A box of chocolates contain 10 milk chocates and 12 plain chocolates. Two chocolates are taken at random without replacement.
Work out the probability that :
a) both chocolates will be milk chocolates
b) at least one chocolate will be a milk chocolate
Answer:
B
explanation:
there's a high chance you might as well get at least one milk chocolate because there's plenty..
Write the standard form of the line that passes through the given points. Include your work for each step in your final answer. Type your answer in the box provided to submit your solution.
(7, -3) and (4, -8)
a) Using variables, write out the formula for the standard form of the equation.
b) Determine the slope of the line.
c) Write the point-slope form of the line.
d) Using the properties of algebra, rearrange the equation into the standard form
a. The standard form of an equation is A x + By = C.
b. The slope of the line is 5 / 3
c. The point slope form of the line is y + 3 = 5 / 3 (x - 7)
d. The standard form of the line is 3y - 5x = -44
How to write the equation of a line?The equation of a line can be represented in different form such as slope intercept form, standard form, general form and point slope form.
The standard form of an equation is represented as follows;
A x + By = C
where
A, B and C are constantTherefore,
let's find the slope of the line passing through (7, -3) and (4, -8).
m = slope = - 8 + 3 / 4 - 7
m = -5 / -3
m = 5 / 3
The point slope form is represented as follows;
y - y₁ = m(x - x₁)
using (7, -3)
y + 3 = 5 / 3 (x - 7)
Let's rearrange the equation into standard form.
y + 3 = 5 / 3 (x - 7)
y + 3 = 5 / 3 x - 35 / 3
y - 5 / 3 x = - 35 / 3 - 3
y - 5 / 3 x = -44 / 3
Therefore,
3y - 5x = -44
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(2.0 × 10-³) × (3.5 × 10²)
Answer:
-42,000
Step-by-step explanation:
10-³ would be -30, so
2.0 x -30 = -600
10² would be 20, so
3.5 x 20 = 70
Multiply the two
-600 X 70 = -42,000
what is the slope of a line that is perpendicular to a line with a slope of 0.4? Do not include a decimal within a fraction in your final answer.
==========================================================
Explanation:
0.4 = 4/10 = 2/5
The original slope as a fraction is 2/5
Flip the fraction to get 5/2, then flip the sign to get -5/2 which is the perpendicular slope
The orginal slope 2/5 and perpendicular slope -5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical nor horizontal.
Rephrased another way: -5/2 is the negative reciprocal of 2/5.
number two
what is the length of PR?
The length of side PR will be 40.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In the isosceles triangle,
Two sides are,
⇒ PR = 5n and QR = (32 + n)
Now,
Since, The triangle is an isosceles triangle.
So, Two sides are equal.
We formulate;
5n = 32 + n
5n - n = 32
4n = 32
n = 8
Thus, The length of side PR = 5n
= 5 x 8
= 40
Therefore, The length of side PR will be 40.
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The perimeter of a triangle is 72 cm and its sides are in the ratio
of 5:6:7 find the area of the triangle (please send how u got it in a picture thank u)
Answer:
235.15 sq.cm
Step-by-step explanation:
Perimeter:Perimeter of a triangle is sum of all three sides.
Ratio of sides = 5 : 6 : 7
Sides are 5x , 6x , 7x
Perimeter = 72 cm
5x + 6x + 7x = 72
Combine like terms.
18x = 72
Divide both sides by 18,
x = 72÷ 18
x = 4
5x = 5*4 = 20 cm
6x = 6*4 = 24 cm
7x = 7*4 = 28 cm
Sides: 20cm , 24 cm , 28 cm
So, it is a scalene triangle.
To find the area of scalene triangle use Heron's formula.
a = 20 cm ; b = 24 cm and c = 28 cm
[tex]\sf s = \dfrac{a + b+ c}{2} \ where \ s \ is \ the \ semi \ perimeter.[/tex]
[tex]\sf =\dfrac{72}{2}\\\\\\ = 36 \ cm[/tex]
s - a = 36 - 20 = 16 cm
s -b = 36 - 24 = 12 cm
s - c = 36 - 28 = 8 cm
[tex]\sf \boxed{Area = \sqrt{s(s-a)(s-b)(s-c)}}[/tex]
[tex]\sf =\sqrt{36*16*12*8}\\\\ = 6*4*4\sqrt{6}\\\\= 96 *2.45\\\\=235.15 \ cm^2[/tex]
9. A Division 1-football team regularly schedules the same ten teams in
a season.
a. How many different schedules are possible if any team can play on
any weekend?
b. How many different schedules are possible if last two games of the
season must be the same teams every season.
The number of schedules that are possible, considering each case and the Fundamental Counting Theorem, is given as follows:
a) No restrictions: 3,628,800.
b) Last two games against the same team: 362,880.
What is the Fundamental Counting Principle?The Fundamental Counting Principle states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Teams play each other only once during the season, hence, if there are no restrictions, the parameters are given as follows:
[tex]n_1 = 10, n_2 = 9, \cdots, n_{10} = 1[/tex]
Hence the number of schedules is:
N = 10! = 10 x 9 x 8 x ... x 1 = 3,628,800.
If the last game is fixed, then the remaining games are an arrangements from 9 games, and thus the number of schedules is:
N = 9! = 362,880.
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suppose the population of iq scores in the town or city where you live is bell-shaped, with a mean of 107 and a standard deviation of 35. describe the frequency curve for possible sample means that would result from random samples of 100 iq scores.
The mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.
We know the population mean and standard deviation, that has a bell-shaped distribution:
μ= 107
σ=35
The sampling distribution, the distribution of the mean of samples of size n out of this population, will have the same mean as the population mean.
μ (m) = μ =107
The standard deviation will be related to the population standard deviation and the sample size as:
σ (m)= σ/[tex]\sqrt{N}[/tex]
= 35/10=3.5
Then, the mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.
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How should i explain 37.287-15=22.287
Answer:
22.287
Explanation:
This is because 15 is a whole number.
It is also 15.000
37.287
-15.000[tex]\\[/tex]
22.287
Find an ordered pair (x, y) that is a solution to the equation.
-x+5y=3
The ordered pair that is the solution to the equation -x + 5y = 3 is (-3,0) and (0, 0.6)
Ordered pair:
Ordered pairs refers a set of 2 numbers that exist in a particular order. The first one represents the x value and the second one refer the y value.
Given,
Here we need to find the ordered pair (x, y) that is a solution to the equation -x + 5y = 3
In order to find the solution ordered pair we have to plot this equation on the graph.
To plot this equation, we have to use the graphing calculator, and then input the given equation as the function, then we get the graph like the following.
While we looking into the graph, we have identified that the solution ordered pairs are (-3,0) and (0, 0.6)
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write the correct function represented in the table below
HELP ASAP
Answer:
Step-by-step explanation:
y=X-2
Gravetter/Wallnau/Forzano, Essentials - Chapter 12 - End-of-chapter question 17 Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or denominator of the F- ratio, and indicate whether the size of the F-ratio would increase or decrease. Increasing the differences between the sample means: As the differences between sample means increase, Shewe also increases, and the F-ratio increases As the differences between sample means increase, Mbetween also increases, and the F-ratio decreases. As the differences between sample means increase, MSbor decreases, and the F-ratio decreases As the differences between sample means increase, MStarwe decreases, and the F-ratio increases Increasing the size of the sample variances: Increases in sample variability cause Mswibh to decrease and thereby decrease the F-ratio. Increases in sample variability cause Mouhinto decrease and, thereby, increase the F-ratio O Increases in sample variability cause MS within to increase and, thereby, increase the Fratio. Increases in sample variability cause MS in to increase and thereby decrease the F-ratio.
The size of the F-ratio value would increase as the numerator of the F-ratio (MS Between) increased and The size of the F-ratio value would increase as the numerator of the F-ratio (MSBetween) increased.
Given that,
The F ratio can be defined as,
F =Mean Sum of Squares of between treatments / Mean Sum of Squares of within treatments
F =MS Between /MS within
Increase the difference between the sample means.
As the difference between the sample means increases, between treatments has larger effect
(MS known ) . This affects the numerator of F-ratio.
Hence, As numerator of F-ratio ( MS Between ) increases, the size of the F-ratio value would increase.
Increase the size of sample variances.
As the size of sample variance increases, with treatments has larger effect ( MS within ). This
affects the denominator of F-ratio.
Hence, As the denominator of F-ratio (MS Within ) increases. The size of F-ratio will decrease.
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The students at Brandon's school voted between a bear and a lion as the new school mascot. Of the 100 students at Brandon's school, 30 voted for the bear. What percentage of students voted for the bear?
Identify the molecular geometry around the nitrogen atom highlighted red in the given organic molecule. CH3 н 4-¢-6 H H Select one: A. Tetrahedral B. Trigonal planar C. Trigonal pyramidal D. Linear
The given organic molecule contains a trigonal pyramidal nitrogen atom, which is underlined in red.
Given;
The provided organic molecule's structural structure, with the nitrogen atom's position around it, is colored red.
Number of electron pairs in Nitrogen = 4 (3 Bond pairs + I Lone pair)
General Formula = AX₃E
Electronic Geometry = Tetrahedral
Molecular Geometry = Trigonal pyramidal
Hybridization = sp³
Hence, the nitrogen atom highlighted in red in the given organic molecule is Trigonal pyramidal.
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A biased dice is rolled and the results are recorded in a table. The dice is rolled once more. a) Use the table to estimate the probability that a 3 will be rolled. b) If the dice is rolled another 500 times, how many sixes would you expect to roll? Score 1 2 3 4 5 6 Frequency 12 35 11 23 7 12
The probability that a 3 will be rolled would be 0.125 and the expected number of 6's roll would be 68.
What is probability?
Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The events' estimated probabilities are as follows, according to the exponential probability theory:
P(3) = 0. 125
P(6 in 500 rolls) = 68 rolls
Number of times event occurs / number of trials
A number of attempts = sum of frequency:
(12+35+11+23+7+12) = 88
So the probability that a 3 will be rolled as
⇒ number of 3's / number of attempts
⇒ 11/88 = 0.125
The number of 6's probable in 500 rolls
⇒ (12 /88) × 500
⇒ 68.18 = 68
Therefore, the expected number of 6's roll would be 68.
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Order these numbers from least to greatest.
1.2, 1.102, 1.1212, 1.12
Answer:
1.102, 1.12, 1.1212, 1.2
Step-by-step explanation:
Answer:
1 ) 1.102
2 ) 1.12
3 ) 1.1212
4 ) 1.2
Hope this helps! :)
Let A =
-4
6
Find 3A + 3B.
3A + 3B =
-3
1
and B =
2 - 4
0
0
The answer is [tex]3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right][/tex]
To solve the given expression, we have to first know about matrix addition and scalar multiplication.
Matrix addition is possible only when both matrices have equal dimensions. Scalar multiplication is the multiplication of a real number and a matrix. Each element of the matrix is multiplied by a scalar value in scalar multiplication.
To solve the given problem, first, substitute the value of A and B in the formula,
[tex]3A+3B=3\left[\begin{array}{cc}-4&-3\\6&1\end{array}\right] +3\left[\begin{array}{cc}2&-4\\0&0\end{array}\right][/tex]
Using scalar multiplication, multiply the real number and the matrix. So we get,
[tex]\begin{aligned}3A+3B&=\left[\begin{array}{ccc}3(-4)&3(-3)\\3(6)&3(1)\end{array}\right] +\left[\begin{array}{ccc}3(2)&3(-4)\\3(0)&3(0)\end{array}\right]\\&=\left[\begin{array}{ccc}-12&-9\\18&3\end{array}\right] +\left[\begin{array}{ccc}6&-12\\0&0\end{array}\right]\end{aligned}[/tex]
To add two matrices with the same dimension, add their corresponding element. So we get,
[tex]\begin{aligned}3A+3B&=\left[\begin{array}{ccc}-12+6&-9-12\\18+0&3+0\end{array}\right] \\&=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right]\end{aligned}[/tex]
Therefore, the answer is [tex]3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right][/tex]
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help please ][][[][][][[][][][][][][[][][[]
Answer:
3.730 = b
Step-by-step explanation:
Givens
<B = 25 degrees
b = ?
a: = 8 meters
Formula
Tan(B) = opposite / Adjacent
Solution
Solve for b (opposite)
Put in values for the letters.
Tan(25) = b /8
0.4663 = b / 8 multiply both sides by 8
0.4663*8 = 8*b/8 Combine
3.730 = b
Help :) (Algebra 1)
*Some help can be in my last question*
The average rate of change of the function g(n) from n = 1 to n = 5 is 0.2 inches.
We are given;
A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days.
g(n) = 10(1.02)^n
which is an exponential function.
We need to find the average rate of change of the function g(n) from n = 1 to n = 5.
We know that the average rate of change = slope of the function.
The slope of the function is given by:
Slope = Change in y-coordinate / change in x-coordinate
We have,
g(n) = 10(1.02)^n;
for n = 1; g(n) = 10(1.02)^1 = 10 * 1.02 = 10.2
for n = 5; g(n) = 10(1.02)^5 = 10 * 1.1 = 11
Put the values in the slope formula;
slope = 11 - 10.2 / 5 - 1 = 0.8 / 4 = 0.2
Thus, the average rate of change of the function g(n) from n = 1 to n = 5 is 0.2 inches.
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PLEASE HELP ASAP!!
find the value of x and y
What is the length of angle DF?
Using Midsegment theorem, the value of x and y are 17 and 2 respectively and the length of DF is 20 units.
How to use mid segment to find length of a triangle?The Midsegment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.
Therefore, DH is midsegment of triangle DEF.
Hence, let's find x
1 / 2 (28) = x - 3
14 = x - 3
add 3 to both sides of the equation
14 = x - 3
14 + 3 = x - 3 + 3
x = 17
Let's find the length DF as follows:
DF = y + 8 + x - 7
Recall x = 17
Therefore,
DF = y + 8 + 17 - 7
DF = y + 8 + 10
DF = y + 18
y+ 8 = 10
y = 2
Hence,
DF = 2 + 18
DF = 20 units
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A teacher wants to compare the mean geology scores of two different classes. She is testing the null hypothesis that there is no difference in the population mean scores of the two classes. The difference of the sample means is 51. 4. If the standard deviation of the distribution of the difference of sample means is 16. 66, what is the 95% confidence interval for the population mean difference?.
The confidence interval for the population mean difference is between -33.2 and + 33.2
You have a 5% probability of being incorrect with such a 95% confidence interval. You have such a 10% probability of becoming incorrect with a 90% confidence interval. In contrast to a 95 % confidence interval, a 99 per cent confidence interval would be larger (plus or minus 4.5 per cent as opposed to 3 per cent, for example).
The answer in this situation would be +/-(2 * 16.6) from the mean, or -33.2 and +33.2 points from the sample mean because the 95% confidence interval is equal to two standard deviations on either side of the mean. This would result in an answer of A.
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Your question is incomplete, but probably the full question was:
A teacher wants to compare the mean geology scores of two different classes. She is testing the null hypothesis that there is no difference in the population mean scores of the two classes. The difference of the sample means is 51.4. If the standard deviation of the distribution of the difference of sample means is 16.66, what is the 95% confidence interval for the population mean difference?
A)between -33.2 and + 33.2
B)between -49.9 and +49.9
C)between -102.8 and +102.8
D)between -154.2 and +154.2
Show 531x47 please thank you
Answer: 24.957
Step-by-step explanation: Calculator
In a video game, Shar ha to build a pen haped like a right triangle for the animal. If he need 16 feet of fence for the hortet ide and 20 feet of fence for the longet ide how many feet of fencing i needed for the entire animal pen?
Shar needs total of 48 Feet of fencing for the entire animal pen.
Pythagoras Theorem gives us a relation between the sides of right triangle . According to the Pythagoras , Square of hypotenuse if equal to sum of square of other two sides.
Right triangle has three side where longest side is given 20 feet and shortest side is 16
Using Pythagoras Theorem ,
(20)² = (16)² + (third side)²
(third side)² = 400 - 256
(third side)² = 144
taking square root
third side = 12 feet
Total feet required = 20 + 16 + 12
= 48 feet
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I have a trouble with this question and I have a maths exam on Sunday on the same lesson. Could anyone please answer this with explanation please asap
The value of p in the given triangle is equal to 99.3°.
What is Law of Cosines?
The Law of Cosines, also known as the cosine formula or cosine rule, is a relation in trigonometry that links the lengths of a triangle's sides to the cosine of one of its angles.When the lengths of two sides and the measurement of the included angle are known (SAS) or the lengths of all three sides (SSS), the remaining pieces of an oblique (non-right) triangle can be found using the Law of Cosines.The formula of the Law of Cosines is given as, [tex]c^{2} =a^{2} +b^{2} -2abcosC[/tex], where, [tex]a,b,[/tex] and [tex]c[/tex] are the side lengths of the triangle and [tex]C[/tex] is the angle between [tex]a[/tex] and [tex]b[/tex].In the given question, the side lengths of the triangle are as follows,
[tex]a=3.6 cm,[/tex] [tex]b=2.8cm,[/tex] and [tex]c=5.3cm[/tex]
Here, the angle between a and b, [tex]\angle C=p[/tex]
We know that the angle p between the two sides of lengths a and b can be found using the Law of Cosines Formula, given as,
[tex]c^{2} =a^{2} +b^{2} -2abcosC[/tex]
Substituting the above values, we get
[tex]5.3^{2} =3.6^{2} +2.8^{2} -2 \times 3.6 \times 2.8 \times cos p[/tex]
Simplifying, we get
[tex]28.09=12.96+7.84-20.16cosp\\\implies 28.09=20.8-20.16cosp\\\implies 7.29=-20.16 cosp[/tex]
Rearranging in terms of p, we get
[tex]cosp=-\frac{7.29}{20.16} \\\implies p=cos^{-1} (-0.3616)\\\implies p=99.3\textdegree[/tex]
Therefore, the value of p is equal to 99.3°.
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Find d using the tan. Explain correctly and will give brainlist
Answer:
d = 8.596m
or
= 8.6m rounded to the nearest tenth
Step-by-step explanation:
Tangent is:
tan(angle) = opp/adj
First, use
tan35° = 12/x
to find the unmarked piece on the bottom of the triangle.
Then find some more angles in the shape. See image.
Next, use
tan 25° = 12/y to find the length of the entire bottom of the whole, big triangle.
Last, subtract the little part from the whole side to find d. See image.
Answer:
In the picture attached
Step-by-step explanation:
The larger triangle is divided into two smaller ones. Take the first one (the triangle with the angle 35) and find the length of A1 using tan (imagine as if it's a triangle on its own). Do the same thing for the whole diagram (both the small triangles combined) using tan to find the whole length which I called A2, then minus A1 from A2 to find d
5100 dollars is placed in an account with an annual interest rate of 7%. To the nearest
year, how long will it take for the account value to reach 13500 dollars?
After 14.39 years the principle amount will reach to 13500 dollars.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practicize of adding interest to the principal amount of a loan or deposit.
Given: 5100 dollars is placed in an account with an annual interest rate of 7%.
Principle amount (P) = 5100 dollars.
Rate of interest = 7% = 0.07
Total amount (A) = 13500 dollars.
Here the interest is compounded annually, so we can use the compound interest formula,
[tex]A = (1+r)^t[/tex]
Plug the values in the formula
[tex]13500 = 5100(1+0.07)^t\\2.6471 = (1+0.07)^t[/tex]
Taking log on both sides,
[tex]log(2.6471) = log(1.07)^t\\log(2.6471) = t log(1.07)\\t = 14.39[/tex]
Hence, after 14.39 years the principle amount will reach to $13500.
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Answer:
The correct answer would be: 18.1
Step-by-step explanation:
help pls How do this
The value of (5 - 6b)² when it is expanded is 25 -60b + 36b² (third option).
What is the equivalent value?The square of a number is the value derived when a number is multiplied by itself. Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.
The square of a number is denoted by the power 2. For example, the square of 2, 2² is 4 (2 x 2).
Thus, (5 - 6b)² is the same as (5 - 6b) x (5 - 6b).
When multiplied, the expression becomes:
(5 - 6b) x (5 - 6b)
When multiplied, the expression becomes: 25 - 30b - 30b + 36b²
Add similar terms together: 25 -60b + 36b²
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without using technology, describe the behavior of f(x)=
The behavior of f(x) from given options is option (4) up on the left, up on the right.
What is the behavior of function:A function f(x) 's end behavior is how the graph of the function f(x) behaves as x gets closer to positive or negative infinity. The functions degree or the polynomial degree and leading coefficient of a given function will determine the end behavior of the function.
Here we have
f(x) = 3x³² + 8x² - 22x + 43
Here
polynomial degree of f(x) is 32
And leading coefficient is 3
Therefore,
The leading term of the given function is 3x³²
As the given polynomial has an even degree (32) and positive leading coefficient (3) then the graph will open upwards on both left and right.
Therefore,
The behavior of f(x) from given options is option (4) up on the left, up on the right.
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g a farmer has 24002400 feet of fencing and wants to fence off a rectangular field that boarders a straight river. he needs no fence along the river. what are the dimensions of the field that has the largest area? (list the smallest dimension first)
Answer:
600 ft by 1200 ft
Step-by-step explanation:
You want the dimensions of the largest rectangular area that can be enclosed on three sides with 2400 feet of fencing.
PerimeterLet x represent the dimension of the field that is parallel to the river, and y the dimension out from the river. The sum of the three side lengths is ...
x + 2y = 2400
Solving for y gives ...
y = (2400 -x)/2
AreaThe area is the product of the two dimensions:
A = xy = x(2400 -x)/2
We observe that this is the factored form of a quadratic with zeros at x=0 and x=2400. Its leading coefficient is negative, so the graph opens downward, and the vertex is the point where area is a maximum.
The vertex is located on the line of symmetry at the x-value that is halfway between the zeros:
x = (0 +2400)/2 = 1200
y = (2400 -x)/2 = (2400 -1200)/2 = 600
The dimensions of the field that has the largest area are 600 ft by 1200 ft.
__
Additional comment
As we observed here, the side parallel to the "river" will use 1/2 of the fencing, and the remaining two sides will each use 1/4 of the fencing. This is the general solution to such a fencing problem.
What is the sum of (3x + 4) + (9x – 10)?
Answer:
12x-6
Step-by-step explanation:
(3x+4)+(9x-10)
= 3x+4+9x-10
=3x+9x+4-10
=12x-6
ANSWER IS 12X-6