Answer:
1170450 yd^2
Step-by-step explanation:
The first thing is to calculate the necessary perimeter, which would be like this:
2 * a + b = 3060
if we solve for b, we are left with:
b = 3060-2 * a
Now for the area it would be:
A = a * b = a * (3060-2 * a )
A = 3060 * a -2 * a ^ 2
To maximize the area, we calculate the derivative with respect to "a":
dA / da = d [3060 * a -2 * a ^ 2
]/gives
dA / day = 3060 - 4 * a
If we equal 0:
0 = 3060 - 4 * a
4 * a = 3060
a = 3060/4
a = 765 and d
Therefore b:
b = 3060 - 2 * a = 3060 - 1530 = 1530
A = a * b
A = 765 * 1530
A = 1170450 and d ^ 2
Final answer:
To find the largest area the owner of the Rancho Grande can enclose, we set up an equation using the perimeter of the rectangular land and the available fencing. By solving the equation and finding the maximum point of a quadratic equation, we determine that the dimensions of the largest area are L = 765 yd and W = 1,530 yd.
Explanation:
To find the dimensions of the largest area the owner of the Rancho Grande can enclose, we need to consider that the rectangular grazing land is situated along the straight portion of a river. Since fencing is not required along the river, the owner can use the available fencing to enclose the other three sides of the rectangular piece of land.
Let's assume the length of the rectangular piece of land is L and the width is W.
Since there are three sides that require fencing, the perimeter of the rectangular piece of land is given by:
P = L + W + L = 2L + W
According to the information provided, the owner has 3,060 yd of fencing available. Therefore, we can write the equation:
2L + W = 3,060
To maximize the area, we need to solve this equation for one variable and substitute it back into the area formula, A = L * W. Let's solve for L:
2L = 3,060 - W
L = (3,060 - W)/2
Substituting L in the area formula:
A = ((3,060 - W)/2) * W
Finally, we can maximize the area by finding the maximum point of the quadratic equation:
A = -0.5W^2 + 1,530W
The maximum point of a quadratic equation in the form A = ax^2 + bx + c occurs at x = -b/2a.
Comparing the quadratic equation to A = -0.5W^2 + 1,530W, we have:
a = -0.5
b = 1,530
Substituting these values into x = -b/2a:
W = -1,530 / (2 * -0.5)
Calculating W:
W = 1,530 / 1
W = 1,530
Now, substituting W back into the equation for L:
L = (3,060 - 1,530) / 2
L = 1,530 / 2
L = 765
Therefore, the dimensions of the largest area the owner of the Rancho Grande can enclose are L = 765 yd and W = 1,530 yd.
Add 49 to the quotient of 125 and 5
Answer is:
125/5+49
=74
The dot plot shows h r. Ruda's class scored on a 5-point math quiz. Mr. Ruda described the data as having a spread from
0 to 5, a center of 3, two clusters, and a peak at 5. Where did Mr. Ruda make an error?
Scores on the Math Quiz
The spread is from 0 to 8.
The center is at 2
There is only one cluster.
The booklet
om
BV
PHILIPS
Answer:
B. The center is at 2
Step-by-step explanation:
Which system of equations has an infinite number of solutions?
A. 2x – 6y = 18
x – y = 9
B. 2x – 6y = 18
x + 3y = 9
C. 2x – 6y = 18
x – 3y = 9
Answer:
we choose C
Step-by-step explanation:
We need to understand an infinite number of solutions happens when all numbers are solutions. This situation means that there is no one solution.
So let analyse 3 options:
A.
2x – 6y = 18 (1) x – y = 9 <=> y = x -9 (2)Substitute (2) in (1) we have:
2x – 6(x - 9) = 18
<=> -4x + 54 = 18
<=> x = 9
=> y = 0
There is only 1 solution => A is wrong
B.
2x – 6y = 18 <=> x = 9 + 3y (1) x + 3y = 9 (2)Substitute (1) in (2) we have:
(9+ 3y) + 3y = 9
<=> 3y = 0
<=> y = 0
=> x = 9
There is only 1 solution => B is wrong
C.
2x – 6y = 18 (1)
x – 3y = 9 <=> x = 9+ 3y (2)
Substitute (2) in (1) we have:
2(9+3y) - 6y = 18
<=> 18 + 6y - 6y = 18
<=> 18=18
Yes, this system of equations has an infinite number of solutions
So we choose C
Final answer:
The system of equations with an infinite number of solutions is when one equation is a multiple of the other, which results in the same line and infinite solutions.
Explanation:
The system of equations that has an infinite number of solutions is:
A. 2x – 6y = 18
x – y = 9
To determine this, we notice that the second equation x - y = 9 is a multiple of the first equation 2x - 6y = 18. Since one equation is a multiple of the other, these equations represent the same line, leading to an infinite number of solutions.
Hiii I need help in this Plzzz helppp
Round these numbers to the nearest hundredth.
1)1.43
2)1.25
3)0.38
To round to the nearest hundredth, look at the third value to the right of the decimal point.
For instance, if there is a value 7.829, it would be rounded to 7.83, because 9 rounds up to 10. If the value was instead 7.821, it would be rounded to 7.82, because 1 rounds to 0.
However, the values listed are already rounded to the nearest hundredth, so no more work is required.
Answer:
No rounded needed.
Step-by-step explanation:
The length of a field, 1.2 km long is represented on a map by a line 40mm long. What is the scale of the map
Final answer:
The scale of the map is 1:30,000.
Explanation:
The scale of a map represents the relationship between the distance on the map and the corresponding distance on the Earth's surface. To find the scale of the map, we need to determine the ratio between the length of the field on the map and its actual length. In this case, the length of the field is 1.2 km, which is represented on the map by a line that is 40 mm long.
To calculate the scale, we can use the formula:
Scale = Actual length on the ground / Length on the map
Substituting the values, we get:
Scale = 1.2 km / 40 mm
First, we need to convert the length on the map to the same unit as the actual length. Since 1 km = 1,000,000 mm, we can convert mm to km by multiplying by 1/1,000,000:
Length on the map in km = 40 mm × (1 km / 1,000,000 mm) = 0.00004 km
Now we can calculate the scale:
Scale = 1.2 km / 0.00004 km = 30,000
Therefore, the scale of the map is 1:30,000.
JK has endpoints at J(0, 7) and K(10, –10). Find the midpoint M of JK.
Step-by-step explanation:
Midpoint=(X1+X2/2,y1+y2/2
[(0+10)/2,(7-10)/2]
(5,-3/2)
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
How many days will it take Amir to catch up to Jesse, and how many pages will they each have read?
Answer the questions to solve this problem using a system of equations.
1. Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read.
Answer:
6 days
210 pages
Step-by-step explanation:
As stipulated by the question, let the number of days Amir has been reading be x and the number of pages he had read to be y.
Now since he reads 35 pages per day.
Then mathematically;
y = 35x
For Jesse, He started reading a day before, this means that the number of days he had read would be x + 1. Since he reads 30 per day, the total number of pages he would have read is 30(x+1)
To find the number of days which is x, we have to assume that at a point in time, the number of books they would have read would be the same meaning that
Also; y = 30(x + 1)
Equating the two situations
35x = 30(x + 1)
35x = 30x + 30
35x -30x = 30
5x = 30
x = 30/5
x = 6 days
This means that it will take Amir 6 days to catch Jese.
The number of books they would have read by then is y = 35x = 30(x + 1)
= 35 * 6 or 30(6+1)
= 210
The total number of pages that he read will be 210 pages.
Based on the equation given, the equation to represent Amir's information will be:
y = 35 × x
y = 35x
Jesse's equation will be:
y = 30(x + 1)
Then, we'll equate both equations together. This will be:
35x = 30(x + 1)
35x = 30x + 30
35x - 30x = 30
5x = 30
x = 30/5
x = 6
Therefore, the number of pages read will be:
y = 35x
y = 35 × 6
y = 210 pages.
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what solution is y=x+6 and 3x-3y=18
Answer:
0
Step-by-step explanation:
Substituting y into equation 2...
3x - 3(x + 6) = 18
3x -3x -18 = 18
3x - 3x = 18 - 18
0 = 0
20 POINTS!!!!!
Shawna can paint a fence in 8 hours. Kevin can paint the same fence in 4 hours. How long will it take them working together? Which of the following equations could be used to solve this problem?
[tex]\Large{8t + 4t = 1}[/tex]
[tex]\Large{ ( \frac {1}{8} ) \cdot t + (\frac {1}{4} ) \cdot t = 1}[/tex]
[tex]\Large{( \frac {1}{t} ) \cdot 8 + (\frac {1}{t} ) \cdot 4 = 1}[/tex]
[tex]\Large{( \frac {1}{8} ) + (\frac {1}{4} ) = t}[/tex]
Answer: the answer is B
Step-by-step explanation:
Answer:
The answer is c
Step-by-step explanation:
The data set below has 6 values.
Find the mean absolute deviation for the data set.
If necessary, round your answer to the nearest hundredth.
8, 6, 6, 18, 17, 11
Calculate the mean of the data set, find the absolute deviation of each data point, and then average those deviations. For this data set, the mean absolute deviation is 4.33.
Explanation:To start off with, the mean absolute deviation is a measure of the dispersion or spread that represents the average difference between the values of the data set and the mean (average).
First, add up all the numbers of the data set. So, 8 + 6 + 6 + 18 + 17 + 11 = 66. Then divide this sum by the number of values (6) to calculate the mean (average). So, 66 ÷ 6 = 11.
Next, find the absolute deviation of each number in the set by subtracting the mean from each number and taking absolute value: |8-11|, |6-11|, |6-11|, |18-11|, |17-11|, |11-11|. This gives us: 3, 5, 5, 7, 6, 0.
Add these absolute deviations: 3 + 5 + 5 + 7 + 6 + 0 = 26. Then divide it by the count of the numbers in the data set (6). So, 26 ÷ 6 = 4.33, which is your mean absolute deviation to two decimal places.
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Final answer:
To find the mean absolute deviation for the data set 8, 6, 6, 18, 17, 11, you first calculate the mean of these numbers, then find the absolute deviations from this mean, and finally calculate the mean of those absolute deviations, which is approximately 4.33.
Explanation:
The student is asking how to find the mean absolute deviation (MAD) for a data set. The data set provided is 8, 6, 6, 18, 17, 11. To calculate the MAD, we first need to find the mean of the data set, then calculate the absolute deviation of each data value from the mean, and finally find the average of those absolute deviations.
Calculate the mean of the data set: (8 + 6 + 6 + 18 + 17 + 11) / 6 = 66 / 6 = 11.
Find the absolute deviation of each data value from the mean: |8 - 11| = 3, |6 - 11| = 5, |6 - 11| = 5, |18 - 11| = 7, |17 - 11| = 6, |11 - 11| = 0.
Calculate the mean of these absolute deviations: (3 + 5 + 5 + 7 + 6 + 0) / 6 = 26 / 6 = 4.33.
Hence, the mean absolute deviation for this data set is approximately 4.33.
A restaurant has 4 appetizers, 5 entrees and 2 desserts. How many different meal combinations could you order?
Step-by-step explanation:
1.) Firstly, you need to count out how many things there are. 4 app, 5 entrees, 2 desserts. This makes 11 different things
2.) for 11 numbers there can be 9 ways for each number for 1st nine places since 0 can't be the fist figure and next two are reciprocated from 10 numbers. Therefore 10!/2!
3.)So 99 combinations have 10!/2! Permutations hence total ways are 99*10!/2!
Jorge wants to find the most popular way for teens to volunteer in the community. He cannot decide between two methods.
Option 1: He will ask every fifth person on each English class roster.
Option 2: He will attend a walkathon to ask teen participants about the ways they volunteer.
Which statement about the methods is true?
Answer
option 2
Step-by-step explanation:
Answer:
option 2
Step-by-step explanation:
just did the test aye
A book is chosen randomly Complete the steps to find
the probability that the book is nonfiction given that it is
hard-covered
n
1 Find the probability that a chosen book is
nonfiction and hard-covered. PNH) =
2 Find the probability that a chosen book is hard-
covered. P(H) = 1
3. Calculate the conditional probability
PN n H
Answer:
1) 4/20
2) 11/20
3) 4/11
Step-by-step explanation:
Answer:
A, D, A or 4/20, 11/20, 4/11
Step-by-step explanation:
i just did it on edge and it was correct
WILL GIVE BRAINLIST!!!!!Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inches? Select three options..
A right rectangular prism with length 15 inches, width of 8 inches, and height of 6 inches.
A cross section parallel to the base is a rectangle measuring 15 inches by 8 inches.
A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches.
A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
Answer:
A cross-section parallel to the base is a rectangle measuring 15 inches by 8 inches.
A cross-section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross-section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
Step-by-step explanation:
the cross sections that are parallel and perpendicular will have the same measurements as the non-intersected sides. the last one will be a diagonal so the intersected edge is 6 and it creates a right triangle so it must be larger than 15 inches.
In the right triangle shown, m∠A=30°m, AB = 12\sqrt{3}AB=12
How long is AC?
The correct length of AC is 18
Consider the cylinder with a volume of 132π cm3. A cylinder with volume of 132 pi centimeters cubed. What is the volume of a cone with the same radius and height as the cylinder? 33 pi centimeters cubed 44 pi centimeters cubed 66 pi centimeters cubed 132 pi centimeters cubed
Answer:
44 pi centimeters cubed
Step-by-step explanation:
Since, base radius and height of cone are equal to to that of cylinder. Hence,
[tex]Volume \: of \: cone \\ = \frac{1}{3} \times Volume \: of \: cylinder \\ = \frac{1}{3} \times132\pi \\ = 44\pi \: {cm}^{3} [/tex]
Answer:44 pi centimeters cubed
Step-by-step explanation:
Please help!! This is due in 5 minutes!!
Answer:
416
Step-by-step explanation:
first find the area of the one triangle
12 times 8/2=96/2=48
and there are two triangles, so 48 times 2=96
and then find the area of one of the rectangle
10 times 12=120
and two are 10 times 10
10 times 10=100
100 times 2=200
200+120=320
320+96= 416
please help me out! I’ll give brainliest ! :)
Answer:
90 men working for a company
4/3 x −4 = 5 + x Help me please!
A) 0.5
B) 2
C) 18
D) 27
Answer:
The answer is D.
Step-by-step explanation:
4/3 x - 4 = 5 + x
4/3 x = 9 +x
1/3 x = 9
x = 27
Margie is planning a dinner banquet. The equation
C=750+42g models the relation between the cost in dollars,
C, of the banquet and the number of guests,
g. Interpret the slope of the equation.
Answer:
The slope, 42, means that for each additional guest the cost of the banquet increases by 42 dollars.
Step-by-step explanation:
The slope of the equation given stands for the rate at which the cost is increasing for each additional guest at the banquet, in this case, $42 per guest.
Explanation:In the equation C=750+42g, the slope is represented by the number 42. In the context of this problem, it is the cost per guest for the banquet. Meaning, for each additional guest (g), the total cost (C) of the banquet increases by $42. Therefore, the slope 42 signifies the rate at which the total cost of the banquet will increase per additional guest.
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Last year, Jane opened an investment account with 5500 . At the end of the year, the amount in the account had increased by 7.8%. How much is this increase in dollars? How much money was in her account at the end of last year? Increase in amount: Year-end amount:
Answer:
429 increase
5929 end of year
Step-by-step explanation:
simply do 5500 times 1.078 to get 5929 as ur total subtract 5500 to tet your increase of 429
The answer is 429.also the amount is 439
Find the length of the third side to the nearest tenth.
Answer: 14
Step-by-step explanation: To get the hypotenus of a triangle all you have to do is:
7 x 7 = 14
1 x 1 = 1
14 x 1 = 14
14 x 14 = 196
square root of 196 is 14
Equation form:
a² + b² = c²
7² + 1² = 14²
Sqrt(196) = 14
Use slope or the distance formula to determine the most precise name for the figure A(-1,-4) B(-1,-1) C(4,1) D(2,-2)
a) kite
b)trapezoid
c)sqaure
d)rhombus
Final answer:
After calculating distances between each pair of points and evaluating the properties of the resulting figure, it has been determined that the most precise name for the figure is a kite. This is due to the specific lengths of its sides and diagonals and their relationship to one another, which fits the definition of a kite.
Explanation:
To determine the most precise name for the figure formed by points A(-1,-4), B(-1,-1), C(4,1), and D(2,-2), we need to calculate the distances between each pair of points (sides of the figure) and evaluate their slopes where applicable.
AB = √(((-1)-(-1))^2 + ((-1)-(-4))^2) = 3
BC = √((4-(-1))^2 + (1-(-1))^2) = √(25 + 4) = √29
CD = √((4-2)^2 + (1-(-2))^2) = √(4 + 9) = √13
DA = √((2-(-1))^2 + ((-2)-(-4))^2) = √(9 + 4) = √13
AC (diagonal) = √((4-(-1))^2 + (1-(-4))^2) = √(25 + 25) = √50
BD (diagonal) = √((2-(-1))^2 + ((-2)-(-1))^2) = √(9 + 1) = √10
With sides AB and CD equal and AD and BC equal, and none of the sides being equal to each other, and considering two unequal diagonals, we can conclude that this figure is a kite, given that a kite has two pairs of adjacent sides that are equal but not all sides are equal and the diagonals are of different lengths.
Help with my homework. Please.
Answer:
Step-by-step explanation: since average speed = total distance/time
a)average speed of the journey from my home town to A = 10 miles/20 minutes = 0.5
b)journey from my home town to B = 20 miles/30 minutes = 0.7
c)10 miles + 20 miles = 30 miles
which takes 50 minutes
so: 30 miles/50 minutes = 0.6
50 POINTS! :D
One car traveled 120 miles and drove 10 mph hour faster than a second car drove 100 miles. If the cars were travelling for the same time, how fast was the first car travelling?
90 mph
50 mph
60 mph
80 mph
The speed of the first car is 60mph.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
One car traveled 120 miles and drove 10 mph hour faster than a second car drove 100 miles.
Let n be the speed of the first car.
And the n + 10 be the speed of second car.
And t be the time take by both of the cars.
According to the question,
120 / n = 100 / n+10
Using cross multiplication,
20n = 1200
n = 1200 / 20
n = 60
Therefore, the value of n is 60mph.
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2x-7=13 what is answer
Answer:
x = 10
Step-by-step explanation:
2x-7=13
2x = 20 (Add 7 to both sides)
x = 10 (Divide by 2 on both sides)
Answer:
10
Step-by-step explanation:
2x - 7 = 13
2x = 13+7 = 20
x = 20/2 = 10
Number 17 pls help me for 13 points !!
Answer:
xfgfjfgxjfgj
Step-by-step explanation:gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg
ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg
What fraction is equivalent to 5.1? is a rationalk number? Explain.
Answer:
5.1 is rational because it can be expressed in the form of a fraction. In proper form the fraction is 5 1/10 and in improper form it is 51/10.
Step-by-step explanation:
You want to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, you can pay $20 per month, plus a $60 signing fee. With the second membership plan, you can pay $40 per month plus no signing fee. At what number of months will both plans cost the same amount?
Answer:
after 3 months, both plans cost the same amount
Step-by-step explanation:
Let x is the number of monthsLet y is the total costGiven the following information:
Plan 1: pay $20 per month, plus a $60 signing fee
=> the equation for this plan is:
y1 = 20x+60
Plan 2: pay $40 per month plus no signing fee
=> the equation for this plan is:
y2 = 40x
To find number of months will both plans cost the same amount, we need to set the equation of plan 1 = equation of plan 2
<=> y1 = y2
<=> 20x+60 = 40x
<=> 20x = 60
<=> x = 3
So after 3 months, both plans cost the same amount
Circletown's limits form a perfectly circular shape. It has a population of 20{,}00020,00020, comma, 000 and a population density of 480480480 people per square kilometer.
What is Circletown's radius?
Answer:
3.64
Step-by-step explanation:
Based on the calculations, the radius of Circletown is equal to 3.64 kilometer.
Given the following data:
Total population = 20,000.Population density = 480.How to calculate Circletown's radius?First of all, we would determine the area of Circletown by dividing the total population by its population density as follows:
Area = 20,000/480
Area = 41.67 square kilometer.
Mathematically, the area of a circle is calculated by using this formula:
Area = πr²
Where:
r is the radius of a circle.
Substituting the given parameters into the formula, we have;
41.67 = 3.142 × r²
r² = 41.67/3.142
r = √13.26
r = 3.64 kilometer.
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