a cattle rancher wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure below). there are 510 feet of fencing available to complete the job. what is the largest possible total area of the four pens?
Answers
The largest area of the rectangle is 6502.5 square feet.
Given that,
Using fence parallel to one of the rectangle's sides, a cattle rancher wants to surround a rectangular area and divide it into four pens (see the figure below). To finish the task, 510 feet of fencing are available.
We have to find what could the four pens' combined total area be.
We know that,
The rectangular shape's length is l and its width is b.
Total fencing= 2l + 5b=510 feet
2l +5b =510 feet
We can write as,
l=1/2(510-5b)
Total area of the rectangle is length into breath
A(b) = l × b
A(b) = 1/2(510-5b)×b
A(b)= 1/2(510b -5b²)
For maximum area
A'(b)=0
1/2(510b -5(2b))=0
b=51
We get l as
l = 1/2(510-5b)
l = 1/2(510-5(51))
l = 127.5
Total area of the rectangle is 127.5 × 51
Total area of the rectangle is 6502.5 square feet.
Therefore, The largest area of the rectangle is 6502.5 square feet.
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Related Questions
Given f(x) = 4x − 8 and g(x) = −3x + 1, what is (f − g)(x)?
Answers
The subtraction between the functions f(x) = 4 · x - 8 and g(x) = - 3 · x + 1 is equal to (f - g) (x) = 7 · x - 9.
How to determine the subtraction between two functions
Herein we find f(x) and g(x) defined as linear functions and we are asked to find the subtraction between two functions, which is defined below:
(f - g)(x) = f(x) - g(x)
If we know that f(x) = 4 · x - 8 and g(x) = - 3 · x + 1, then the result of the subtraction of the two functions is:
(f - g) (x) = f(x) - g(x)
(f - g) (x) = (4 · x - 8) - (- 3 · x + 1)
(f - g) (x) = 7 · x - 9
The subtraction between the two functions is (f - g) (x) = 7 · x - 9.
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What is the image of ( 0 , − 8 ) (0,−8) after a reflection over the line y = x y=x?
Answers
Answer:
(- 8, 0 )
Step-by-step explanation:
under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
(0, - 8 ) → (- 8, 0 )
Express 2x=3y-7 in the form of ax+by+c=0 write the values
Answers
The final answer of the given quadratic equation is 2x - 3y + 7= 0.
What is the quadratic equation?
Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.
We have,
2x = 3y - 7
Converting the given equation in the form of ax + by + c = 0, we get
2x - 3y + 7= 0
Hence, the final answer of the quadratic equation is 2x - 3y + 7= 0.
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What transformation occurs from the graph y = x² to the graph of y = (x − 5)² + 7?
A a vertical shift up 5 units and a horizontal shift right 7.
B a vertical shift down 5 units and a horizontal shift right 7
C a vertical shift up 7 units and a horizontal shift left 5
D a vertical shift up 7 units and a horizontal shift right 5
Answers
The transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
What do we mean by the graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.So, the transformation from:
y = x² to y = (x - 5)First, plot both graphs.
(Refer to the graph attached below)
Now, notice that the graph of the function y = (x - 5)² + 7 has shifted vertically upwards by 7 units and horizontally right by 5 units.Therefore, the transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
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Can anyone write the equation of the graph?
Answers
The equation of the absolute value function graph is: y = |x - 3| + 5.
What is the Equation of the Absolute Value Function?The equation of the absolute value function can be written in the vertex form as y = a|x – h| + k, where:
The vertex of the graph = (h, k)The value of a is determined by whether the graph opens up or opens down.The horizontal translation factor, which determines how far left or right the parent function is translated = hThe vertical translation factor, which determines how far up or down the parent function is translated = k.From the given graph, we have the following:
(h, k) = (3, 5) [the vertex]
Substitute the values into the equation, y = a|x – h| + k:
y = a|x - 3| + 5
A point on the graph is (2, 6). To find the value of a, substitute (x, y) = (2, 6) into y = a|x - 3| + 5:
6 = a|2 - 3| + 5
6 = a|-1| + 5
6 = a + 5
6 - 5 = a
1 = a
a = 1
To write the equation of the graph, substitute a = 1 into y = a|x - 3| + 5:
y = 1|x - 3| + 5
y = |x - 3| + 5
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Can anyone write the equation of the graph?
Answers
On the graph
This should answer your question
.0
Given f(x) = -x - 1, find f(1).
Answers
Answer:
f(1) = -2
Step-by-step explanation:
f(1) = -(1) - 1
f(1) = -1 - 1
f(1) = -2
The sum of the squares of two consecutive positive numbers is 1,105. Find the numbers.
Answers
Answer:
23 and 24
Step-by-step explanation:
let the 2 consecutive numbers be n and n + 1 , then
n² + (n + 1)² = 1105
n² + n² + 2n + 1 = 1105 ( subtract 1105 from both sides )
2n² + 2n - 1104 = 0 ( divide through by 2 )
n² + n - 552 = 0 ← in standard form
(n + 24)(n - 23) = 0 ← in factored form
equate each factor to zero and solve for n
n + 24 = 0 ⇒ n = - 24
n - 23 = 0 ⇒ n = 23
However, n > 0 , then n = 23 and n+ 1 = 23 + 1 = 24
the numbers are 23 and 24
a medical researcher is studying the effects of a drug on blood pressure. subjects in the study have their blood pressure taken at the beginning of the study. after being on the medication for 4 weeks, their blood pressure is taken again. the change in blood pressure is recorded and used in doing the hypothesis test.change: final blood pressure - initial blood pressurethe researcher wants to know if there is evidence that the drug reduces blood pressure. at the end of 4 weeks, 35 subjects in the study had an average change in blood pressure of -2.4 with a standard deviation of 5.2.find the p -value for the hypothesis test. your answer should be rounded to 4 decimal places.
Answers
Answer: 0.0099
Step-by-step explanation:
this shows that the percentage in a normal distribution that is at most 1.65 sds above average is about 95%. explain why 1.65 is the right number of sds to use when constructing a 90% confidence interval. (6 points)
Answers
The correct number of Standard deviation to generate a confidence interval is therefore 1.65.
Given that;
This shows that the percentage in a normal distribution that is at most 1.65 standard deviation above average is about 95%.
Percentage above 1.65 SD equals 100 - 95 = 5.
Now, because of the symmetric distribution,
Percentage above 1.65 SD = % below 1.65 SD is what we can see:
Below 1.65 SD + between 1.65 SD below and 1.65 above + above 1.65 SD + % above 1.65 SD = 100%
=> 5% + between -1.65 SD below and 1.65 above + 5% = 100%
=> % between -1.65 SD and 1.65 SD above mean = (100 - 5 - 5)% = 90%
The correct number of SDs to generate a confidence interval is therefore 1.65.
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if g(x) = x^2 - 4x find the value for g(2n)
Answers
Answer: [tex]g(2n)=4n^2 -8n[/tex]
Step-by-step explanation:
Substituting [tex]2n[/tex] for [tex]x[/tex],
[tex]g(2n)=(2n)^2 -4(2n)\\\\g(2n)=4n^2 -8n[/tex]
all in image, please help asap
Answers
The angle that is same side exterior angle to ∠ABC is ∠EFH.
How to find angles?When parallel line are cut by a transversal line, angle relationships are formed such as corresponding angles, vertically opposite angles, alternate angles, same interior angles, etc.
AD and EG are parallel to each other.
CH is a transversal line to the parallel lines.
Therefore, let's find the angle that has the same relationship as same side exterior angles as angle ABC.
Two angles that are exterior to the parallel lines and on the same side of the transversal line are called same-side exterior angles.
Same side exterior angles are supplementary.
Therefore,
∠ABC and ∠EFH are same side exterior angles.
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Determine which equation is false, based on the solution set S:{4}.
3t = 12
3m + 7 = 14
4(4c + 1) = 68
9 = 5p − 11
Answers
Based on the solution set S:{4}, the false equation is 3m + 7 = 14, because the solution of the equation is not 4
The first equation is
3t = 12
t = 12/3
t = 4
The solution is {4}
The second equation is
3m + 7 = 14
3m = 14 - 7
3m = 7
m = 7/3
The solution is not {4}
The third equation is
4(4c + 1) = 68
4c + 1 = 68/4
4c + 1 = 17
4c = 17-1
4c = 16
c = 16/4
c = 4
The solution is {4}
The fourth equation is
9 = 5p - 11
5p = 9 + 11
5p = 20
p = 20/5
p = 4
The solution is {4}
Hence, Based on the solution set S:{4}, the false equation is 3m + 7 = 14, because the solution of the equation is not 4
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Find the slope of a line crossing through the following points: (4, -3) and (10,-7). (Answer in a simplified fraction if necessary... Example: 4/5)
Answers
(y2-y1)/(x2-x1)
(-7 - (-3))/(10 - 4)
-10/6
-5/3
An artist connects stained glass pieces with lead strips. In this rectangular window, the strips
are cut so that FH = 22 in. Find JG.
Answers
An artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.
What is a rectangle?
A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Here, we have
FH ≅ GH
FH = EG = 22in
If diagonals bisect each other then, an artist connects stained glass pieces with lead strips
1/2(EG) = JG
1/2 (22) = JG
11 = JG
Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.
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A right triangle contains a 25° angle.
a.) If one leg is of length 5 inche, what is the length of the hyp?
b.) There are 2 answers. How is this possible?
Answers
If one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.
According to the question,
We have the following information:
A right triangle contains a 25° angle and length of one leg is 5 inches.
Now, the leg for which length is given can be opposite to given angle or adjacent to given angle. So, there are two possible for the length of hypotenuse (H).
Now, when it is opposite to the given angle:
Sin 25 = 5/H
H = Sin 25*5
H = 0.4226*5
H = 2.113 inches
Now, when it is adjacent to the given angle:
Cos 25 = 5/H
H = Cos 25*5
H = 0.9063*5
H = 4.5315 inches
Hence, if one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.
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Determine the sum of the factors of 100
Answers
The factors of the number 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100. If you add them up, you will get the total of 217
Plot a point for some of the ordered pairs from the example problem shown at the right. Model the relationships by drawing a line from the y-axis through each point. Explain how the graphs show which relationship is proportional and which is not proportional.
Answers
Both the pairs of the points are linear.
Here i made the plot for the points and both the pairs of the points shows that the it follows a straight path which means it will be linear i nature.
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y = -6x - 2
12x + 2y = −6
Answers
Solve for the first variable in one of the equations, then substitute the result into the other equation.
in a hypothesis test, we choose a 5% level of significance. which p-value is statistically significant at this level?
Answers
The value of p that is statistically significant at a 5% level of significance refers to a p-value of 0.05 or less.
The fixed probability of incorrectly eliminating the null hypothesis when it is actually true is what is meant by the term "level of significance." The probability of type I error is defined as the degree of significance, which is decided by the researcher using the results of the error. The statistical significance is measured by the level of significance. It specifies whether or not the null hypothesis is thought to be true. The null hypothesis is anticipated to be shown as untrue or rejected if the result is statistically significant.
The symbol indicates the degree of significance (alpha). Therefore, the following definition applies to the level of significance:
Level of Significance = p (type I error) =
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Me ayudan a resolver la numero 5 porfa
Answers
The solution to the inequality 6 + t ≤ 13 is given as follows:
t ≤ 7.
How to solve an inequality?An inequality is solved similarly to an equality, isolating the variable of which the solution we want to find.
The difference, of the inequality compared to an equality, is that the solution contains an infinity number of values, instead of a finite number of values. This is because the solution of an inequality is composed by a range of values in one of the infinity number sets.
For this problem, the inequality is given as follows:
6 + t ≤ 13
Hence the solution for variable t is found isolating it as follows:
t ≤ 13 - 6 (moving every term that is not the variable to the opposite side)
t ≤ 7.
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ben has 172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?
Answers
The number of months Ben can be a member of the fitness club is 7 months .
In the question ,
it is given that Ben wants to join a fitness club ,
initial membership fees for fitness club is = $49.50
monthly fees for fitness club = $17.50
let the number of months be [tex]=[/tex] x
the total fees that Ben paid = $172
So ,according to the question
the equation to represent the situation is
49.50 + 17.50x = 172
17.50x = 172 - 49.50
17.50x = 122.5
x = 122.5/17.50
x = 7
Therefore , Ben can be a member of fitness club for 7 months .
The given question is incomplete , the complete question is
Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50 , Ben has $172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?
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What integers are the solutions to
|x-4| < 8 and |-3x| > 12
Answers
Answer:
x-4<12 x<-4
-3x<12
-3x/-3=x
12/-3=-4
x-4+4=x
8+4=12
Use the properties of operations to multiply (8-2x) (-0.25x)
_x + _x^2
the _ is the blanks im supposed to fill in
Answers
The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)
What does the term Algebraic Expression means?
In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
Solution:
Given the expression, we need to solve it by using the properties of basic multiplication.
= (8 - 2x)*(-0.25x)
= (8*(-0.25x)) + (-2x * (-0.25x))
= -2x + 0.5[tex]x^{2}[/tex]
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Suppose you toss a coin 100 times and get 80 heads and 20 tails. Based on these results, what is the probability that the next flip results in a tail?
The probability that the next flip results in a tail is approximately__
(Type an integer or decimal rounded to two decimal places as needed.)
Answers
The probability of the next flip result in a trail is 0.5.
Given that,
If you flip a coin 100 times and receive 80 heads and 20 tails.
We have to find what is the probability that the upcoming flip will result in a tail based on these findings.
What is probability?Probability refers to potential. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.
Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty.
One is the probability of every event in a sample space.
Next flip result is independent of the past results.
P(Next flip result is tail) = 1/2 = 0.5
Therefore, The probability of the next flip result in a trail is 0.5.
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alice passes through four traffic lights on her way to work, and each light is equally likely to be green or red. independent of the others. (a) what is the pmf, the mean, and the variance of the number of red lights that alice encounters?
Answers
The value for the number of red lights that Alice encounters are found.
Mean = 2; Var = 1; PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾What is meant as the independent events?The set of findings from an experiment is thought to as events in probability. There are numerous sorts of events, including independent, dependent, and mutually exclusive ones.X = no of red lights crossed by Alice.
X is Binomial distributed
In which n=4, p=0.5, q = 0.5
Mean value is found by the formula,
Mean = np
Mean = 4×0.5
Mean = 2
And, variance = npq
Var = np(1-p)
Var = 4×0.5×0.5
Var = 1
PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾
Thus, the value for pmf, the mean, and the variance of the number of red lights that Alice encounters are found.
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re-write the statement 19 + 7 divided by 2 - 5
by including one pair of brackets to make the total value equal to 8
Re-write the statement 19 + 7 divided by 2 x 6 + 1 by including two pairs of brackets to make the total value equal to 2
Answers
Answer:
[19+7] / [2 x 6 + 1]
Step-by-step explanation:
[19+7] / [2 x 6 + 1]
[26] / [13]
[2]
A small park in the shape of a rectangle has dimensions 20m by 50m. a road through the park follows the diagonal of the rectangle. find the length of the road in simplest radical form.
Answers
The length of the road in the simplest radial form is 10[tex]\sqrt{29}[/tex].
Here a rectangle of dimensions is 20m by 50m. So the length of 50m and the breadth is 20m
As the road is diagonal of the rectangle.
So we have to find the length of the diagonal of the rectangle.
Formula to find the diagonal of rectangle:
Diagonal = [tex]\sqrt{l^{2} + b^{2} }[/tex]
length (l) = 50m
Breadth(b) = 20m
Diagonal = [tex]\sqrt{50^{2} + 20^{2} }[/tex]
= [tex]\sqrt{2500 + 400}[/tex]
= √2900
= 10√29
Therefore the length of the road is 10√29.
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Ms. Nettleton wants to create an outdoor space for her dogs. The distance between the furthest corners is 4 feet. The width of the area is 2 feet. How long is the length of the area?
(please help)
Answers
The length of the area is 8 feet.
What is the shape of outdoor space?
We know that Square has equal length, Rectangle has opposites sides of equal length.By the given length we found that it is Rectangular outdoor space.Step-by-step explanation:
Given :
Distance between the furthest corners(Length)= 4 feet
Width(breadth) = 2 feet
Area of rectangle = Length * Breadth
= 4 * 2
=8 feet
Hence, The length of the area is 8 feet.
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The approximate average distances from the sun to Mars and Mercury are listed below:
Mars: 2.28\times 10^{8}2.28×10
8
kilometers
Mercury: 5.79\times 10^{7}5.79×10
7
kilometers
How much farther from the sun is Mars? Express your answer using scientific notation?
Answers
The distance from the Sun to Mars is 3. 9 times farther
What is ratio?Ratio can be described as a mathematical comparison between two or more numbers or elements in relation to each other on the basis of their sizes or magnitudes.
It is however known to show how many times one number or elements contains another.
Based on the information given, we have;
Distance from the Sun to Mars = 2.28×10^8Distance from the Sun to Mercury = 5.79×10^7To determine the ratio of their distances from the Sun, we have;
Distance from the Sun to Mars /Distance from the Sun to Mercury
Substitute the values
2.28×10^8/5.79×10^7
Divide through
3. 9 times
Hence, the distance is 3. 9 times farther.
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