Answer
Maximum area A_max = 11250 ft^2
Step-by-Step Explanation
Declaring Variables:-
The length of the rectangle = y
The width of the rectangle = x
Solution:-
- The perimeter of a rectangle can be expressed using the above two variables as follows:
Perimeter (P) = 2*Length + 2*Width
= 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. The length of the fence required L is:
Length (L) = P - y
= 2*x + y
- We are given 300 feet of fencing. So we equate the length equal to 300 and develop a linear relationship between width and length of the barn.
300 = 2x + y
y = 300 - 2x
- The area (A) of the rectangle is given by the following expression:
A = Length*width
A = x*y
- Substitute the relationship developed between x and y in the Area (A) expression above. Then we have:
A = x*(300 - 2x)
A = 300x - 2x^2
- We will take first derivative of the expression of area (A) developed with respect to x and find the critical point of the area function by setting the first derivative A'(x) = 0.
A(x) = 300x - 2x^2
A'(x) = 300 - 4x
0 = 300-4x
x = 300 / 4 = 75 ft
- The critical point of the given function lies for the width (x) of 75 ft. We will plug in the critical value x = 75 ft back into the original function of Area and find the maximum area.
A(x) = 300x - 2x^2
A(75) = 300 (75) - 2(75)^2
A_max = A(75) = 11250 ft^2
- The maximum area that can be enclosed by the fencing is 11250 ft²
Answer:11250
Step-by-step explanation:
If the radius of a circle is 14 ft, then the diameter of the circle is _____.
A.) 7 ft
B.) 28 ft
C.) 42 ft
D.) 87.92 ft
A clown needed 275 balloons for a party he was going to, but the balloons only came in packs of 2.How many packs of balloons does he need to buy?
Final answer:
To provide 275 balloons when they are sold in packs of 2, the clown will need to purchase 138 packs, which will include one extra balloon as you cannot buy half a pack.
Explanation:
The clown needs 275 balloons for a party and they come in packs of 2. To find out how many packs of balloons the clown needs to buy, one must divide the total number of balloons by the number in each pack.
The calculation is as follows:
Number of packs = Total balloons ÷ Balloons per packNumber of packs = 275 ÷ 2Number of packs = 137.5Since packs cannot be purchased in halves, the clown will need to buy 138 packs to have enough balloons, understanding that this means having one extra balloon.
which of the following is a radical equation? 1. x+sqrt(5)=12 2. x^2=16 3. 3+xsqrt(7)=13 4. 7sqrt(x)=14
Answer:
4. [tex]7\sqrt{x}=14[/tex]
Step-by-step explanation:
Radical equation is a equation that has a variable under the radical .
From the given options we have radical square root
We need to choose an option that has a variable under the square root.
1.[tex]x+\sqrt{5}=12[/tex]
This equation has 5 under the radical square root. Variable is outside, So this is not a radical equation.
2. x^2=16
Here there is not radical . So this is not a radical equation.
3. [tex]3+x\sqrt{7}=13[/tex]
This equation has 7 under the radical square root. Variable is outside, So this is not a radical equation.
4. [tex]7\sqrt{x}=14[/tex]
This equation has x under the radical square root. So this is a radical equation.
Find 5% of $43.79. $218.95 $2.19 $21.90 $2,189.50
There are 8 hamsters at crazy Pete pet shop that are completely brown the rest of the hamsters at the shop are mixed colors that ate brown hamsters represent 2/5 of the total Number of hamsters at the pet shop right and solve an equation using the variable H to find the total number of hamsters at the pet shop
The farmer originally planted 15 apple trees.
Let's denote the original number of rows as [tex]\( r \)[/tex] and the original number of columns as [tex]\( c \).[/tex]
In the original arrangement, the total number of trees is [tex]\( r \times c \).[/tex]
If 5 more rows and 3 fewer columns are added, the new number of rows becomes [tex]\( r + 5 \)[/tex] and the new number of columns becomes [tex]\( c - 3 \).[/tex]
According to the given information, the new arrangement has 25 more trees than the original arrangement. So, we can set up the equation:
[tex]\[ (r + 5) \times (c - 3) = r \times c + 25 \][/tex]
Expanding the left side:
[tex]\[ r \times c + 5r - 3c - 15 = r \times c + 25 \][/tex]
Now, let's simplify:
[tex]\[ 5r - 3c - 15 = 25 \][/tex]
[tex]\[ 5r - 3c = 40 \][/tex]
Now, let's solve this equation to find the relationship between [tex]\( r \)[/tex] and [tex]\( c \).[/tex]
Given the information, let's make some assumptions about the number of rows and columns to fit the situation realistically.
Let's start with 1 row and 3 columns ( [tex]\( r = 1, c = 3 \)[/tex] ):
[tex]\[ 5(1) - 3(3) = 5 - 9 = -4 \][/tex]
It doesn't satisfy the condition.
Next, let's try 2 rows and 4 columns ( [tex]\( r = 2, c = 4 \)[/tex] ):
[tex]\[ 5(2) - 3(4) = 10 - 12 = -2 \][/tex]
Still doesn't satisfy the condition.
Next, let's try 3 rows and 5 columns ( [tex]\( r = 3, c = 5 \)[/tex] ):
[tex]\[ 5(3) - 3(5) = 15 - 15 = 0 \][/tex]
This satisfies the condition.
So, the original arrangement had 3 rows and 5 columns, and the total number of trees is [tex]\( 3 \times 5 = 15 \)[/tex].
Dalia is installing a tile floor in a rectangular room. Dalia has 152152152 tiles available to tile the room. If each row requires 9\large\frac{1}{2}9 2 1 9, start fraction, 1, divided by, 2, end fraction tiles, and 191919 tiles break while Dalia is laying the floor, how many full rows of unbroken tile can she install before running out of tiles?
how do you do the elimination method? Example: -8+6y=2;16x-3y= -13
(click on picture to see the full thing)
You are choosing between two different cell phone plans. the first plan charges a rate of 25 cents per minute. the second plan charges a monthly fee of $49.95 plus 10 cents per minute. how many minutes would you have to use in a month in order for the second plan to be preferable
Which economic system is friendliest to entrepreneurs?
a.socialismb.communismc.capitalismd.They are all equally accepting, since entrepreneurship relies on the individual.
Answer:
The answer is capitalism.
Step-by-step explanation:
Capitalism is friendliest to entrepreneurs and market economies also rely on capitalism. This is because capitalism and free enterprise helps to create a marketplace where producers and consumers are free to sell and buy what they choose.
How do you write 50% as a fraction or whole number in simplest form?
please someone help me on this
Brainliest available :)
If the test scores of a class of 36 students have a mean of 75.2 and the test scores of another class of 28 students have a mean of 67.4, then the mean of the combined group is
The mean of the combined group is 71.78.
What is arithmetic mean?Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations.
Let the total sum of the scores of the first class of 36 students be ∑x.
Here, the mean is 75.2 .
⇒ ∑x/36 = 75.2
⇒ ∑x = (75.2)(36)
⇒ ∑x = 2707.2
Also, let the total sum of the scores of the second class of 28 students be ∑y.
Here, the mean is 67.4.
⇒ ∑y/28 = 67.4
⇒ ∑y = (67.4)(28)
⇒ ∑y = 1887.2
The total students in combined group = 36+28 =64
The sum of their scores = ∑x + ∑y = 2707.2 + 1887.2 = 4594.4
The mean of the combined group = (∑x + ∑y)/64
The mean of the combined group = 4594.4/64 = 71.78
Learn more about the arithmetic means here:
brainly.com/question/13000783
#SPJ2
To find the mean of the combined group of two classes, calculate the total sum of scores of each class, combine them, and then divide by the total number of students. The mean of the combined group is approximately 71.8.
Explanation:To calculate the mean of the combined groups of students, you can use the total sum of scores from both classes divided by the total number of students. The first class has 36 students with a mean score of 75.2, and the second class has 28 students with a mean score of 67.4.
First, find the total sum of scores for each class:
Next, combine the total sums and the number of students:
Finally, divide the combined total sum by the combined number of students to find the mean:
Mean of combined group = 4594.4 / 64 = 71.7875
Therefore, the mean of the combined group is approximately 71.8.
Which pair of expressions is equivalent for any variable value greater than zero?
Answer:
D. b+b+3c and 2b+3c
Step-by-step explanation:
The question wants us to find out expressions is equivalent for any variable value greater than zero. So let's analyse all the possible answers to find the correct one.
A. (x+3) and 3x+ 2
If x = 1 , we have:
(x+3) = 4 3x+2 = 5Both of the two sides are not equivalent
B. 4d+2e and 8d+e
If e=1 and d=1, we have:
4d+2e = 88d+e = 9Both of the two sides are not equivalent
C. f+f+f+g and 3fg
If f=1 and g=1, we have:
f+f+f+g = 43fg = 3Both of the two sides are not equivalent
D. b+b+3c and 2b+3c
If b=1 and c=1, we have:
b+b+3c = 52b+3c = 5Both of the two sides are equivalent
Or we will simplify the left side: b+b+3c = 2b+3c, hence 2b+3c = 2b+3c are apparent
So we choose D.
Need help on 8,9,10,11 and 12
What is the sum of −3x+6 and 7x−8 ?
Answer:
-80
Step-by-step explanation:
Help me please !!!!!!!
Sandy is observing the velocity of a runner at different times.
After one hour, the velocity of the runner is 4 km/h. After two hours, the velocity of the runner is 2 km/h. Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times. Show your work and define the variables used. Part B: How can you graph the equations obtained in Part A for the first 4 hours?
Use the given times and velocities to make two points: (1,4) and (2,2)
Part A:
Slope is the change in Y over the change in X from the two pints you made:
Slope = (2-4) / (2-1 )= -2
Now you have the slope, calculate the Y-intercept
y = -2x + b
Using (1,4)
4 = -2(1) + b = 4 =-2 +b. b = 6
Equation is: y = -2x+6
Part B:
using the above equation replace x with 1, 2, 3, and 4 and solve for the Y
then plot those onto a graph
Using graph paper graph the following equation then click on the graph until the correct one is display. 3x-y-1=0
The graph of the equation [tex]3x - y - 1 = 0[/tex] is attached below.
Further explanation:
The linear equation with slope m and intercept c is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Given:
The equation is [tex]3x - y - 1 = 0.[/tex]
Explanation:
The given equation is [tex]3x - y - 1 = 0.[/tex]
Solve the equation to obtain the standard form.
[tex]\begin{aligned}3x - y - 1&= 0\\y&= 3x - 1\\\end{aligned}[/tex]
Compare [tex]y = 3x - 1[/tex] to the standard equation [tex]y= mx + c.[/tex]
The slope of the line is 3 and the y-intercept is -1.
Substitute 0 for [tex]x[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}y &= 3 \times 0 - 1\\y&= 0 - 1\\y&= - 1\\\end{aligned}[/tex]
Substitute 1 for [tex]x[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}y&= 3 \times 1 - 1\\y&= 3 - 1\\y&= 2\\\end{aligned}[/tex]
Substitute 2 for [tex]x[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}y&= 3 \times 2 - 1\\y&= 6 - 1\\y&= 5\\\end{aligned}[/tex]
The graph of the equation [tex]3x - y - 1 = 0[/tex] is attached below.
Learn more:
Learn more about inverse of the function https://brainly.com/question/1632445.Learn more about equation of circle brainly.com/question/1506955.Learn more about range and domain of the function https://brainly.com/question/3412497Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.
Find the dimensions of a rectangle with a perimeter of 72 cm if the length is 8 cm less than three times the width.
The rocks near the shore between two lighthouses at points A and B make the waters unsafe. The measure of arcAXB is 300. Waters inside this arc are unsafe. Suppose you are a navigator on a ship at sea. How can you use the lighthouses to keep the ship in safe waters?
A ship's navigator can keep the ship in safe waters by staying outside the 300-degree arc between two lighthouses and using the beams as navigational guides. Additionally, in areas with water breaks, navigators should account for wave diffraction to determine the safest angles for mooring.
Explanation:To navigate safely and avoid the unsafe waters near the coastline marked by the 300-degree arc between two lighthouses at points A and B, a ship's navigator should use both lighthouses as reference points for establishing a safe navigational path. Typically, lighthouses are equipped with rotating beams, which can serve as a guide to determine a ship's position relative to hazardous areas. If the ship maintains a course outside of the direct line of sight between the two lighthouses, it can stay within the safe waters.
The navigator should also consider wave action when near a coastline or harbor entrance. If any breakwater structure or water break exists, such as a rock barrier with an opening, the navigator would need to be mindful of the wave patterns. As waves enter the opening, they diffract, and boats are generally safest at angles where the wave intensity is minimized.
Given: g ∥ h and ∠2 ≅ ∠3
Prove: e ∥ f
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorme
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?
A. vertical angles theorem
B. alternate exterior angles theorem
C. converse corresponding angles theorem
D. converse alternate interior angles theorem
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
Given: g ∥ h and ∠2 ≅ ∠3
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2.corresponding angles theorem
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. Converse alternate interior angles.
As we know that if alternate angles are equal then two lines would be parallel using converse alternate interior angles.
Hence, Option 'D' is correct.
Answer:
d. converse alternate interior angles theorem
Step-by-step explanation:
If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?
In the proportion a/b = c/d, if this is true then the product of the extremes (a*d) is equal to the product of the means (b*c). Any statement that contradicts this property is considered false.
Explanation:Looking at the given condition, a/b = c/d, it represents a proportion or a statement of equality between two fractions. Within this proportion, `a` and `d` are referred to as the extremes, while `b` and `c` are known as the means.
If the proportion is true, meaning it accurately reflects a relationship of equality between two ratios, several properties become applicable. Importantly, the product of the means equals the product of the extremes. In other words, in a valid proportion, `a*d` is equal to `b*c`.
Consequently, if any statement contradicts these properties, it is false. So, without knowing the specific statements to analyze here, we cannot accurately decide on the false one. Always remember, you need to comply with the stated properties of a proportion in mathematical contexts.
Learn more about Proportions here:https://brainly.com/question/34018947
#SPJ12
The perimeter of a rectangular garden is 102 meters. the length is 6 meters longer than twice the width. find the dimensions of the garden.
Final answer:
The width of the garden is 15 meters and the length is 36 meters.
Explanation:
To solve this problem, we can use the formulas for perimeter and length. Let's assume that the width of the rectangular garden is x.
According to the given information, the length is 6 meters longer than twice the width, so the length can be represented as 2x + 6.
The perimeter is the sum of all four sides of the rectangle, which is given as 102 meters. We can set up the equation:
2(2x + 6) + 2x = 102
Simplifying the equation, we get:
6x + 12 = 102
6x = 90
x = 15
Therefore, the width of the garden is 15 meters and the length is 2(15) + 6 = 36 meters.
The pentagon in Washington DC is immense in size, with each outside wall 921 feet in length. What is the perimeter of the pentagon?
In this box-and-whisker plot, what is the median value of the data?
A. 48
B. 53
C. 56
D. 58
Identify three of the key terms from the video. Check the boxes next to three words.
brain
mouse
consciousness
memory
definition
Answer:
brain
consciousness
memory
Which graph shows a system of equations with a solution at (–1, 1)?
Answer:- The second graph shows a system of equations with a solution at (–1, 1) .
Explanation:-
In the given pictures we have different lines intersecting parabola .
Given point is (-1,1) ,here x coordinate is negative and y coordinate is positive , which happen only in second quadrant of a Cartesian plane.
In graph 1 , there are two intersection points and none of them lie in the second quadrant. In graph 2 , there are two intersection points and one of them lie in the second quadrant and that is (-1,1). Therefore it shows a system of equations with a solution at (–1, 1) .In graph 3 , there are two intersection points and none of them lie in the second quadrant. In graph 4 , there are two intersection points and none of them lie in the second quadrant.Is it possible for a system to have more than one solution? Explain your answer
A rectangular playground is 888 meters wide. It is 333 times as long as it is wide.What is the area of the playground?
The required area of the playground is given as, 192 square meters.
Given that,
A rectangular playground is 888 meters wide. It is 333 times as long as it is wide. The area of the playground is to be determined.
Surface area is defined as the measure of a region or surface is called as surface area.
Here,
The area of the playground = l × w
As mentioned in the question,
l = 3w = 3 × 8 = 24
Area = 24 × 8
Area = 192 square meters.
Thus, the required area of the playground is given as, 192 square meters.
Learn more about the surface area here: https://brainly.com/question/2835293
#SPJ5
Which graphic organizer would help you visualize important events in the history of the U.S. space program? timeline point-by-point diagram cause-and-effect chart Venn diagram
Answer with explanation:
If we have to visualize important events in the history of the U.S. space program, we have to keep following things in mind
Year Program
19... Satellite A
19.. On Moon ....
.... ............
...... .........
So, while scaling , we will keep year , that is time on any of the axis and program on another axis.
→→The Appropriate option will be
(a) Time line
IMAGE ATTACHED
A research organization recently issued a statement suggesting that 80% of American voters are dissatisfied with the work of Congress. You designed a simulation to generate sample data to reflect this proportion. An automated random number sample program is used that has a sample of size 50, is run 100 times, and uses the numbers 1 through 16 to represent dissatisfied voters and the numbers 17 through 20 to represent satisfied voters. The dot plot below represents the outcome of the simulation, with the margin of error displayed.
Dot plot titled Simulation of 80 percent Dissatisfaction with Congress with x axis labeled Number of Yeses in Sample of 20 and ranges from 33 to 48 and y axis labeled Frequency ranges from 0 to 20. The sample size is 50 and the number of trials is 100. The mean is shown to fall somewhere between 39 and 40 on x axis and margin of error is represented with vertical lines on either side of the mean, one at approximately x equals 38 and one half and the other at approximately x equals 40 and one half. There are three dots arranged vertically from 35,1 to 35,3 and six dots arranged vertically from 36,1 to 36,6 and four dots arranged vertically from 37,1 to 37,4 and fifteen dots arranged vertically from 38,1 to 38,15 and nineteen dots arranged vertically from 39,1 to 39,19 and eighteen dots arranged vertically from 40,1 to 40,18 and ten dots arranged vertically from 41,1 to 41,10 and thirteen dots arranged vertically from 42,1 to 42,13 and seven dots arranged vertically from 43,1 to 43,7 and two dots arranged vertically from 44,1 to 44,2 and two dots arranged vertically from 45,1 to 45,2 and one dot at 46,1.
Using the data from this simulation, what is the sample mean (rounded to the nearest tenth), x bar comma and approximately what proportion of voters are dissatisfied?
x bar equals 39.6 and approximately 79.2% of voters are dissatisfied with Congress
x bar equals 39.8 and approximately 79.6% of voters are dissatisfied with Congress
x bar equals 39.9 and approximately 79.8% of voters are dissatisfied with Congress
x bar equals 40.0 and approximately 80.0% of voters are dissatisfied with Congress