A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
Enter your answer in the box.
ft²
Answers
y------> the length of the rectangle
x-----> the width of the rectangle
we know that
perimeter of the rectangle=2*[x+y]
Since the barn is used as one of the sides (let's say y) we can subtract y
we don't need fencing for this side
That makes the perimeter 2x + y
Since we have 300 feet of fencing
we set these equal:
2x + y = 300-------> y=(300-2x)------> equation 1
area of the rectangle=x*y
substitute the equation 1 in the area formula
Area=[(300-2x)]*x-----> Area=(-2x²)+300x
This is a quadratic equation
Since the leading coefficient is negative (-2) we know it opens downward
We are looking for the x-coordinate of the highest point called the vertex
using a graph tool
see the attached figure
the vertex is the point (75,11250)
that means for x=75 (width of the rectangle)
the area is 11250 ft²
the answer is
the maximum area that can be enclosed by the fencing is 11250 ft²
Answer:
The Answer is 11250 ft~
Step-by-step explanation:
I did the test and got it correct
Related Questions
what are the properties of real numbers?
Answers
Final answer:
The properties of real numbers include closure, commutative, associative, identity, and inverse properties. These properties govern how real numbers behave in addition and multiplication operations.
Explanation:
The properties of real numbers refer to the characteristics and behavior of numbers that belong to the real number system. The real number system includes all rational and irrational numbers, such as whole numbers, integers, fractions, decimals, and square roots.
The properties of real numbers include:
Closure property: The sum or product of any two real numbers is also a real number. For example, the sum of 3.14 and 4 is 7.14, which is a real number.Commutative property: The order of addition or multiplication does not affect the result. For example, 2 + 3 is equal to 3 + 2, and 2 × 3 is equal to 3 × 2.Associative property: The grouping of real numbers in addition or multiplication does not affect the result. For example, (2 + 3) + 4 is equal to 2 + (3 + 4), and (2 × 3) × 4 is equal to 2 × (3 × 4).Identity property: The sum of a real number and zero is equal to the number itself. For example, 2 + 0 is equal to 2. The product of a real number and one is equal to the number itself. For example, 3 × 1 is equal to 3.Inverse property: Every real number has an additive inverse and a multiplicative inverse. The additive inverse of a real number is the number that, when added, gives zero as the result. For example, the additive inverse of 5 is -5, as 5 + (-5) = 0. The multiplicative inverse of a non-zero real number is the number that, when multiplied, gives one as the result. For example, the multiplicative inverse of 2 is 1/2, as 2 × (1/2) = 1.These properties of real numbers are fundamental in algebraic operations and calculations. They provide a basis for solving equations, simplifying expressions, and working with mathematical concepts.
What is the projection of (3,4) onto (3,1)?
Answers
= 13/10 · (3, 1)
= (3.9, 1.3)
the answer can also be written as 1.3(3,1)
Input in standard form the equation of the given line. The line with m=1/2 and b=3
Answers
You are given a slope of m = 1/2 and b = 3. Note that m is used in the slope intercept form of a line, so let's first express this using slope intercept form of for a line, which is y = mx + b.
Plugging in given values you get
y = (1/2)x + 3.
Standard form requires coefficients to be integers, so multiply both sides by 2 to get rid of the fraction.
2y = x + 6
Finally reorder the terms. Subtract both sides by 2y then subtract both sides by 6.
x - 2y = -6
Final answer:
To find the equation of a line with a given slope and y-intercept in standard form, substitute the values of the slope and y-intercept into the equation y = mx + b.
Explanation:
To write the equation of a line given the slope m and y-intercept b in standard form y = mx + b, you can directly substitute the values of m = 1/2 and b = 3 into the equation.
Substitute m = 1/2 and b = 3 into y = mx + b: y = (1/2)x + 3
Therefore, the equation of the line in standard form is y = (1/2)x + 3.
hepppppppppppppppppppppppppppppp
Answers
x= (-b +- √(b²-4ac) )/2a
Filling a, b and c in yields
x = (8 +- √(64-164) ) / 2 =>
x = (8 - √-100)/2 or x = (4 + √-100)/2
Well, √-100 = 10i, so then you simplify to the last answer, D:
x = 4-5i or x=4+5i
Answer:
D
Step-by-step explanation:
Evaluate faith’s check register
Answers
What is the discriminant D of the equation?
a^2-2a+5=0
Enter your answer:
D=___
Please help! Thank you to who knows how to do this. You WILL be rewarded.
Answers
[tex]D={b}^{2}-4ac[/tex]
First, find a, b and c
The standard form of a quadratic function is:
[tex]f(x) = {ax}^{2} + bx + c[/tex]
So if we look at the formula we get:
[tex]a = 1[/tex]
[tex]b = - 2[/tex]
[tex]c = 5[/tex]
Then, insert them into the formula:
[tex]( { - 2}^{2} ) - 4 \times 1\times 5[/tex]
[tex]D=4-20[/tex]
So the dicriminant is:
D = -16
Meaning that the graph of the function has no roots (zeroes).
I added more CORRECT answers for everybody. Your answer is in the last pic.
The 1997 value of an object was $9500. In 2012, it was worth $5000. The annual percent of decay has been constant. What is the annual percent of decay? A) 1.19% B) 2.19% C) 3.19% D) 4.19%
Answers
A prism is completely filled with 1120 cubes that have edge lengths of 1/2 in. What is the volume of the prism? Enter your answer in the box. in³
Answers
V = 1/2 * 1/2 * 1/2
V = 1/8 cu in
There are 1120 of these cubes so the volume of the prism is 1/8 * 1120 = 140 cubic inches.
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Answers
We have then:
x ^ 2 + 10x + 12 = 36
Rewriting:
x ^ 2 + 10x-24 = 0
The roots for this case are:
x1 = 2
x2 = -12
Answer:
The roots of the polynomial are:
x1 = 2
x2 = -12
What is the sum of (7x-6y) and (x+y)
Answers
7x-6y+x+y
8x-5y
(Remember that x=1x and y=1y)
What is the 32nd term of the arithmetic sequence -12 -7?
Answers
The answer is a₃₂=143
A circle has an area of 40 square meters. Which answer is closest to the measure of its diameter?
A.1.8 meters
B.4 meters
C.3.6 meters
D.7.1
Answers
A circle has an area of 40 square meters. Which answer is closest to the measure of its diameter?
Answer:
Option D. [tex]7.1\ m[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
In this problem we have
[tex]A=40\ m^{2}[/tex]
substitute and solve for r
[tex]40=\pi r^{2}[/tex]
[tex]r^{2}=40/( \pi)[/tex]
[tex]r=3.57\ m[/tex]
Multiply the radius by [tex]2[/tex] to obtain the diameter
so
[tex]3.57*2=7.14\ m[/tex]
Which of the following units represents the surface area of a solid?
inches
square inches
cubic inches
quartic inches
Answers
Answer:
Option B is correct.
Step-by-step explanation:
We are given units.
we have to find unit that represents the surface area of a solid.
We know that unit of area is square unit.
⇒ Unit for surface area is also square unit.
inches is a unit of a length.
square inches is unit of area
cubic inches is unit of volume
quadratic inches does not exist as unit.
Therefore, Option B is correct.
If you double Lucien’s age and then subtract 6, you get Paul’s age. 2 years ago the sum of their ages was 29. How old is each person?
Answers
Answer:
Step-by-step explanation:
Find the volume of a box that will hold nine 9.425 cm3 cylindrical containers that each measure 3 centimeters long. (round to nearest whole number)
Answers
Final Answer:
The volume of the box that will hold nine 9.425 cm³ cylindrical containers, each measuring 3 centimeters long, is approximately 108 cm³.
Explanation:
First, we need to find the radius of each cylindrical container since we have its volume and the length. The volume V of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where r is the radius and h is the height (or length) of the cylinder. We are given:
[tex]\[ V = 9.425 \text{ cm}^3 \\\\\[ h = 3 \text{ cm} \][/tex]
We need to solve for r:
[tex]\[ 9.425 = \pi r^2 (3) \\\\\[ r^2 = \frac{9.425}{3\pi} \\\\\[ r^2 = \frac{9.425}{3 \times 3.14159} \\\\\[ r^2 = \frac{9.425}{9.42477} \\\\\[ r^2 \approx 1 \\\\\[ r \approx 1 \text{ cm} \][/tex]
Now we know the radius of one cylindrical container is approximately 1 cm. Although this rounding might lead to a slightly inaccurate result, we'll proceed with this approximation for simplicity's sake.
Since each container is a cylinder with a radius of 1 cm, the diameter of each container is [tex]\( 2 \times 1 = 2 \)[/tex] cm. If we wanted to pack these containers without any wasted space in one layer, we would arrange them in a 3 by 3 grid, given there are 9 containers. The length and the width of the box would then each be 3 times the diameter of one container.
Hence:
Length of box = Width of box = [tex]\( 3 \times 2 \)[/tex] cm = 6 cm.
The height of the box would be equal to the length of one of the containers, which is 3 cm.
Now we can find the volume of the box:
Volume of box [tex]\( V_{\text{box}} \) = Length \( \times \) Width \( \times \) Height[/tex]
[tex]\[ V_{\text{box}} = 6 \text{ cm} \times 6 \text{ cm} \times 3 \text{ cm} \\\\\[ V_{\text{box}} = 36 \text{ cm}^2 \times 3 \text{ cm} \\\\\[ V_{\text{box}} = 108 \text{ cm}^3 \][/tex]
Rounding to the nearest whole number, the volume of the box that will hold nine 9.425 cm³ cylindrical containers, each measuring 3 centimeters long, is approximately 108 cm³.
A) Inverse Property of Multiplication
B) Commutative Property of Addition
C) Commutative Property of Multiplication
D) Associative Property of Addition
Answers
This is the Commutative property of multiplication, which states that two numbers can be multiplied in any order to create the same number.
That tells us that when we're multiplying, it gives us the same value when you multiply two numbers in different orders. Just like here, we have the same numbers, -7/8 and 10, but the difference is they're in different orders, they mean the same thing. For example:
4 *5 = 5* 4
Keep in mind that it doesn't always work with other operations. Observe:
4-5 ≠ 5-1
Also,
4/5 ≠ 5/4
Commutative doesn't work in subtraction and division, only multiplication and adding.
Hope this helps!
What is an equivalent expression to 4+3(5+x)
Answers
Tim's age is two thirds of sara's age. sara's age is three fifths of mark's age. mark is 9 years older than tim. how old is sara? answer
Answers
T = 2/3S
S = 3/5M, M = 5/3S
M - 9 = T
5/3S - 9 = 2/3S
S = 9
Use the image
A) 6
B) 36
C) –6
D) –36
Please explain your answers.
Thanks! : )
Answers
How many x intercepts appear on the graph of this polynomial function?
Answers
For this case what we can do is graph the function and see the behavior of it.
We have then that the function grows upwards (see attached image)
It has two cutting points with the x axis in:
x = 0
x = 1
Therefore, the other roots of the polynomial are imaginary.
Answer:
2 x intercepts appear on the graph of this polynomial function
Answer:
B) 2 x-intercepts
Rachel pays $131.44 for a desk, including tax. The task is 31 cents less than 1*16 the desk’s price. What is the price for the desk before adding the tax?
Answers
Answer:
The cost of the desk is 124 dollars.
Step-by-step explanation:
irst, change this into an equation
tax=1/16x-.31
x equals the cost of the desk without tax:
x+tax=131.44
tax=131.44-x
Set the first equation equal to the second:
1/16x-.31=131.44-x
Solve for x:
17/16x=131.75
x=$124
Hope that helps
The equivalent percentage value for the decimal number 1.16 is 116% which is obtained by multiplying the decimal by 100. Before including the tax the price of the desk was $60.99.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
And to convert a fraction or a decimal into percentage, they are multiplied by 100.
Given that,
The amount paid by Rachel for a desk is $131.44.
Suppose the price of desk is before adding the tax is x.
Then, as per the problem the following expression can be written for the tax amount as,
1.16x - 0.31
Now, the expression for the price of desk after tax is,
x + 1.16x - 0.31 = 131.44
⇒ 2.16x = 131.44 + 0.31
⇒ 2.16x = 131.75
⇒ x = 131.75 / 2.16
⇒ x = 60.99
Hence, the price for the desk before adding the tax is $60.99.
To know more about percentage click on,
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If apples are on sale at 15 for $3, what’s the cost of each apple?
A. 50 cents
B. 25 cents
C. 20 cents
D. 30 cents
(I answered A originally but It was wrong. Please explain why it was wrong, do I need to put the decimals down? I'm really bad at this please help me! Thank you.
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Answers
3/15 is 0.20
That is 20 cents
Your answer is C.)
Hope this helps
The cost of each apple will be 20 cents per apple. Then the correct option is C.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Conversion means to convert the same thing into different units.
If apples are on sale at 15 for $3.
We know that $1 = 100 cents
Then the number of the cents in 3 dollars will be
⇒ 3 x 100
⇒ 300 cents
Then the cost of each apple will be the ratio of the 300 cents and 15 apple.
⇒ 300 / 15
⇒ 20 cents per apple
Thus, the cost of each apple will be 20 cents per apple.
Then the correct option is C.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
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Answers
θ has a 60-degree reference angle and is located in quadrant II or IV
Explanation:
First, we will get the reference angle:
√3 / 3 is equivalent to 1/√3
This means that the reference angle for θ is 60
Second, we will locate the quadrant:
Based on the ASTC rule, the tan is positive in the first and third quadrants.
Since the given value is negative, therefore, θ is located in either the second or fourth quadrant
Hope this helps :)
Tan30 = - (1/2) / (root (3) / 2)
Tan30 = - (root (3)) / (3)
The tangent is positive in the first quadrant and in the third quadrant.
Therefore the answer is:
Angle 60 in quadrants II and IV
Answer:
Angle 60 in quadrants II and IV
option 3.
Which of the following are opposite rays?
A. TV and TS
B. TX and TL
C. TS and TX
D. TL and TV
Answers
The correct answer is:
B. TX and TL
Explanation:
Opposite rays are rays that have the same endpoint and extend in opposite directions. The ones in the diagram that fit this description are TX and TL.
Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline. Annabella can express her average cost per gallon of gasoline as 2.25x+2.15(x+5)/2x+5 .
Answers
Answer:
THE NUMERATOR OF THE RATIONAL EXPRESSION REPRESENTS THE TOTAL COST OF GASOLINE PURCHASED.
THE DENOMINATOR OF THE RATIONAL EXPRESSION REPRESENTS THE TOTAL GALLONS OF GASOLINE PURCHASED
The complete problem is:
Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline.
Annabella can express her average cost per gallon of gasoline as [tex]y = \frac{(2.25x + 2.15(x+5))}{2x+5}[/tex]
What is the meaning of the parts of this rational expression in the context of the situation?
THE NUMERATOR OF THE RATIONAL EXPRESSION REPRESENTS THE __________.
(select one)
1. total cost of the gasoline purchased
2. total number of gallons of gasoline purchased
3. cost per gallon of gasoline
THE DENOMINATOR OF THE RATIONAL EXPRESSION REPRESENTS THE ________.
1. total cost of the gasoline purchased
2. total number of gallons of gasoline purchased
3. cost per gallon of gasoline
So, in this context and based on the given data, the numerator of the expression is referring to the total cost of gasoline purchased, and the denominator is expressing the total gallons of gasoline purchased.
You can deduct this because, the numerator contains the amounts of costs per gallon, being x gallons. On the other hand, you can see in the denominator that there's no costs multiplying the variable, it's just a quantity which refers to the amount of gasoline, not the cost.
What is the approximate area of the shaded sector in the circle shown below?
Answers
Answer:
Correct option is B.
Step-by-step explanation:
Given the radius of circle and the angle in sector we have to find the area of shaded region i.e minor sector.
[tex]Radius=r=16 in.[/tex]
[tex]Angle=\theta=110^{\circ}[/tex]
[tex]Area of sector=}\frac{\theta}{360}\times\pi r^2[/tex]
[tex]=\frac{110}{360}\times\frac{22}{7}\times(16)^2[/tex]
[tex]=\frac{11}{36}\times \frac{22}{7}\times 16\times 16=245.841=246(approx.)[/tex]
∴ Area of sector is [tex]246in^2[/tex]
Correct option is B.
Answer:B
Step-by-step explanation:
NICE
Match the systems of equations to their solutions. Tiles 2x + y = 12 x = 9 − 2y x + 2y = 9 2x + 4y = 20 x + 3y = 16 2x − y = 11 y = 11 − 2x 4x − 3y = -13 y = 10 + x -3x + 3y = 30 2x + y = 11 x − 2y = -7 Pairs x = 2, y = 7 arrowBoth x = 5, y = 2 arrowBoth x = 3, y = 5 arrowBoth x = 7, y = 3 arrowBoth
Answers
1) systems of equations 1
2x + y = 12
x = 9 − 2y
using a graph tool
see the attached figure
the solution is the point ------------> (5,2)
2) systems of equations 2
x + 2y = 9
2x + 4y = 20
using a graph tool
see the attached figure
the solution is the point -------> has no solution the two lines are parallel
3) systems of equations 3
x + 3y = 16
2x − y = 11
using a graph tool
see the attached figure
the solution is the point ------------> (7,3)
4) systems of equations 4
y = 11 − 2x
4x − 3y = -13
using a graph tool
see the attached figure
the solution is the point ------------> (2,7)
5) systems of equations 5
y = 10 + x -----------> multiplying by 3-----> 3y=30+3x------> -3x + 3y = 30
-3x + 3y = 30
equation 1 and equation 2 are equals--------> the system has no solution
6) systems of equations 6
2x + y = 11
x − 2y = -7
using a graph tool
see the attached figure
the solution is the point ------------> (3,5)
a rope is sq rt. 250 units long. If cut into 2 pieces so that the lengths of the pieces are in the ratio of 3:2 what is the length of longer piecein simplest radical form? 3:2 =5/3(?) Do i set x/sq.rt.250=5/3? I end up with 25 sq rt. 10/3. This isn't correct.
Answers
Let 3x = the length of the first rope
2x = the length of the second rope
This representation is based on the given that the ratio of the two ropes is 3:2.
3x + 2x = sq rt. 250
5x = sq rt. 250
x = sq rt. 250 / 5
x = sq rt. 25(10) / 5
x = 5 sq rt. 10 /5
The five would be cancelled resulting to:
x =sq rt. 10
Finish the steps below to write a quadratic function for the parabola shown. Use the vertex form, f(x) = a(x – h)2 + k, and substitute in the values for h and k. f(x) = a(x – 5)2 + 3 Use another point and substitute in values for x and f(x). Solve for a. 5 = a(6 – 5)2 + 3 Write the function, using the values for h, k, and a. The function is f(x) = (x – )2 + .
Answers
f(x) = a(x – h)² + k
we know the vertex v(5,3)
substitute in the values for h and k
f(x) = a(x – 5)² + 3
Use another point and substitute in values for x and f(x).
for the point (6,5)
Solve for a.
5 = a(6 – 5)2 + 3-------------- > 5=a+3-------------> a=2
The function is f(x)=a(x – h)2 + k-------- > 2(x – 5)² + 3
f(x)= 2(x – 5)² + 3-------- > 2[x²-10x+25]+3=2x²-20x+50+3=2x²-20x+53
f(x)=2x²-20x+53
the answer is f(x)= 2(x – 5)² + 3----------------- > (f(x)=2x²-20x+53)
Here we want to write the quadratic function for the parabola shown in vertex form.
We will get the function: f(x) = 2*(x - 5)^2 + 3
So the general function of a parabola with vertex (h, k) and leading coefficient a is:
f(x) = a*(x - h)^2 + k
Here, we know the formula:
f(x) = a*(x - 5)^2 + 3
where:
h = 5k = 3So the vertex is the point (5, 3), and we only must find the value of a to completely determine the parabola's function
We also know that:
f(6) = 5
So we can solve:
5 = a*(6 - 5)^2 + 3
5 = a*(1)^2 + 3
5 = a + 3
5 - 3 = a = 2
So we just found the value of a, replacing this on the parabola's function we get:
f(x) = 2*(x - 5)^2 + 3
If you want to learn more about parabolas, you can read:
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Write an expression to represent: One more than the quotient of a number x and 4.
Answers
9514 1404 393
Answer:
x/4 +1
Step-by-step explanation:
The quotient of a number (x) and 4 is written ...
x/4
One more than that is ...
x/4 +1