Graphically, the feasible solutions represent the points in the x-y plane that are inside the region defined by the three lines, and they can be found by plotting the three lines and shading the region below each line. The feasible solutions are the points in the shaded region that are common to all three.
Let x be the number of cubic yards of mix A used, and y be the number of cubic yards of mix B used. Then the total amount of phosphoric acid, nitrogen, and potash can be expressed as follows:
Phosphoric acid: 20x + 10y >= 460
Nitrogen: 30x + 30y >= 960
Potash: 5x + 10y >= 220
These inequalities represent the minimum monthly requirements for phosphoric acid, nitrogen, and potash. To find the feasible solutions, we need to find the values of x and y that satisfy all three inequalities simultaneously. This can be done graphically by plotting the three inequalities on the same coordinate plane and finding the region that is common to all three.
To plot the inequalities, we can choose convenient values for x and y, substitute them into the inequalities, and find the corresponding values of the right-hand side. For example, if we choose x = 0 and y = 0, then we have:
Phosphoric acid: 20 * 0 + 10 * 0 >= 460
Nitrogen: 30 * 0 + 30 * 0 >= 960
Potash: 5 * 0 + 10 * 0 >= 220
which gives us:
Phosphoric acid: 0 >= 460
Nitrogen: 0 >= 960
Potash: 0 >= 220
These values are all negative, which means that x = 0 and y = 0 do not satisfy the inequalities.
Next, we can choose x = 1 and y = 0, then we have:
Phosphoric acid: 20 * 1 + 10 * 0 >= 460
Nitrogen: 30 * 1 + 30 * 0 >= 960
Potash: 5 * 1 + 10 * 0 >= 220
which gives us:
Phosphoric acid: 20 >= 460
Nitrogen: 30 >= 960
Potash: 5 >= 220
These values are also negative, which means that x = 1 and y = 0 do not satisfy the inequalities either.
We can continue this process until we find values of x and y that satisfy all three inequalities. The feasible solutions are the values of x and y that satisfy all three inequalities, and they are represented by the region in the x-y plane that is common to all three. The feasible solutions can be found by shading the region below each of the lines representing the inequalities, and the set of feasible solutions is the region that is common to all three shaded regions.
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x[tex]x^{4} -41x^{2} +400=0[/tex]
Answer:
Values of x are ±4 and ±5
Step-by-step explanation:
Let y = [tex]x^{2}[/tex]
Which means: [tex]y^{2} = x^{4}[/tex]
Therefore:
A quadratic equation is formed:
[tex]y^{2} - 41y + 400 = 0[/tex]
The above quadratic equation can be simplified either by The Double Bubble Method or using the quadratic formula
Double Bubble Method:
[tex]y^{2} - 41y + 400 = 0[/tex]
The pair of factors of 400 that add together to give 41 are 25 and 16. Use these two factors to rewritre -41y:
[tex]y^{2} - 25y - 16y + 400 = 0[/tex]
Then do Factorization by grouping (i.e group the terms with common factors before factorizing):
[tex]y(y -25) - 16(y - 25) = 0[/tex]
[tex](y - 25)(y - 16) = 0[/tex]
The product of two expressions is zero, which means either of the two expressions is equal to Zero:
Either: [tex]y - 25 = 0[/tex]
Substituting [tex]y = x^{2}[/tex]:
= [tex]x^{2} - 25 = 0[/tex]
= [tex]x^{2} = 25[/tex]
= [tex]\sqrt{x^{2}} = \sqrt{25}[/tex]
∴ x = ±5
Or: [tex]y - 16 = 0[/tex]
Substituting [tex]y = x^{2}[/tex]
[tex]= x^{2} - 16 = 0[/tex]
[tex]= x^{2} = 16[/tex]
[tex]= \sqrt{x^{2}} = \sqrt{16}[/tex]
∴ x = ±4
∴Values of x are ±4 and ±5
Choose the correct sum of the polynomials (3x3 − 5x − 8) + (5x3 + 7x + 3).
8x3 + 2x + 5
2x3 − 12x − 11
2x3 + 12x − 5
8x3 + 2x − 5
Answer:
8x3 + 2x − 5
Step-by-step explanation:
A flag is shown. Determine the area of the shaded part of the flag.
Answer:
84 square inches
Step-by-step explanation:
The shaded region comprises of two same trapeziums:
∴Area of shaded region = 2 × (Area of a trapezium)
= 2 × [tex]\frac{1}{2}[/tex] × (Sum of parallel sides) × (perpendicular height of trapezium)
= [tex]\frac{2}{2}[/tex] × (4 + 8) × (6)
= 84 square inches
Determine the slope and the y-intercept of the equation. b=3.99a
The equation b = 3.99a has a slope of 3.99 and the y intercept is 0.
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
The standard form of a linear equation is:
y = mx + b
Where y, x are variables and b is the y intercept
Given an equation:
b = 3.99a
Comparing with the standard linear equation:
The slope is 3.99 and the y intercept is 0.
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what’s the answer to this question? i’ve been having a hard time figuring it out
Answer:
10.305
Step-by-step explanation:
First you calculate for the angle of 12ft down the wall secondly you calculate for the angle of 8ft down the wallthirdly you subtract the angle of the 8ft frpm the 12ftthe remainder it the angle that the projector needs to be tilted to focus on 8ft down the wallI need help with this question
The amount of Tylenol remaining after 8 hours is 47.1g
What is half life?half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive.
R = A(0.5)^t/3
R = 300(0.5)^8/3
R = 300( 0.157)
R = 47.1
therefore after 8 hours 47.1 g of Tylenol is is left
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Find the measure of the missing angles.
At the beginning of a snowstorm, Abigail had 12 inches of snow on her lawn. The snow then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow was melting, how much snow would Abigail have on her lawn 5 hours after the snow began to fall? How much snow would Abigail have on her lawn after tt hours of snow falling?
The snow on the lawn after 5 hours is 14.50 inches.
The snow on the lawn after tt hours is 12 + 0.5tt inches
How much snow is on the lawn?The equation that represents the amount of snow after a number of hours is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
The form of the equation is:
Total snow = snow on the lawn + (rate at which the snow falls x number of hours)
Snow after 5 hours = 12 + (0.5 x 5)
= 12 + 2.5 = 14.50 inches
Snow after tt hours = 12 + (0.5 x tt)
= 12 + 0.5tt inches
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please answer!!!!!!!!!!!!!!!!!
The value of t is,
⇒ t = 28
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
The circle is shown in figure.
Now, From the figure we can formulate;
t = 1/2 (3t - 28)
2t = 3t - 28
3t - 2t = 28
t = 28
Thus, The value of t is,
⇒ t = 28
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Can anyone help in number 12 pls… I don’t have to draw anything just have to write down the equation of a and b
Answer:
y=3x-2
Step-by-step explanation:
help. I’m stuck with this
Answer:
$14
Step-by-step explanation:
i multiplied 2.80 times 5 and got 14.
i hope this helped :)
There are 32 students in a 5th grade classroom. Each table seats 6 students. How many tables are needed so that every student has a seat?
5 tables 30 tables 6 tables 7 tables
To sit comfortably, the students need a total of 6 tables. The correct option is 3.
There are 32 students in a classroom. In 5th grade. Now to sit comfortably, the students need 6 tables. In each table, a total of 6 students can fit. In 5 tables, only 30 students can sit but two students will remain table less. With 1 extra table, 2 students can sir and each student from a table can sit in the las bench, i.e., 6th table.
The number of pupils in the classroom is 32. in grade five. The pupils now require 6 tables in order to sit comfortably. A total of 6 pupils can fit at each table. Only 30 pupils can fit at 5 tables, however 2 students will be tableless. With one extra table, two students can sit at the sixth table and each student from a table can use the last bench. Therefore, students need a total of 6 tables.
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Charles is flying a kite
that is on a string that
112 feet long. If the
angle of depression from
the kite to the ground is
27°, how high off of the
ground is the kite?
The height of the kite is 56 feet.
Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.
Let h represent the height of the kite. Hence, using trigonometric ratios:
[tex]sin(30)=\frac{h}{112}[/tex]
h = 56 feet
Therefore, the height of the kite is 56 feet.
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How do you check the factorization of a polynomial?
Completely factorize the polynomial using any methods that are appropriate, then look for shared factors and the polynomial's roots. Next, double-check your work to confirm accuracy.
Follow these steps to determine a polynomial's factorization:
Completely factor the polynomial using any relevant techniques, including grouping, utilizing the difference of squares or cubes, or using the quadratic formula.
By multiplying them all together, you can verify that each factor is accurate. The final figure must match the initial polynomial.
Look for shared factors among the polynomial factors. If the polynomial has common components, remove them from the equation and rewrite it as the product of the common factors and the other factors.
The polynomial's roots can be verified by setting each factor to zero and calculating the variable. The roots ought to correspond to the original polynomial.
Verify your work a second time to make sure all relevant elements have been identified and taken into consideration.
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You can rent a video game for $3.50. Your total cost of rentals for the month was $31.50.
This can be represented by the equation 3.5x = 31.5
What does the quantity 3.5x represent in this situation?
PLEASE BE ACCURATE!!! THANK YOU!!:)
According to the equation, when 9 video games are rented, the total cost is $31.5 which is expressed in the equation as 3.5x.
What is an equation?
A formula known as an equation uses the equals sign (=) to express how two expressions are equal. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have left hand side equal to right hand side in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as an expression.
Given,
The cost of renting a video game = $3.50
The total cost of rentals for the month = $31.50
The equation given is:
3.5x = 31.5
The term 3.5x in the equation represents the total cost of a month when the number of video games rented is x.
In this case x = 31.5/3.5 = 9
Therefore, according to the equation, when 9 video games are rented, the total cost is $31.5 which is expressed in the equation as 3.5x.
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find x. show your work.
PLEASE HELP, FIFTY POINTS!!!!!
Answer: Choose Option D (look at the image for the solution and make sure to give me brainliest)
Step-by-step explanation:
Find the area of the figure. Round your answer to the nearest hundredth.
5 ft
4 ft
14 ft
4 ft
The area of the figure nearest hundredth will be 84.13 square feet.
What is the area?The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
The figure is the combination of the rectangle and the semicircle. Then the area of the figure is the addition of the rectangle and the semicircle. Then we have
A = L x W + (π / 8) D²
A = 14 x 5 + (3.14/ 8) (14 - 4 - 4)²
A = 70 + 0.3925 x 36
A = 70 + 14.13
A = 84.13 square feet
The area of the figure nearest hundredth will be 84.13 square feet.
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The missing diagram is given below.
Which phrase describes the algebraic expression Three-fourths x + 2?
The phrase to describes the algebraic expression Three-fourths x + 2 is three-fourths of a number plus two.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given in question;
The algebraic expression;
Three-fourths x + 2
Now,
The phrase that describes the algebraic expression Three-fourths x + 2;
three-fourths of a number plus two.
Therefore, the phrase of expression will be three-fourths of a number plus two.
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Write a short essay to explain how you would guide learners to move from the concrete level, to the semi-concrete level and finally to the abstract level in relation to their understanding of the more than/less than concept. -8
In order to guide learners to move from the concrete level to the semi-concrete and finally to the abstract level in relation to their understanding of the more than/less than concept, I would use a step-by-step approach.
At the concrete level, I would introduce the concept of more than/less than with a hands-on activity. For example, I would have students compare the number of counters or blocks and have them determine which group has more or less. This would help them develop a fundamental understanding of the concept.At the semi-concrete level, I would introduce the concept of more than/less than with written numerals. I would have students compare numbers on paper, such as 4 and 6, and have them determine which number is more or less. I would also ask them to use concrete objects to represent the numbers, such as using four counters for 4 and six counters for 6.At the abstract level, I would introduce the concept of more than/less than with larger numbers. I would ask students to compare numbers such as 12 and 15, and determine which number is more or less. I would also ask them to use abstract symbols, such as 12 + and 15 -, to represent the numbers.By using this step-by-step approach, students will be able to move from the concrete level to the semi-concrete and finally to the abstract level of understanding the more than/less than concept. This will help them develop a strong foundation of the concept, which will allow them to solve more complex problems in the future.
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Select all the expressions that show breaking the addends 7 5/12 and 11 2/3 apart to make a whole.
A. 7 + 5/12 + 11 + 2/3
B. 7 + 5/12 + 8/12 + 11
C. 7 + 5/12 + 7/12 + 11 1/12
D. 7 + 5/12 + 5/12 + 11 3/12
E. 7 + 1/12 + 4/12 + 8/12 + 11
Please help out on question 1
1. Cosx = 5/√(41)
2. An equation {tan(x) + cot(x)}/{tan(x)} =csc²(x)
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
1. tanx = -4/5
and tanx = perpendicular/adjacent leg
So, P = -4 and A = 5
So, H = √(-4)² + (5)²
H = √(41)
So, Cosx = 5/√(41)
2. A trigonometric identity,
{tan(x) + cot(x)}/{tan(x)}
Simplifying,
= {tan(x)/tan(x) + cot(x)/{1/tan(x)}
= 1 + cot²(x)
= csc²(x)
Therefore, Cosx = 5/√(41)
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10. Find the original price of an antique which was sold at £545 at a profit of 9%.
495.95
convert the percentage into a decimal
0.09
then do b=1-r
1 - 0.09 = 0.91
Now do 545 x 0.91
Answer: 495.95
Let's assume that the original price of the antique was x.
We know that the antique was sold at a profit of 9%, which means that the selling price is 109% of the original price:
[tex]Selling \: price = Original \: price + Profit[/tex]
[tex]£545 = x + 0.09x \\ £545 = 1.09x[/tex]
To find the original price, we can divide both sides of the equation by 1.09:[tex]x = \frac{545}{1.09} [/tex][tex]x = 500[/tex]
Therefore, the original price of the antique was £500.Please help in the math
Answer:
Step-by-step explanation:
reflict means to put the point in the other way but in the same point.
The graph of a sinusoidal function has a maximum point at (0, 7) and then intersects its midline
at (3, 3).
Answer: 4cos(pi/6x)+3
Step-by-step explanation:
(SAT Prep) Find the value of x
2x
3x
Answer:
36°
Step-by-step explanation:
2x+3x=5x
5x=180°
x=180°:5=36°
Helppppp asapp plsssssss I’ll give brainly
The opposite sides of FGHJ are parallel.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners.
FGHJ is a quadrilateral.
From the figure we can observe that opposite sides are equal which means the quadrilateral is a parallelogram.
A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
The line segment FG≅JH
GH≅FJ
The sides are congruent and parallel.
Hence, the opposite sides of FGHJ are parallel.
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ez 25 points+brainliest: two times a number is plus another number is 18. three times the first number minus the second number is 7. what are the numbers?
The numbers required in the word problem are
x = 3 4/3 and y = 13 1/3.How to find the numbersLet's call the numbers x and y
From the first equation, we have:
2x + y = 18
From the second equation, we have:
3x - y = 7
Solving simultaneously by substitution method
3x - y = 7
3x = 7 + y
x = (7 + y)/3
substitute this expression for x into the first equation:
2x + y = 18
2((7 + y)/3) + y = 18
14/3 + 3y/3 = 18
14/3 = 18 - 3y/3
14/3 = 18 - y
collecting like terms
y = 18 - 14/3
y = 18 - 4 2/3
y = 13 1/3
substituting to solve for y
x = (7 + y)/3
x = (7 + 13 1/3)/3
x = 10 4/3/3
x = 3 4/3
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Elish was required to write a 600 word Literature essay. After working away for one hour, the word count on her computer showed that she had typed 240 words. What fraction of the essay does Elish still need to complete? Write your answer in simplest form
If Elish was required to write a 600 word Literature essay and word count on her computer showed that she had typed 240 words Elish still needs to complete 3/5 of the essay.
To find the fraction of the essay that Elish still needs to complete, we need to determine how many words she has left to write. We can do this by subtracting the number of words she has already written from the total required word count:
Words left to write = Total word count - Words already written
Words left to write = 600 - 240
Words left to write = 360
Now, to find the fraction of the essay that Elish still needs to complete, we can express the remaining words as a fraction of the total word count:
Fraction of essay left to complete = Words left to write / Total word count
Fraction of essay left to complete = 360 / 600
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 120:
Fraction of essay left to complete = (360 ÷ 120) / (600 ÷ 120)
Fraction of essay left to complete = 3 / 5
This means that she has completed 2/5 of the essay so far (which is the equivalent fraction of 240/600).
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Identify the quadratic function(s). (Select all that apply.)
A. 2b(b - 7) + b = 0
B. (4a + 2)(2a - 1) + 1 = 0
C. 2y + 2(3y - 5) = 0
D. 8 - 5x = 4(3x - 1)
There are two quadratic functions as A. 2b(b - 7) + b = 0 and B. (4a + 2)(2a - 1) + 1 = 0.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
A. 2b(b - 7) + b = 0 is a quadratic function because it can be simplified to the form of ax² + bx + c = 0 where a, b, and c are constants and x is the variable. In this case, a = 2, b = -13, and c = 0.
B. (4a + 2)(2a - 1) + 1 = 0 is also a quadratic function because it can be simplified to the form of ax² + bx + c = 0. In this case, a = 8, b = -2, and c = 1.
C. 2y + 2(3y - 5) = 0 is not a quadratic function because it can be simplified to the form of mx + b = 0 where m and b are constants and x is the variable.
D. 8 - 5x = 4(3x - 1) is not a quadratic function because it can be simplified to the form of mx + b = 0 where m and b are constants and x is the variable.
Thus, the correct answer would be options A. 2b(b - 7) + b = 0 and B. (4a + 2)(2a - 1) + 1 = 0.
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