values are always positive
Answer:
Step-by-step explanation:
102.06
Absolute value is just the positive of any value.
Hope this helps! Have a nice day!
The graphs below have the same shape. f(x) = x2What is the equation of the graph of g(x)?10g(x)f(x)X10510-10O A. g(x) = (x+3)2B. g(x) = (x - 3)2C. g(x) = x2 - 3D. g(x) = x2 + 3
Answers
The equation of f(x) is
[tex]f(x)=x^2[/tex]The graph of g(x) is shifted 3 units to the left. This is a horizontal translation.
For horizontal translation, we follow the following rule >>>
Let parent function be f(x), then
• f(x+a) is the parent translated "a" units left
,• f(x-a) is the parent translated "a" units right
Thus, following the rule, we can clearly say that g(x) = f(x+3)
We can write >>
A particle moves along the x-axis so that at time t\ge 0t≥0 its velocity is given by v(t)=3t^2-18t+15.v(t)=3t2−18t+15. Determine all values of tt when the particle is at rest.
Answers
When a particle is at rest, the velocity = 0. Therefore, we equate the v(t) term to zero (0)
[tex]undefined[/tex]Simplify using exponent: B³ x B⁵
HELPPPPPP
Answers
Answer:
B⁸
Step-by-step explanation:
When you have the same base, which in this case is B, you add the exponents and you get 8.
Hope this helps!
P.S, could I get Brainliest? Thanks!
If a1 = 7 and an3an-1 + 4 then find the value of a4.
Answers
A1 = 7
An = 3A(n-1) + 4. According to this, A2 would be= 3*7 + 4 =25
A1 = 7, A2 = 25, then the difference is d = 18
The general formula for an aritmethic progression is An = A1 + (n -1)d
For A4 = 7 + (4-1)*18 = 61
Central Bank pays 8.5% interest, compounded daily, from the date of deposit to the date of withdrawal. The daily interest rate (to the nearest millionths place) forJuly 28 (92 days in the quarter) on this account is:0.000198.0.0002070.000231.0.000216None of these choices are correct.
Answers
ofGiven the yearly interest rate as 8.5%
To find the daily interest, we will divide the yearly interest rate by 365 as shown below:
[tex]\text{daily interest rate=}\frac{yearly\text{ interest rate}}{365}[/tex][tex]\text{daily interest rate=}\frac{\frac{8.5}{100}}{365}=\frac{0.085}{365}=0.0002328767[/tex]Hence, the daily interest rate (to the nearest millionths place)= 0.000232, The third option