The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.
To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.
To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length) + 2(width)
Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:
2x + 2y = 60,000
To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:
60,000 - x = 3x + 2y
The total length of the three sides that are not the front is 3x + 2y.
Now we can calculate how much the builder will pay for each type of fence:
Cost of front fence = $20/m * x = $20xCost of other three sides = $10/m * (3x + 2y) = $30x + $20yTotal cost of the fence = $20x + $30x + $20y = $50x + $20y
To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.
However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:
x meters of $20/m fence for the front side3x + 2y meters of $10/m fence for the other three sides.This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.
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Find the equation of the line passing through the given point and parallel to the given line.
Answer:
[tex]y-2=-\frac{1}{2}(x-3)[/tex]
Step-by-step explanation:
[tex]x+2y=5 \\ \\ 2y=-x+5 \\ \\ y=-\frac{1}{2}x+\frac{5}{2}[/tex]
The slope of the given line is [tex]-\frac{1}{2}[/tex].
This means the slope of any line parallel to the given line is also [tex]-\frac{1}{2}[/tex].
Using point-slope form, the equation is [tex]y-2=-\frac{1}{2}(x-3)[/tex].
Why is it called logarithmic function?
A logarithm is the inverse operation of exponentiation, that is to say, log(a^b) = b, where log is logarithm, a is the base and b is the exponent.
A logarithmic function is called such because it relates the logarithm of a number to the number itself.
In other words, it is a function that expresses the value of the logarithm for a given number. This function is represented by the notation y = logb(x) where y is the logarithm, b is the base, and x is the number.
The logarithmic function is used to solve exponential equations, it is also useful in many fields such as mathematics, physics, engineering, and finance.
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Law of sines: Which measures are accurate regarding triangle JKL? Check all that apply. M∠K = 84° m∠K = 94° k ≈ 3. 7 units k ≈ 4. 6 units KL ≈ 2. 5 units KL ≈ 3. 2 units
The median's class interval is 20 hours and 30 minutes. And the average number of hours is thought to be 26.17.
Who defines median?The median is the exact middle value of a dataset after it has been sorted. A measure of central tendency is the distance between the bottom 50% of data and the top 50% of values. The methods for determining the median will vary depending on whether you have an odd or even number of data points.
the class interval that have median.
total is frequency is as -
∑f = 30
median class of corresponds to half of the value
∑th is the value
i.e. 15th value.
least cumulative frequency higher than or equal to 15 is obtained by accumulating frequencies starting at the top.
[tex]2+8+9=19[/tex]
So, corresponds to the class interval = [tex]20 < h\leq 30.[/tex]
Hence, median class is [tex]20 < h\leq 30.[/tex]
Since this is a grouped data we use the midpoint
The median:-
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a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes
pls help, explanation required
Sandy ate 1/6 of the candy bar John ate 3/4 of it how much more of the candy bar did John eat then Sandy
Answer: 7/12
Step-by-step explanation:
Based on the given conditions, formulate: 3/4 - 1/4
Find the common denominator and write the numerators above the common denominator: 9/12 - 2/12
Calculate the product or quotient:
Write the numerators over the common denominator: 9-2
12
Calculate the sum or difference: 7/12
Answer: 7/12
From the top of a lighthouse, the angles of depression to the top and bottom of a flagpole are 23° and 42°, respectively. If the flagpole is 75 feet from the lighthouse, how tall is the pole? [Round your answer to the nearest tenth of a foot. Type in the number only.]
Back with the braids.
Chee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos. Graphically solve a system of equations in order to determine the number of bananas, x,x, and the number of mangos, y,y, that Chee bought.
We get the number of bananas as 8 and the number of mangoes as 4.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that Chee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos.
We can write the system of equations as -
x = 2y ..... (1)
(1/2)x + 2y = 12 ..... (2)
We can write equation (2) as -
(1/2) x 2y + 2y = 12
3y = 12
y = 4
then -
x = 8
Therefore, we get the number of bananas as 8 and the number of mangoes as 4.
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Select all that are equivalent to sin∠GFH
A. Sin∠GEJ
B. Sin∠EGJ
C. Cos∠FGH
D. Cos∠GEJ
E. Cos∠GFH
F. Tan∠GEJ
All that is the equivalent angle to the given angle sin∠GFH is cos∠GEJ.
Corresponding angles are those angles which are created in the matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).
From the image, we get JE and HF are parallel.
So ∠GFH and ∠GEJ are corresponding angles. That means they are equal.
⇒sin(∠GFH) = sin(∠GEJ).
From triangle GFH, ∠GFH + ∠FGH = 90.
⇒sin(∠GFH) = cos(∠FGH).
Again ∠FGH = ∠EGJ.
⇒sin(∠GFH) = cos(∠EGJ)
All that is equivalent to sin∠GFH is cos(∠EGJ).
Thus, the correct answer is D.
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J31) what are the undefined values for sinx cosx / 1 - sin²x , where 0 ≤ x < 2pi ?
how?
Answer:Mathematics2 minutes ago
+5 pts
J31) what are the undefined values for sinx cosx / 1 - sin²x , where 0 ≤ x < 2pi ? how?
Step-by-step explanation:
Find the distance between the two points rounding to the nearest
(if necessary)
tenth
(1, -6) and (-8, -4)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.22[/tex]
What’s is
2^x=1/32•x=
Answer:
I believe it would be x=-5
Step-by-step explanation:
..
-x+6=-2(x+2)-5
Solve for x
Answer:
x = -15
Step-by-step explanation:
-x+6=-2(x+2)-5
Solve for x
-x + 6 = -2(x + 2) - 5
-x + 6 = -2x - 4 - 5
x = -15
------------------------
check- (-15) + 6 = -2(-15 + 2) - 5
21 = 21
the answer is goodx = -15
Pls help
(3 x 8 x 5)⁷
To evaluate (3 x 8 x 5)⁷, you need to first multiply 3, 8, and 5 together to get the base, then raise that result to the seventh power.
What does a math exponent mean?
The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) signifies 2 x 2 x 2 = 8. 23 and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.
So,
(3 x 8 x 5)⁷ = (120)⁷ = 120 x 120 x 120 x 120 x 120 x 120 x 120
= (1.2 x 10^2)^7 = 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2
=1.2^7 x 10^14 = 1.2^7 x 10^14
=4096 x 10^14
=4.096 x 10^17
Therefore (3 x 8 x 5)⁷ = 4.096 x 10^17
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Here are two points: (-3, 4), (1, 7). What is the slope of the line between them?
A.4/3
B.3/4
C.1/6
D.2/3
Answer:
B. 3/4
Step-by-step explanation:
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P = P ( -3 , 4 )
Let the second point be Q = Q ( 1 , 7 )
Now , the slope of the line between the two points is given by the formula ,
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 7 - 4 ) / ( 1 - ( -3 ) )
On simplifying the equation , we get
Slope m = 3 / 4
You have a 5 inch by 7 inch picture that you framed. When you hung the picture, you found that the entire area is 69.56 inches squared. What is the width of the frame?
The width of the frame is 2.4 inches
How to determine the width of the frame?
Let w represent the width of the frame
Then the area of the frame is:
(w + 5)(w + 7) = 69.56
Rewrite it in Standard form of a quadratic equation:
w² + 12w + 35 = 69.56
w² + 12w - 34.56 = 0
Use Quadratic Formula to solve for w:
w = (-b±√(b²-4ac))/(2a)
w = (-12±√(12²-4×1×(- 34.56)))/(2×1)
w = (-12±√(144+138.24))/(2)
w = (-12±16.8)/2
w = -6 ± 8.4
w = -6 + 8.4 or -6-8.4
w = 2.4 or w = -14.4
Since the width cannot be negative.
Thus, w = 2.4 inches
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Is the function f/x )= x x − 4 − − − − √ is continuous on the interval 4 [infinity]?
No, the function f(x) = x - √x - 4 is not continuous on the interval [4, infinity].
Here's why, A function is considered continuous if the function is defined at every point in its domain and there are no breaks or jumps in the function's graph. In this case, the function f(x) = x - √x - 4 is defined for all x > 4, However, the function includes a square root of x-4, which is defined only for non-negative real numbers, thus for x < 4, the function is undefined. Therefore, the function is not continuous on the interval [4, infinity].
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A triangle has 2 sides of length 2 and 18 what compound inequality describes the possible lengths for the third side length
I'm pretty sure the answer is 72 :))
For how many integer values of $n$ between 1 and 349 inclusive does the decimal representation of $\frac{n}{350}$ terminate
The decimal form of n/350 terminates after 49 integer values of n between 1 and 349 inclusive.
What is prime factorization?The technique of expressing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We may divide this into two categories. "Well, that's 4 times 5," we may remark. Also, 5 is a prime number. The number four is not a prime number. All numbers are made up of prime numbers. "Factors" are numbers that are multiplied to generate another number. As an example. "Prime factorization" is the process of determining which prime numbers multiply to produce the original number.
Here,
first, find the prime factorization of 350. (2*5^2*7)
then we need to find all multiples of 7 that are between 1 and 350.
the first multiple of 7/350.
The first multiple of 7 between 1 and 350 is 7.
so 7/350=0.02.
Then, drop the two zeros and find out what is 100% (1 whole, ignoring the percent) /2.
Then, we get 49.
49 integer values of n between 1 and 349 inclusive does the decimal representation of n/350 terminate.
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what is the percent change from 99 to 71?
To calculate the percent change of two numbers such as 99 to 71, you use the Percent Change Formula, where a is the start value and b is the end value. When we insert a = 99 and b = 71 in the formula above, then we get the following that we can simplify and solve to get the percent change from 99 to 71.
Change ≈ -28.2828%
Find the EXACT values of ALL SIX trigonometric functions of θ(sin, cos, tan, cot, sec, csc) from the information given. (a) cosθ=7/12, sinθ<0 (b) tanθ=4/3, θ in Quadrant III
(a) Since cosθ = 7/12 and sinθ < 0, we can find the other four trigonometric functions as follows:
sinθ = √(1 - cos²θ) = √(1 - (7/12)²) = √(1 - 49/144) = -√(95/144)
tanθ = sinθ / cosθ = (-√(95/144)) / (7/12) = -4√(5/18)
cotθ = 1 / tanθ = -1 / (-4√(5/18)) = 1/(4√(5/18))
secθ = 1 / cosθ = 1 / (7/12) = 12/7
cscθ = 1 / sinθ = -1 / (-√(95/144)) = √(95/144)
(b) Since tanθ = 4/3 and θ is in Quadrant III, we can find the other five trigonometric functions as follows:
cosθ = √(1 / (tan²θ + 1)) = √(1 / (16/9 + 1)) = √(9 / 25) = 3/5
sinθ = cosθ * tanθ = (3/5) * (4/3) = 4/5
cotθ = 1 / tanθ = 1 / (4/3) = 3/4
secθ = 1 / cosθ = 1 / (3/5) = 5/3
cscθ = 1 / sinθ = 1 / (4/5) = 5/4
What is trigonometric functions?Trigonometric functions are a set of functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The six most commonly used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
The sine function, represented by sin, gives the ratio of the side opposite the angle to the hypotenuse. The cosine function, represented by cos, gives the ratio of the adjacent side to the hypotenuse. The tangent function, represented by tan, gives the ratio of the opposite side to the adjacent side.
The cotangent function, represented by cot, gives the ratio of the adjacent side to the opposite side. The secant function, represented by sec, gives the ratio of the hypotenuse to the adjacent side, and the cosecant function, represented by csc, gives the ratio of the hypotenuse to the opposite side.
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A weight is suspended from a spring is set into oscillating
motion by compressing it into a point 3 cm above its resting
position and releasing it. It will displace 3 cm past its resting
point. From the time it is released it will bounce at a rate of 3
cycles per second.
a. Draw a graphical representation and give the equation
involving the situation.
b. What is the displacement of the spring after 2.5
seconds?
a. The graphical representation of the oscillation of the weight suspended from a spring is a sine wave, with the displacement of the weight on the y-axis and time on the x-axis. The equation involving the situation would be y = Asin(2pift + phi) where A is the amplitude of the oscillation (3 cm in this case), f is the frequency of oscillation (3 cycles per second in this case), t is the time elapsed since the weight was released, and phi is the phase offset (0 in this case).
b. To find the displacement of the spring after 2.5 seconds, we can substitute 2.5 seconds for t in the equation: y = Asin(2pift + phi) = 3sin(2pi32.5 + 0) = 3sin(15pi) = 3*0 = 0 cm. So the displacement of the spring after 2.5 seconds is 0 cm.
What is an oscillation period?By definition, period of oscillation of an oscillator is the time interval that the oscillating object needs to pass through its equilibrium position with velocity in the same direction.
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A line has a slope of – 1/7 and passes through the point (4,5). What is its equation in point-slope form?
Answer:
y-5=-1/7(x-4)
Step-by-step explanation:
The equation of the line in point-slope form is y-5=-1/7(x-4)
Answer:
y = -1/7 x + 39/7
Step-by-step explanation:
An equation in point slope form is
y = mx+b where m is the slope and b is the y intercept
We are given the slope
y = -1/7 x + b
Substitute in the point for x and y and solve for b
5 = -1/7(4) +b
5 = -4/7 +b
5 + 4/7 = b
5*7/7 + 4/7 = b
35/7 + 4/7 = b
39/7 = b
The equation is
y = -1/7 x + 39/7
Tlaloc pumped up 565656 ball. He pumped up 555 dodge ball for every 999 other ball. Complete the table. Original ratio Number Tlaloc pumped up
Dodge ball 555
Other ball 999
Total ball
5656
20 dodgeballs have been pumped up by Ttaloc.
Ttaloc has 36 additional pumped-up balls.
The complete ball's original number is 14.
The relationship between two or more numbers is expressed by the ratio. It displays the frequency of how often one value is encapsulated by another value (s).
The number of dodgeballs Ttaloc pumped up = (5/14) x 56 = 20
The number of other balls Ttaloc pumped up = (9/14) x 56 = 36.
A ratio in mathematics demonstrates how many times one number is present in another.
A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations.
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Approximately how many plant made pharmaceuticals are currently under different stages of discovery?
a. 100
b. 200
c. 300
d. 400
please select the best answer from the choices provided a b c d
Approximately 300 plants are made pharmaceuticals currently under different stages of discovery.
Why do you use the term pharmaceutical?
pharmaceutical, material used for repairing, changing, or treating organic processes as well as for illness diagnosis, treatment, or prevention. Pharma (Bachelor of Pharmacy): Course, Qualifications, Admission, Syllabus, Pay, and Scope.
What function do drugs serve?
Drugs are created, produced, and distributed by the pharmaceutical business. Its goal is not to define sickness. Drug manufacturers typically focus on ailments that have already been identified by the medical community.
The positive side effects of medications, such as those that lower blood pressure, treat infections, or reduce pain, are considered their advantages. The possibility that anything unfavorable or unexpected will occur to you as a result of using a medication is what we mean by "risks."
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Complete the table with values for x or y that make this equation true : 3x+y=15.
Answer:
Step-by-step explanation:
So first, with the given table you need to "plug-in" the numbers that are there for x and y.
Ok, for example 2 is listed in the "x" row. So plug it 2 for "x":
3x+y=15
3(2)+y=15
6+y=15
-6 -6
y=9
So do this for all of them...the same goes with all of the values...just plug in one, complete the steps then you'll get the answer for the other variable.
Hope this helps!
What are my financial goals? What major purchases should I save for?
It depends on your personal financial situation and goals. Generally, it is important to save for major purchases such as a house, car, and vacations, as well as setting aside money for retirement. Additionally, you may want to consider investing in stocks, bonds, or mutual funds to achieve your long-term financial goals.
△ABC, BD &CE are the altitude of the ide AC & AB and BD=CE. Prove that △BCD≅△CBE
We have proved that △BCD≅△CBE.
What are congruent triangles?
Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.
By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.
It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC
So, In right triangles BCD and CBE
BC=CB=common side⋯⋯[hypotenuse]
And BD=CE=given⋯⋯[sides of right triangles]
So, by RHS condition
△BCD≅△CBE.
Hence, we have proved that △BCD≅△CBE.
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We have proved that △BCD≅△CBE.
What are congruent triangles?
Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.
By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.
It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC
So, In right triangles BCD and CBE
BC=CB=common side⋯⋯[hypotenuse]
And BD=CE=given⋯⋯[sides of right triangles]
So, by RHS condition
△BCD≅△CBE.
Hence, we have proved that △BCD≅△CBE.
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How do you identify an exponential graph?
Exponential graph is identified by its curve.
An exponential graph is a graph that shows a rapid increase or decrease of a value over time, where the rate of change is proportional to the current value. It is usually represented by a curve that bends upward or downward.
The key characteristic of an exponential graph is that the Y-axis is on a logarithmic scale, and the curve of the graph is a steep curve going either up or down. The equation of an exponential graph is usually of the form y = ab^x, where a is the initial value, b is the growth or decay factor, and x is the independent variable.
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What is called composite function?
A composite function is a type of function that is made up of two or more other functions. It is created by combining two or more functions together. The resulting function can be written as a single expression, or as a composition of multiple functions.
A composite function is a type of function that is formed by combining two or more other functions. It is created by combining two or more functions together using the mathematical operations of addition, subtraction, multiplication, division, or composition. The resulting function can be written as a single expression, or as a composition of multiple functions. A composite function is often used to simplify a complex problem, or to manipulate and analyze data. For example, if a data set contains two sets of data, a composite function could be used to combine the two sets of data into a single expression. Additionally, composite functions can be used to solve problems that involve multiple variables, as the resulting function can be used to represent the relationship between the variables. Furthermore, composite functions can be used to create graphs, which can be used to further analyze the data.
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A sample of fish from a river showed
that of the fish were less than one
year old. If there are an estimated
8,000 fish in the river, about how
many of them are less than one year
old?