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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PLEAS EHLPE BESTIES
Look at the venn diagram. How many people like vanilla only?
1 point
vanilla
8
4
chocolate
Your answer
answer:
8 people like vanilla only
hope this helped!
Answer:
8
Step-by-step explanation:
Brainliest??
Why are Trig ratios only for right triangles?
For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.
What are Trigonometric functions?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Here,
We have to find out why trigonometric ratios are used only for right triangles.
We concluded that when we are dealing with triangles other than right triangles, the solution is to draw a perpendicular line to create right triangles. For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.
Hence, for Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.
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A boat is traveling due east for 130 miles. The boat travels another 72 miles at a bearing N38E. Determine the distance, direction angle, and bearing of the boat from its original location.
The distance of the boat is 191.2 miles, 12.8° and N12.8E from the original location.
Using Trignometry to find the boat's distance:To calculate the distance, direction angle, and bearing of the boat from its original location, we will need to use trigonometry to determine the final position of the boat.
a) The distance traveled in the eastward direction is 130 miles. Then, using the bearing of N38E, we can calculate the northward and eastward distances traveled in the second leg of the journey. The bearing of N38E can be thought of as an angle of 38 degrees measured clockwise from due east.
Using trigonometry to calculate the northward distance traveled, we have,
(72 miles) * (sin 38°)
= 36 miles
And the eastward distance traveled is (72 miles) * (cos 38°)
= 59.04 miles.
The final position of the boat is at a distance can be calculated by:
130 miles east + 59.04 miles east
= 189.04 miles east and 36 miles north from the original location.
b) To find the distance from the original location, we use the Pythagorean theorem,
d = [tex]\sqrt{189.04^{2} +36^{2} }[/tex]
d = 191.2 miles
To find the direction angle, we use arctan(north/east) = arctan(36/189.04) = 12.8°
Bearing is the direction angle measured clockwise from north. So, bearing = 12.8°
Hence, the final position of the boat is 191.2 miles, 12.8°, and N12.8E from the original location.
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The geometric sequence an = 2an – 1 with an initial value of a1 = LaTeX: \frac{1}{8}1 8 represents the amount of money a person has saved after n years of investing. What is the sum of the first 11 terms?
The sum of the first 11 terms of the geometric sequence aₙ = 2aⁿ - 1 with an initial value of a₁ = 1/8 is -10.71.
Therefore the answer is -10.71.
The geometric sequence aₙ = 2aⁿ - 1 with an initial value of a₁ = 1/8 represents the amount of money saved after n years of investing.
So sum of n terms
Sn = 2a - 1 + 2a² - 1 + ... + 2aⁿ - 1
Sn = 2( a + a² + ... + aⁿ) - n
The sum of the first n terms of a geometric sequence aₙ = arⁿ⁻¹ with first term a₁ and common ratio r is given by the formula:
Sn = a₁(1 - rⁿ)/ (1 - r), that is
[tex]S_{n} = a_{1}\frac{ (1 - r^n)}{1 - r}[/tex]
So a + a² + ... + aⁿ = a(1 - aⁿ)/ (1 - a)
Thus Sn = 2( a + a² + ... + aⁿ) - n
Sn = 2a(1 - aⁿ)/ (1 - a) - n
In this case, a₁ = a = 1/8 and n = 11
So the sum of the first 11 terms of the geometric sequence is:
Sn = 2×1/8×( 1 - (1/8)¹¹)/ (1 - 1/8) - 11
Sn = -10.71
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(m-12)divided by 44=32
Answer: (m-12)
Step-by-step explanation:
(m-12)divided by 44=32
can anyone help with this one?! will mark brainliest!
Answer:
D =44°
Step-by-step explanation:
Angle ACB = 2 angle ADB
So, ADB = ACB/2
= 88°/2
= 44°
ANSWER ASAP! WILL
MARK BRAINLIEST
8. Find x and y.
A) x = 56, y = 68
B) X = 68, y = 56
C) x = 57, y = 66
D) X = 66, y = 57
Answer:
i depends on what the equation is.
80 people were laying out on the beach. Clouds started forming, and it looked like it was going to rain. 42 people left. What is a reasonable estimate for the percentage of people that left the beach?
Select the best answer from the choices provided.
A. 10%
B. 25%
C. 50%
D. 75%
Answer:
C. 50%
Step-by-step explanation:
Since 40 is half of 80, and 50% means half, and 42 out of 80 is close to half, then 42 out of 80 is close to 50%.
Answer: C. 50%
Answer:
b25
Step-by-step explanation:
beacuse that is a rain and reasonable he percentage
The perimeter of a square is given as 24x + 20. Write two diffrerent expressions to represent the perimeter. Use factoring to write one of the expressions
The perimeter of a square is given as 24x + 20 and can be written as 4 ×(5x+6) and 2 × (10x+12).
The perimeter of a square is the sum of all of the 4 sides of the square. Here, the perimeter of the square is given as the function of x, for finding the length of each side of the square.
Here, in the given problem, we can factorize the expression 20x+24 as, 4 ×(5x+6) so this is the 1st different way of writing the given expression. For another expression, we can take 2 commons from 20 x+24 that will be 2 × (10x+12).
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Please help If x = V15 cm and y= 3/2 cm what is the length of
133 cm
3 cm
33 cm.
3cm
Answer:
I think it is 33cm...... i hope this helped
Step-by-step explanation:
F the altitude of a triangle meet at one of the triangles vertices then the triangle is
When the given altitude of the triangle meet at one of the vertices of the given triangle then it represents the option 1. right angled triangle.
As given in the question,
Given is the altitude of the triangle.
Given Condition is :
Altitude of the triangle meet at one of the vertices of the triangle.
⇒ This means altitude is representing the height of the triangle.
Height is always represented by perpendicular line.
⇒One of the side having altitude forms a angle of measure 90°.
⇒Given triangle is right angled triangle.
Therefore, when the altitude of the triangle meet at one of the vertices of the given triangles it represents the option 1. right angle triangle.
The above question is incomplete, the complete question is :
If the altitudes of a triangle meet at one of the triangle’s vertices, then the triangle is
1) a right triangle
2) an acute triangle
3) an obtuse triangle
4) an equilateral triangle
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wacky wizards offers beginner and advanced magic classes. The beginner class costs 6 more than half the cost of the advanced class.Last week they taught 7 beginner classes and 11 advanced classes and earned $390. Write a system that represents the cost of the beginner class, b and the advanced class, a. HELP!!!!!
The system represents the cost of the beginner class will be $18 and the advanced class will be $24.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Both basic and expert magic lessons are available at Wacky Wizards. More than half as much is spent on the introductory class as there is on the advanced level. They made $390 last week by instructing 7 basic lessons and 11 advanced classes.
Let 'x' be the cost of beginner classes and 'y' be the cost of advanced classes. Then the equations are given as,
x = y / 2 + 6
y = 2x - 12 ...1
7x + 11y = 390 ...2
From equations 1 and 2, then we have
7x + 11(2x - 12) = 390
7x + 22x - 132 = 390
29x = 522
x = 18
Then the value of the variable 'y' is calculated as,
y = 2(18) - 12
y = 36 - 12
y = 24
The system represents the cost of the beginner class will be $18 and the advanced class will be $24.
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What is a 9 sided shape called?
A 9-sided shape is called a nonagon.
Therefore the answer is nonagon.
A nonagon is a polygon with nine sides and nine angles. A nonagon can be regular or irregular, depending on the lengths of its sides and angles. A regular nonagon has equal sides and angles, while an irregular nonagon has sides and angles of different lengths.
Nonagons are two-dimensional shapes, and they can be described by their number of sides, angles, and vertices. They are considered a type of polygon, which is a closed geometric figure that is made up of straight lines. In addition to nonagons, there are other types of polygons such as triangles, quadrilaterals, pentagons, hexagons, heptagons, and so on.
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help me please i really need this im failing pls try to understand and help me
Answer:
Blaaaaaaaa Blaaaaaaaa Blaaaaaaaa I do not know
Please answer! I’m kinda stuck lol
Answer:
Answer D
Step-by-step explanation:
Number of hours, 3
Cost: 105
divide 105 by 3 = 35
35 = cost of boat for 1 hour
so the answer is D :)
C = 35h
C = cost
H = hours
:)
Answer:
D. C = 35h
Step-by-step explanation:
105/3 = 35
that means it cost $35 an hour to rent the boat
so 35 x number of hours you rent = total cost
which is C = 35h
What is a midpoint for zero?
The midpoint for zero is (0,0).
The midpoint can be zero. This is dependent on the value of the two points. For two points on a number line on points with values -4, and 4, the midpoint is 0. And for two points such as (-2, 5), and (2, -5), the midpoint is equal to (0, 0).
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.
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C) Will Qamar have enough lacquer to cover the floor below? (pictured)
D) Justify your answer.
E) If your answer is “No,” how much more lacquer does she need? If your answer is
“Yes,” how much lacquer will she have left over? Show your work to justify your
answer.
Based on the information provided, Qamar will have enough lacquer to cover the floor and 24 square feet will be left over.
How much lacquer does Qamar have?Based on the information given, Qamar has 600 square feet.
How much lacquer does Qamar need?To calculate the total lacquer Qamar needs, it is necessary to calculate the area of the floor that has to be covered. In the case of a parallelogram, the area can be calculated using the following formula:
Area = Base x heigh (in a parallelogram, the height is the distance between the two horizontal lines using a straight line)Area = 48 feet x 12 feetArea = 576 square feetNow, if the total of material available is 600 feet, it can be concluded there is enough material to cover this floor. Let's calculate the lacquer left over:
600 - 576 = 24 feetNote: This question is incomplete; here is the missing information:
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a A trader opens a bank account with #250 000. In one month, she pays out two cheques for #49 000 and 34 000 and pays in one cheque for N14000. How much money does she have in her account after one month?
Answer: #181000
Step-by-step explanation:
So, to solve the problem, recall these definitions:
payout - withdrawal
pay in - deposits.
Normally, deposits add money to your balance, and withdrawals take out money.
So, there is one cheque for paying in 14,000, and two cheques for paying out 49,000 and 34,000
So, the balance is 250000 + 14000 - (49000+34000)
The balance is 181,000
Can someone help me!!!!!!
The y - intercept of the graph, given the formula of 2 y - 5x = 16, is y - intercept : ( 0, 8)
How to find the y - intercept ?To find the y - intercept, use the slope - intercept form of the equation of a line which is:
y = mx + b
m = slope
b = y - intercept
So first rewrite the formula given to look like the slope - intercept :
2 y - 5x = 16
2 y = 5x + 16
( 2 y = 5x + 16 ) / 2
y = 5/ 2 x + 8
The y- intercept is therefore 8. As a point on the graph, this is ( 0, 8 )
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A boy wants a game which cost $180, but he only has 1/3 of the money, how much more money does he need to buy the game?
Answer: $120
Step-by-step explanation:
So you find 1/3 of 180, basically, you multiply them which is 60.
So if he has a third of the money, he has $60, but he needs 180. So we subtract $180 (how much money he needs) from $60 (the money he has). Which is 120 dollars, so the boy needs $120.
Or 2/3 more.
I have x N50 note and y N100 note. There are eight note altogether and their total value i N550. How many of each note do I have?
So I have 5 and 3 notes each
You need to use simultaneous equations to solve this problem since there are 2 variables.
50x + 100y = 550 (value of the notes x the number of each note)
x + y = 8 (the number of each note added).
Multiply the second equation by 50 so that it the x variables are the same in both equations. Thus, 50x + 50y = 400.
Subtract 50x + 50y = 400 from 50x + 100y = 550.
The subtraction results in 50y = 150.
Divide by 50. y = 3, so x must equal 5.
So I have 5 and 3 notes each
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Translate: (x - 2)/3 + x^2. Select the one answer.
Answer:
its the first answer choice
Step-by-step explanation:
So I was doing a math problem and they gave me the perimeter and told me to find the radius from that, how do I do that?
the swim team trains 4 days every week. Mon, Tues, and Thurs, the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. how many hours per week does the team train?
The number of hours that the team trains per week is 17 hours.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:
( 1 1/4 + 1/2 + 2 1/2) × 4
= 4.25 × 4
= 17 hours.
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i need help asap!!! thx u
The distance of the ball thrown is 67 ft. approx.
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here θ=63 and length of the field as 60 and let d be the distance
∴ Cos (180-63-90)=60/d
d = 60/cos(27)
d = 67 (approx)
Hence, The distance of the ball thrown is 67 ft. approx.
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THIS IS A TEST!!!
HOW DO YOU SOLVE FOR X?
If you get this right, or you give an explanation. ill mark you as blranliest.
Answer:
[tex]x = \frac{9}{5} [/tex]
Step-by-step explanation:
[tex] - 7( - 7 \times ( - x - 1)) = 6 (- \times ( - 2x - 3))[/tex]
[tex] - 7 + 7x + 7 = 6 + 2x + 3[/tex]
[tex]7x - 2x = 6 + 3 + 7 - 7[/tex]
[tex]5x = 9[/tex]
[tex] \frac{5x}{5} = \frac{9}{5} [/tex]
[tex]x = \frac{9}{5} [/tex]
What is the coefficient of 5x² in 5x² 5x?
The coefficient of expression 5x^2 in 5x^2 5x is 5.
The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. In this expression, the number multiplied with 5x^2 is 5, so the coefficient of 5x^2 is 5.
The expanded expression is 5x^2 5x = 5x^3 + 5x^2. The coefficient of 5x^2 in this expression is still 5.
The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. When we expand the expression 5x^2 5x, it becomes 5x^3 + 5x^2. The number that is multiplied with 5x^2 in this expression is still 5, so the coefficient of 5x^2 is 5.
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can someone please help me with this question and give step by step so i understand it better? tysm
Answer:
2,304
See below
:)
Step-by-step explanation:
You are supposed to find the volume.
To do this, find the volume of the green figure and blue(ish) figure separately and then add them together.
For volume, it is
length times width times height
[tex]l*w*h[/tex]
it doesn't matter what you say is length or height or whichever.
so let's do green
12 * 12 * 6
12*12 is gross aka 144
then 144*6 is... 864
The volume of the green figure is 864 cubic inches.
Now let's find the blue(ish) figure.
18 * 8 * 10
that equals 1,440 (calculator)
The volume of the blue(ish) figure is 1,440 cubic inches.
Now add the two volumes together.
1,440+864 = 2304
2,304 in³
In a 45°-45°-90° triangle, the length of the hypotenuse is 11. Find the length of one of the legs.
The length of the leg of the right-angled triangle is (11√2) / 2. The correct option is C.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the right angles triangle has 45-45-90 angles. The hypotenuse is 11.
The length of the leg will be,
Cos45 = Base / Hypotenuse
1 / √2 = Base / 11
Base = 11 / √2
Rationalize the numbers,
Base = 11√2 / 2
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− 10/1 −x 3 +x 4 +3x
i need help asap
Answer:
Step-by-step explanation: