So, Mathilda should mix 600 grams of OMT with 300 grams of WMT to sell the resulting mixture at Php 1.80 per gram.
Define the unitary method.The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.
The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
What is a unit?A unit is a quantity with a fixed magnitude that is used to gauge the sizes of other quantities that behave similarly.
The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grams (g). Milliliter (ml) and liter are used to measure volume (L).
Let x be the amount of OMT powder in grams. We know that the total amount of powder in the mixture is x + 300 grams since Mathilda is mixing x grams of OMT with 300 grams of WMT.
(x * Php 2 + 300 * Php 1) / (x + 300) = Php 1.80
Solving for x, we can get the amount of OMT powder in grams:
x = (300 * Php 1.80 - 300 * Php 1) / (Php 2 - Php 1.80) = 300 * (Php 1.80 - Php 1) / (Php 2 - Php 1.80) = 600
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For what value of k does the pair of linear equations 3x +5y 3 6x KY 8 do not have any solution?
The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 does not have any solution for any value of k.
We can rewrite the equations as:
3x + 5y = 3
6x + ky = 8
To solve this system, we need to eliminate one of the variables. To do this, we can multiply the first equation by 2 and the second equation by -3. This will give us:
6x + 10y = 6
-18x - 3ky = -24
Now we can add the two equations together and get:
-12x - 3ky = -18
Since the coefficient of x is 0, this equation does not have any solution for any value of k.
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3) Breanna thought of a number, subtracted 4 from it, and then multiplied her answer by 3. She got
a final number of 24. What was her starting number?
John and Wesley both work for telephone companies installing internet connections into new homes, but they do not work for the same company. John's paycheck at the end of the month includes his base pay of $2,000 and his commission of $65. 25 for each installation he makes that month. Wesley is paid $380 plus a commission of $105. 75 for each installation he makes each month. In September of last year, they both made the same number of installations and they both earned the same amount of money
The number of installations in September were forty that lead to John and Wesley earning same amount of money.
Let the number of installations be x. The equation of be formed for each paycheck will be -
Total paycheck = base pay + number of installations × comission on each installation
The total paycheck and number of installations is same. So equating the equations by keeping x.
2000 + 65.25x = 380 + 105.75x
Rewriting the equation -
105.75x - 65.25x = 2000 - 380
Performing subtraction on each side of the equation
40.5x = 1620
x = 1620/40.5
Performing division on Right Hand Side of the equation
x = 40
There were 40 installations.
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3. ) Mary is the director of the Washington Performing Arts Center. Her employer offers a pension. Mary’s employer uses a formula to calculate the pension. Marina is planning on retiring at the end of this year after 30 years of employment. A retiring employee receives 1. 6% of his or her average salary for the last 5 years of employment multiplied by the number of years worked. Mary would receive this amount each year until her death. Her salaries for the last 5 years are $80,900; $90,200; $95,000; $99,000; and $104,000. Calculate Marina’s pension
Marina's pension amount is calculated by multiplying 1.6% of her average salary for the last 5 years by the number of years she has worked, which is 30.
1.6% x $80,900 = $1,282.40
1.6% x $90,200 = $1,444.32
1.6% x $95,000 = $1,520.00
1.6% x $99,000 = $1,584.00
1.6% x $104,000 = $1,664.00
Total = $7,604.72
Pension amount = $7,604.72 x 30 years
= $228,141.60
Marina's pension amount is determined using a formula set by her employer, the Washington Performing Arts Center. This formula takes into account her average salary for the last five years, which is $469,100, and multiplies it by 1.6%, then by the number of years she has worked for the Center, which is 30. This results in a pension amount of $228,141.60. This amount will be paid each year until her death. This pension amount is calculated based on the salaries she has earned over the past five years, which include $80,900; $90,200; $95,000; $99,000; and $104,000.
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The sales tax in one town is 8%.So, the total cost of an item can be written as c=0.08cents .what is the total cost of an that sells for $12 ?its due tmrr asap
Answer: 12.96
Step-by-step explanation: you should multiply 12 * 0.08 = 0.96
then just add 0.96 + 12 = 12.96
the sum of 1/4 a number and 5 is 3. What is the number?
Answer:
x = -2/4 = -1/2
Step-by-step explanation:
The sum of 4 times a number and 5 is 3.
Let sum = +
times = *
is means =
a number = x
So, 4x + 5 = 3. Then we solve it !
Subtract 5 to both sides to get 4x = - 2.
Next, we divide 4 to both sides to get x = -2/4 = -1/2
Answer:
The number is -8
Step-by-step explanation:
You can set up the question as (x/4)+5 = 3
x/4 = -2
x = -8
5. There are 42 teachers who work in a school. On Monday, 29 teachers were present. What percentage of the teachers showed up for work?
Answer:
69%
Step-by-step explanation:
There are 42 teachers who work in a school. On Monday, 29 teachers were present. The percentage of the teachers that showed up for work will be:
= 29 / 42 × 100
= 69%
Answer:
Step-by-step explanation:
In any case where you're asked, "what percentage of A is B?" you can simply divide the number B by the A. The decimal you get is the answer. for example, if you're being asked what percentage 12 is of 25, you just divide 12 by 25 to get 0.48, which translates to 48 percent. in your case, 29/42 is 0.69 (rounded down from 0.6904761905) which equals 69%.
In a case where B is larger than A, you still do the same, only with the addition of the whole number. Ex: what percentage of 25 is 86?
86/25 is 3.44, so your answer is 344%.
Hope this helped :)
What will be the coefficient of XYZ in the product of 2xy 3zx and Y 2z )?
The coefficient of XYZ in the product of 2xy 3zx and Y 2z is 0.
The formula for coefficient is C = a*b, where a and b are the coefficients of the terms being multiplied.
In the given example, the coefficients for the terms being multiplied are 2 for 2xy, 3 for 3zx, and 0 for Y 2z. Since 0 multiplied by any number is 0, the coefficient of XYZ in the product is 0.
Mathematically, this can be expressed as:
C = 2*3*0 = 0
Therefore, the coefficient of XYZ in the product of 2xy 3zx and Y 2z is 0.
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What is the slope of the line? (30 points)
Answer:
Slope = -1 or (-1/1)
Step-by-step explanation:
slope = m
Point 1: (0, 2); Point 2: (2, 0)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 0 - 2 -2
m = ----------- = ---------- = ------- = -1 or (-1/1)
x₂ - x₁ 2 - 0 2
I hope this helps!
Reason Abstractly Determine if the
statement is true or false. Justify your
response.
The point (1, r) on the graph of a proportional
relationship shows the unit rate r.
Yes, the statement is true. If a proportional relation has the point (1, r), then r is the unit rate.
Is the statement true or false?Here we have the following statement:
"The point (1, r) on the graph of a proportional relationship shows the unit rate r."
First, remember that a proportional relationship between two variables x and y can be written as:
y = k*x
There k is what we call the constant of proportionality or the unit rate.
If we evaluate that equation in x = 1, we will get:
y = k*1
y = k
Then we have the point (1, k).
In this case, we know that our proportional relation has the point (1, r), comparing this with the case above, we can see that r is the unit rate of the proportional relation.
So the statement is true.
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What is similarity example?
When two figures have the same shape but differ in size, they are said to be similar figures. In other words, two figures are said to be comparable when they have many characteristics but aren't necessarily identical.
For instance, despite appearing to be the same size, the sun and moon are actually different sizes. However, because both of our figures are circular in shape, we are comparable figures. This phenomenon is seen as a resemblance property while taking shape and distance into consideration.
When two shapes, such triangles, polygons, or quadrilaterals, have the same dimension or common ratio but a different size or length, they are referred to as comparable figures in geometry.
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Rewrite 16r²s² as a power of a product.
The solution is
[tex]16r^2s^2[/tex] as the product of power is written as [tex](4rs)^2[/tex]
How would you characterize a product's strength?The power of a product rule states that [tex](a^m)(a^n) = a^(m+n)[/tex], where "a" is the base, "m" is the exponent of the first term, and "n" is the exponent of the second term. This rule allows us to simplify expressions where multiple variables are being raised to a power and multiplied together by adding the exponents.
For example, [tex](a^2)(a^3) = a^(2+3) = a^5[/tex].
It is also important to remember that when we are using the power of a product rule, the bases must be the same. If we have different bases, we cannot use this rule.
For example, [tex](a^2)(b^3) = a^2 * b^3, not a^(2+3) = a^5[/tex].
Rewritten as power of product:
[tex]16r^2 s^2= 4*4*r*r*s*s\\16r^2s^2= 4^2*r^2*s^2\\16r^2s^2=(4rs)^2[/tex]
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Equivalent fractions for 1 3/4 and 1 4/5 using 20 as the common denominator
Answer:
35/20 and 36/20
Step-by-step explanation:
please awnser the question below
The various statements regarding the given scatter plot is checked and found to be true or false.
What is a scatter plot?
A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities.
1)The equation of the line is y = 2500x - 125.
From the graph we can take two points on the line,
( 2,2250) and ( 10,1250)
Standard equation of line is y = mx + b
where b is y - intercept and m is slope
m = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex] = [tex]\frac{1250 - 2250}{10 - 2}[/tex] = -125
From graph, b = 2500
Equation of line is
y = -125x + 2500
Therefore the given equation is false.
2) The group of hikers descends about 250 feet every minute.
From the graph it is evident that for the interval between two points on y-axis is 250 feet and interval of x-axis is 1 minute.
So the hikers descend 250 feet every minute.
Therefore the given statement is true.
3) The hikers began at the elevation of 2500 feet.
The x-intercept of the graph is 2500 feet.
So the beginning elevation is 2500 feet.
Therefore the statement is true.
4) The graph shows a negative association.
Since the line in the graph is going down and the slope is negative, the graph shows a negative association.
Therefore the statement is true.
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Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. -2 1 1 - 4 3 4 ; 2 = -1,4 -2 2 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. For P=___ D= 0 4 0 0 0 4 -1 0 0 O B. For Pa = ___ D = 0 -1 0 0 04 OC. O The matrix cannot be diagonalized.
The correct answer is option A. For P= -1/2 0 1/2 1/2 0 -1/2 0 0 1 D= 0 4 0 0 0 4 -1 0 0. The matrix can be diagonalized using the eigenvectors.
To diagonalize the matrix, the eigenvectors must be found first. The eigenvectors can be found by solving the characteristic equation and finding the eigenvalues. The eigenvalues of the matrix are 2 and -1. The eigenvectors associated with each eigenvalue are determined by solving the eigenvalue equation.
The eigenvectors for the matrix are [1, -2], [1, 2], [1, 0], and [0, 1]. After the eigenvectors are found, the matrix can be diagonalized by constructing the transformation matrix P. The transformation matrix P is composed of the normalized eigenvectors. The transformation matrix P is: P=[-1/2, 0, 1/2, 1/2, 0, -1/2, 0, 0, 1], and the diagonal matrix D is composed of the eigenvalues.
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A construction worker is tasked with tiling two square rooms, room A and room B. Room B has side lengths that are double the side lengths of room A. The construction worker uses one box of tiles to complete the flooring of room A.
How many boxes of tiles will they need to complete the flooring of room B? Assume the boxes of tiles are identical.
Therefore, since the area of room B is four times the area of room A, four boxes of tiles will be needed to complete the flooring of room B.
Define Volume and Area.The area is the volume a flat, two-dimensional item occupies in a plane. The space occupied by a three-dimensional object is referred to as its volume. Area is measured in square units. Volume is measured in cubic units.
What is Surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
Since the side lengths of room B are double the side lengths of room A, the area of room B is four times the area of room A.
The number of tiles needed to cover a floor is equal to the area of the floor divided by the area of each tile.
Since the boxes of tiles are identical, the number of tiles in each box must also be identical.
Therefore, since the area of room B is four times the area of room A, four boxes of tiles will be needed to complete the flooring of room B.
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A mum of 5 children has truncated her children’s heights in metres to 2 decimal places, and written them down in the table.
a) Write down the intervals within which each child’s actual height lies.
b) Write down the minimum and maximum height difference between the tallest and shortest child.
Each child's real height falls between 1.60 and 1.28, with the tallest child's height difference at 0.32 and the smallest child's height difference at 0.04 respectively.
a) The ranges that each child's actual height falls within is ;
Here, Daisy is 1.28 meters short while Isaac is 1.56 meters tall at his tallest.
b) The largest height difference between the tallest and shortest child is 1.60-1.28 =0.32m , while the smallest height difference is 1.60-1.56 = 0.04meters.
Error interval: What does it mean?A number's possible range of values before being rounded or truncated is known as an error interval. Inequalities are frequently used to express error intervals as a range having a lower bound and an upper bound.
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PLEASE HELP ME
6.
Dom is selling pizza at Hoopfest to help him raise money to go on a road trip. He wants each topping to increase the total price at a rate of $1.25. When someone ordered a 3-topping pizza the price was $16.25. Write an equation to represent this data.
Answer : if each topping is 1.25 then multiply that by 3 because there's 3 toppings on the pizza and if the total was 16.25 the original price of the pizza is 12.5. I hope this was the answer you were looking for a good luck :)
Step-by-step explanation:
A store marks up a laptop 150% from its original price of $399. There is a sale for 25% off all items in the store. What is the sale price for the computer
Answer:
multiply the original price ($299) by the first markup percentage (150%)
299*1.50= $448.50
that is markup price!
then you have to do the sale % (25%)
so you'll multiply your (25%) by your new price ($448.50)
448.50*.25= $112. 125
then you will subtract the sale price ($112.125) by the upcharged price ($448.50)
448.50-112.125= 336. 375
= $336. 38(round off)
For what value of a the system of linear equations Ax 3y a 3 12x ay A has no solutions?
The system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.
To determine if the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a, we can use the elimination method.
We want to eliminate one of the variables, so let's start by multiplying the first equation by 3 and the second equation by -1.
This gives us:
3Ax + 9y = 3a, -3x - ay = -A.
Now we add the equations together to get:
2Ax + 8y = 3a - A.
Now we can see that the equation is not solvable as there is no value of a that will make the equation true. Therefore, the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.
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can someone help me with this but please with details on how u got the answer:
The function’s average rate of change over the interval from x: 1 to x:2 is:
The function’s average rate of change over the interval from x = 1 to x = 2 is: -2. The correct option b.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
We have the interval from x = 1 to x = 2.
To find the function’s average rate of change over the interval from x = 1 to x = 2 is:
We interpreted the interval in the coordinate form.
The curve from (1, 2) to (2, 0) is a straight line.
And the slope of the line is the average rate of change of the function.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (0-2) / (2-1)
m = -2/1
m = -2
Therefore, the average rate of change is -2.
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7{-7+8[5-3(4+6)]-9(9-4)}
Answer:
-1764
Step-by-step explanation:
use BODMAS rule
⇒7{-7+8[5-3(4+6)]-9(9-4)}
solve round brackets
⇒7{-7+8[5-3(10)]-9()}
multiply 3 by 10 within the square bracket
⇒7{-7+8[5-30]-9(5)}
solve square bracket
⇒7{-7+8[-25]-9(5)}
move to curly brackets and multiply first
⇒{-7-200-45}
subtract
⇒7{-252}
multiply
⇒-1764 Answer
hope that helps...
What is the value of aaa when we rewrite 6^{x}6 x 6, start superscript, x, end superscript as ax4 ?
The equation can be rewritten as: [tex]ax^4 = (log(6))(2^4)[/tex]
Therefore, [tex]a = log(6) \ and\ x=2[/tex]
What is logarithm?A logarithm is a mathematical function that describes the relationship between a number and its exponent. It is the inverse operation of exponentiation. Logarithms are typically written as log base b, where b is the base of the logarithm and is a positive number.
The logarithm of a number x to base b is denoted as [tex]logb(x)[/tex] and it is the exponent to which we need to raise the base b in order to get the number x.
For example, if we are given [tex]log10(100) = 2[/tex], this means that [tex]10^2 = 100[/tex].
The equation [tex]6^x * 6 * 6[/tex] can be rewritten as [tex]6^x * 6^2[/tex].
To convert 6^x to ax form, we need to take the logarithm of both sides of the equation:
[tex]log(6^x) = log(6^2)[/tex]
And we can simplify the equation as:
[tex]xlog(6) = 2log(6)[/tex]
So, the value of a is log(6) and the value of x is 2.
Therefore, the equation can be rewritten as:
[tex]ax^4 = (log(6))(2^4)[/tex]
Therefore, [tex]a = log(6)\ and\ x=2[/tex]
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What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required to be determined is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It is evident from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
Therefore, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Ultimately, it can be inferred that the greatest possible quotient as required is; 25.
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Carlos bought two packages of rope, each containing 12 feet of
rope. He needs to cut pieces of rope that are each 20 inches in
length. What is the greatest number of pieces that he can cut
from these two packages of rope?
1 foot = 12 inches
Answer: 14 pieces.
Step-by-step explanation: 1 foot = 12 inches
12 feet of rope = 144 inches of rope
144 / 20 = 7.2 = 7 sections can be cut from each package.
The greatest number of pieces from 2 packages = 14 pieces
Answer
14 pieces
Step-by-step explanation:
First you need to convert the 24 feet into inches. Do this by multiplying 24 (feet) by 12 (inches) since 1 foot has 12 inches in it and you have 12 feet. This means he has 288 inches of rope. Then divide 288 by 20 since he wants to see how many 20 inch pieces he can cut. You should get 14.4 but since it asks for the greatest number of pieces you need to round it down to 14 since he wants full 20 inch pieces.
The table shows a linear function. What is the rate of change?
Hours
Pay
1
18
1.5
23
2
28
2.5
33
3
38
Using the regression concept to find the equation and applying derivative, The rate of change is 10.
What do you mean by regression?Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. The dependant variable's predicted value in basic linear regression is given by the equation = b0 + b1x. In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X.
What do you mean by derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.
from the given data,
y= a + bx is our regression line.
a=8 and b =10
y=8+10x is the line.
derivate the line , we get,
[tex]\frac {dy}{dx} = 10[/tex]
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What is the name of 3 side?
The three sides of a triangle are referred to as the base, the height, and the hypotenuse.
The base and height of a triangle can be used to calculate the area of the triangle using the formula:
Area = (Base x Height) / 2
To calculate the hypotenuse of a triangle, the Pythagorean Theorem is used. The theorem states that the sum of the squares of the lengths of the two sides of a right triangle is equal to the square of the length of the hypotenuse.
The formula for the Pythagorean Theorem is:
a2 + b2 = c2
where a and b are the two sides of the triangle and c is the hypotenuse.
To calculate the hypotenuse of a triangle, the following steps are taken:
1. Measure the length of each side of the triangle.
2. Square the length of each side (multiply the length by itself).
3. Add the two values together.
4. Find the square root of the sum. This is the length of the hypotenuse.
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The figure shows two circles, with centers A and B, externally tangent at point C. The common tangents to the two circles meet at point P and AP = 30. If the radius of the circle with center A is 10, what is the length of BP?
The length of the line segment BP = 15 using the trigonometric ratio of sine for the angle P.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangles formed by points at P, A and the tangent to the bigger circle with its radius as base;
radius r = 10 and hypotenuse AP = 30
sinP = 10/30 {opposite/hypotenuse}
sinP = 1/3
Also for the smaller circle, with right triangle formed by points at P, B and the tangent to the smaller circle with its radius as base;
radius r and hypotenuse BP = 20 - r
sinP = r/(20 - r)
1/3 = r/(20 - r)
3r = 20 - r {cross multiply}
3r + r = 20 {collect like terms}
4r = 20
r = 20/4 {divide through by 4}
r = 5
BP = 20 - 5
BP = 15
Therefore, length of the line segment BP is derived using the trigonometric ratio of sine as 15.
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Limx→0 e^x -e^5/ x-5
Answer:e5
Step-by-step explanation:
Here you go
What are ideal and real solutions?
Solutions refers to the answer to the problem, Real Solutions are realistic and practical whereas ideal solutions are the best cases for the solutions.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
Ideal Solutions - Best cases, Usually not possible.
Real Solutions - Practical and possible to attain.
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