The properties of the graph of a function include domain, range, symmetry, asymptotes, intercepts, increasing or decreasing, continuity, smoothness, behaviour at infinity and shape.
1) Domain: The set of all input values (x-values) that produce a valid output (y-value) for the function.
2) Range: The set of all output values (y-values) that can be produced by the function for any valid input value in the domain.
3) Symmetry: A graph may be symmetric with respect to the x-axis, y-axis, or origin.
4) Asymptotes: A line that the graph of a function gets arbitrarily close to, but never touches.
5) Intercepts: The points where the graph of a function crosses the x- and y-axes.
6) Increasing or Decreasing: A function can be increasing over a certain interval, decreasing over a certain interval, or both.
7) Continuity: A function is continuous if its graph has no breaks or gaps.
8) Smoothness: A function is smooth if its graph has no sharp corners or links.
9) Behavior at Infinity: The behavior of a function at positive or negative infinity can be determined by analyzing the degree and leading coefficient of its equation.
10) Shape: The shape of a graph can be used to classify functions as linear, quadratic, exponential, logarithmic, etc.
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Help needed please and thank you
Answer:
see image
Step-by-step explanation:
Right at the point (1,2) there's a nice point. Going up and right along the line there's another nice point at (5,5)
To get from one point to the next, you can draw a stair-step line that goes up3 and over4. The slope is up3/over4.
m = 3/4
The slope is 3/4. See image.
Mr Davis is creating a spice mixture for a recipe.2/5 of the spice mixture was oregano. 1/5 of the mixture was basil. The rest of the mixture was chilli powder
Answer:2/5
Step-by-step explanation:
2/5+1/5 equals 3/5, so if the rest of the mixture is chili powder, it would be 2/5
A forest covers 78,000 acres. A survey finds that 0. 4% of the forest is old-growth trees. How many
acres of old-growth trees are there?
There are
acres of old-growth trees.
Answer:
There would be 312 acres of old tree growth for 0.4% of the forest. There would be 31.2 acres of old tree growth for 0.04%. I wasn't sure if you meant 0.4 or 0.04.
What is the domain of the following function?
Therefore , the solution of the given problem of equation comes out to be each diagonal measures 8.4 units in length..
Define equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.
Here,
Given: 16x + 2 = 36x - 6
8 = 20x
x = 8/20,
simplifying to 2/5, or 0.4
You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.
Re-enter the value of x into a single of the equations.
=>16(0.4) + 2
=>6.4 + 2
=>8.4
To make sure, confirm with the other diagonal.
=>36(0.4) - 6
=>14.4 - 6
=>8.4
Each diagonal measures 8.4 units in length..
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The complete question is "To find the diagonal x value by the given equation 16x + 2 = 36x - 6 "
50PTS 50PTS don’t explain just answer.
Answer:
[tex] \sf \: x = 7[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of x.
Forming the equation,
→ 2x + 5 = 3x - 2
Then the value of x will be,
→ 2x + 5 = 3x - 2
→ 2x - 3x = -2 - 5
→ -x = -7
→ [ x = 7 ]
Hence, the value of x is 7.
A pizza delivery driver must make three stops on her route. She will leave the restaurant and travel 4 miles north to the first house. The next house is 6 miles away in the direction of east. She delivers the last pizza to the third stop, which is 5 miles south of the restaurant before she returns to the restaurant to pick up more pizza. What is her displacment for the entire trip
The displacement of the pizza delivery driver for the full journey is therefore 6.08 miles.
The pizza delivery driver's displacement for the entire trip is the total distance and direction that she travels from the restaurant to her last delivery and back.
To find her displacement, we can use the Pythagorean theorem to find the total distance from the start to the endpoint.
The displacement is the distance between the start and end point and the direction of the trip. Here we can see that she traveled 4 miles north, 6 miles east, and 5 miles south,
To find the displacement we will use the Pythagorean theorem (ax2 + bx2 = cx2)
where c is the displacement and a and b are the east-west and north-south distances respectively.
so, a = 6 miles (east-west)
b = (4 miles - 5 miles) = -1 miles (north-south)
so, c = √(ax2 + bx2)
c = √(6x2 + (-1)x2)
c = √(36 + 1)
c = √(37)
c = 6.08 miles
So the pizza delivery driver's displacement for the entire trip is 6.08 miles.
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What is line segment in maths class 7?
A line which is confined between two endpoints is known as a line segment. In other words, we can say that a line segment is a portion of a line that is connected by two points.
The length of the line segment does not vary and the distance between them does not change. The units in which a line can be calculated in centimetres, millimetres, meters, inches, or feet.
The difference between a line segment and a line is that the line segment had two endpoints while the line extends indefinitely. When only one side of the line has an endpoint, it is called a ray or a half-open line segment.
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Darnell and Hector ride their bikes at constant speeds. Darnell leaves Hector's house to bike home. He can bike the 8
miles in 32 minutes. Five minutes after Darnell leaves, Hector realizes that Darnell left his phone. Hector rides to catch
up. He can ride to Darnell's house in 24 minutes. Assuming they bike the same path, will Hector catch up to Darnell
before he gets home?
a. Write the linear equation that represents Darnell's constant speed.
i need this ASAP
Darnell's constant speed, as determined by the solution, is 20 miles per hour.
What is the process of linear algebra?It covers linear transformations more broadly as well as vectors, matrices, and vector spaces. One area of mathematics is linear algebra. In comparison to other areas of mathematics that are frequently driven by innovative ideas and unresolved problems, linear algebra is a discipline that is very well understood.
According to the given information:Distance=8 miles
Time taken is=32 minutes
speed=distance/time
speed=15 miles/hour
Darnel has travelled a distance of 1.5x5/60=0.125 miles in under five minutes.
Hector bicycle speed = distance/time
hector speed of bike= 20 miles/hour
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help help help help use slope form to write the equation of a line that passes through the point (7,-16) with slope 3.
required equation is, y=3x-37.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Here, given that,
we have to find,
the equation of a line that passes through the point (7,-16) with slope 3.
we know,
y = mx+c
i.e. -16 = 3*7+c
so, c= -37
hence, required equation is, y=3x-37.
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How to find the legs of a 45 45 90 triangle given the hypotenuse?
If the hypotenuse is given to the 45 45 90 triangles, the leg of the triangle is calculated after dividing the hypotenuse by [tex]\sqrt{2}[/tex].
The 45, 45, and 90 triangle is a type of isosceles triangle where the two legs are the same as each other and other non-right angles are both 45 degrees. Most of the time, Pythagoras' theorem is used for finding out the missing legs and hypotenuses of 45, 45, and 90 triangles.
If the leg of the triangle is equal to a, then:
The second leg is also equal to a;The hypotenuse is a√2;The area is equal to a²/2; andThe perimeter equals a(2 + √2).Read more about the isosceles triangle:
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raph of the function f(x) = (x+2)(x+6) is shown
-4 2
4
2+
N
-2
-6
2
4 6
X
What is true about the domain and range of the function?
O The domain is all real numbers, and the range is all
real numbers greater than or equal to -4.
O The domain is all real numbers greater than or equal
to
-4, and the range is all real numbers.
O The domain is all real numbers such that -6 ≤x≤-2,
and the range is all real numbers greater than or equal
to-4.
O The domain is all real numbers greater than or equal
to
-4, and the range is all real numbers such that -6 sx
≤-2.
The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = (x+2)(x+6) is defined for all real numbers, so the domain is all real numbers.
What do a function example's range and domain mean?
A straightforward function, such as f(x) = x2, can have a domain (what goes in) of just the counting numbers 1, 2, 3, etc., and a range (what comes out) of the set 1, 4, 9, etc. Another function, g(x) = x2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...
The range of a function is the set of all possible output values (y-values) produced by the function. The function f(x) = (x+2)(x+6) is a polynomial, and all polynomials of the form (ax^2 + bx + c) with real coefficients (a,b,c) have range is all real numbers. The range of the function f(x) = (x+2)(x+6) is also all real numbers.
So the answer is
The domain is all real numbers, and the range is all
real numbers.
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A six-foot long ladder is leaning against a wall. The bottom of the ladder is 3 feet away from the wall. How high up the wall is the ladder
The six-foot long ladder is 3√5 feet high up the wall having 3 feet distance from bottom of the ladder.
How to find height ?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the ladder is the hypotenuse, and the wall and the ground make up the other two sides.
The ladder is 6 feet long, and the bottom of the ladder is 3 feet away from the wall, so the triangle is a 3-4-5 right triangle, which means the wall is 3 feet high.
So, if we square the length of the ladder (6^2 = 36)
The length of the base (3^2 = 9),
and add them together, then take the square root of that, we get the height of the wall.
sqrt(36+9) = sqrt(45) = 3*sqrt(5)
so the ladder is 3√5 feet high up the wall.
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1/4 + 3/8 (i would love a explanation)
what is the answer to 415÷23
Answer: 18
Step-by-step explanation:
Answer: 18.04347826086957
Step-by-step explanation: you could use a calculator too-
What must be added to 5x³ 2x² 6x 7 to make the sum X 3x² x 1?
To make the sum X 3x² x 1, you must add -5x³ -2x² -6x -7 to 5x³ 2x² 6x 7.
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign.
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Is polynomial Y^4+4Y^2+5 have zeroes or not?
Yes, polynomial Y^4+4Y^2+5 has zeroes. Its zeroes can be found by factoring or using the quadratic formula: Y = -2 +/- sqrt(4-5) / 2 = -1 +/- sqrt(-1) / 2 = -1 +/- i/2.
[tex]Y^4+4Y^2+5[/tex]
=[tex](Y^2+1)²-3[/tex]
=([tex]\sqrt{Y^2+1-sqrt3}[/tex])([tex]\sqrt{Y^2+1+sqrt3}[/tex])
=(Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1)
=(Y+ sqrt3)(Y-sqrt3)(Y²-1)
=(Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1)
=0
Therefore the zeroes are Y=-√3, Y=1, Y=√3, Y=-1
Polynomial Y^4+4Y^2+5 is a fourth degree polynomial equation and can be solved by factoring or using the quadratic formula. To solve this equation by factoring, we need to use the difference of squares method. First, we rewrite the equation as (Y^2+1)²-3. Then we factor out the square of the binomial (Y^2+1): (Y^2+1-sqrt3)(Y^2+1+sqrt3). Next, we expand the first binomial to get (Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1). Then, we factor out the second binomial from the first two terms to get (Y+ sqrt3)(Y-sqrt3)(Y²-1). Finally, we expand the last binomial to get (Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1). This results in a product of zero, which means the equation has zeroes. The zeroes are Y=-√3, Y=1, Y=√3, and Y=-1.
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The admission fee to the carnival is $4. 50 for children and $7. 25 for adults. If a large group purchased 28 tickets and paid $159 how many adult tickets did they purchase?
The number of adult tickets purchased is 12.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Let no. of adult = x
No. of children = 28 -x
So, 7. 25 * x + (28 - x) *4. 50 = 159
⇒2.75x +126=159
⇒2.75x =33
⇒x=33/2.75
x=12
Hence, the number of adult tickets purchased is 12.
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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.
The table shown represents a linear relationship. x 0 1 3 4 y −8 −6 −2 0 Based on the table, what is the equation of the linear relationship in slope-intercept form? y = 2x − 8 y = 2x + 8 y = −2x + 4 y = −2x − 4
Based on the table, an equation of the linear relationship in slope-intercept form include the following: A. y = 2x − 8
What is the slope-intercept form?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept.Next, we would determine the slope of the data points in this table as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-6 - (-8))/(1 - 0)
Slope, m = 2/1
Slope, m = 2.
At point (0, -8), an equation of this line can be calculated in slope-intercept form as follows:
Note: The y-intercept is equal to -8.
y = mx + c
y = 2x + (-8)
y = 2x - 8.
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Answer:
A. y = 2x − 8
Step-by-step explanation:
An item is regularly priced at $90. It is now priced at a discount of 40% off the regular price. What is the price now?
Answer:
Price after discount is $54
You save $36
Step-by-step explanation:
best buy has a sale on video games and dvds for labor day weekend Katie bought 2 games and 3DVD's and spent $134 dollars Emily bought 1 less game but 2 more DVD's and spent $179 how much does each DVD and game cost
Each video game = $19 and each DVD = $ 32
What is equation?An equation is a mathematical statement that represent that two expressions are equal. An equation can be formed by one or more variables along with numerical terms.
How to solve the equation as stated in the question?let, x denotes the cost of each video games.
y denotes the cost of each DVD
Katie bought 2 games and 3 DVD and total spent $134.
the equation can be written as 2x + 3y = $134 .......equation 1
Emily bought 1 less video game than Katie that means she bought 1 game.
and 2 more DVD than Katie that means 5 DVD bought by Emily.
total spent of Emily = $179
The equation will be x + 5y = $179...... equation 2
in order to solve the two equations by addition method
we multiply by 2 to the second equation.
2x + 10y = 358
the first equation 2x +3y = 134
2x + 10y = 358
- - -
by subtracting we get,
- 7y = -224
y = 32
from the 2nd equation we get x = -5×32 + 179
x = 19
each video game cost $ 19 and each DVD cost $ 32
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How do you find the area of the pre image and the image?
Coordinates for the pre-image are X(3,18) Y(18,18) and Z(18,9) and the image coordinates are X’(1,6) Y’(6,6) Z’ (6,3)
and what is the relationship between the two areas?
Answer: To find the area of the pre-image and the image, you can use the coordinates of the vertices of the shapes to calculate the lengths of the sides and use the formula for the area of a triangle:
Area = (base * height)/2
For the pre-image, the coordinates are X(3,18) Y(18,18) and Z(18,9). The base of the triangle is the distance between X and Z, which is 18 - 3 = 15. The height of the triangle is the distance between Y and Z, which is 18 - 9 = 9. The area of the pre-image is therefore:
Area = (15 * 9)/2 = 67.5
For the image, the coordinates are X’(1,6) Y’(6,6) Z’ (6,3). The base of the triangle is the distance between X’ and Z’, which is 6 - 1 = 5. The height of the triangle is the distance between Y’ and Z’, which is 6 - 3 = 3. The area of the image is therefore:
Area = (5 * 3)/2 = 7.5
The relationship between the two areas is that the area of the image is smaller than the area of the pre-image. This is because the image has been scaled down in size relative to the pre-image. The amount by which the image has been scaled down can be calculated by dividing the area of the image by the area of the pre-image:
Scale factor = area of image / area of pre-image = 7.5 / 67.5 = 0.11
This means that the image has been scaled down by a factor of 0.11 relative to the pre-image.
Step-by-step explanation:
Answer:
preimage area: 67.5 square unitsimage area: 7.5 square unitsimage area is 1/9 of preimage area, the square of the scale factorStep-by-step explanation:
You want to know the areas and their relationship of the preimage with coordinates X(3,18), Y(18,18), and Z(18,9), and the image with coordinates X’(1,6), Y’(6,6), Z’ (6,3).
TrianglesWhen you plot the points on a graph, you see they define right triangles. Each has sides aligned with the x- and y-axes, so it is easy to find their dimensions by counting grid squares or subtracting coordinates.
The preimage triangle is 18-3 = 15 units in the x-direction, and 18-9 = 9 units in the y-direction.
The image triangle is 6-1 = 5 units in the x-direction, and 6-3 = 3 units in the y-direction.
We notice that both the coordinates and the dimensions of the image triangle are 1/3 those of the preimage triangle.
AreasThe area of each triangle is given by the formula ...
A = 1/2bh
Using the dimensions we found above, the areas are ...
preimage area: 1/2(15)(9) = 135/2 = 67.5 . . . . square units
image area: 1/2(5)(3) = 15/2 = 7.5 . . . . square units
Relationship
We have observed that the image dimensions are 1/3 those of the preimage. The image area is 7.5/67.5 = 1/9 of that of the preimage. This value is the square of the scale factor of the dimensions,
Hello what x of a triangle
Solving for X in a Right Triangle
Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X
How can I do math fast?
To do Maths fast follow the steps:
Read attentively, comprehend, and specify the category of the issue.Draw a diagram of your issue.Create a plan to resolve it.Resolve the issue.What is Maths ?Mathematical subjects include quantities and their changes, forms and the spaces in which they are contained, formulae and associated structures, and numbers.
The scientific study of numbers, forms, and their meanings is known as mathematics. The majority of individuals use maths every day to measure and count. Geometry, algebra, and calculus are all forms of mathematics; nonetheless, they are typically referred to as single.
There are many ways to solve math problems, but a three-step technique is a streamlined approach that may assist anybody in solving even the most challenging issue.
Read attentively, comprehend, and specify the category of the issue.Draw a diagram of your issue.Create a plan to resolve it.Resolve the issue.To learn more about Maths refer to :
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You have $9 to spend on lip balm and hand sanitizer. The equation $1.5x+2.5y=9$ represents this situation, where x is tubes of lip balm and y is bottles of hand sanitizer. How many tubes of lip balm can you buy when you do not buy any bottles of hand sanitizer?
Answer:
6 tubes of lip balm
Step-by-step explanation:
We can start solving this problem by isolating the variable x.
Given the equation 1.5x + 2.5y = 9, and we know that y = 0 (because we're not buying any bottles of hand sanitizer), we can substitute this into the equation:
1.5x + 2.5(0) = 9
Simplifying this, we get:
1.5x = 9
To solve for x, we can divide both sides of the equation by 1.5:
x = 9/1.5
x = 6
So we can buy 6 tubes of lip balm if we do not buy any bottles of hand sanitizer
A truck uses 2.5 litres of fuel to travel 8 kilometres.
a How far will the truck travel on 1 litre of fuel?
b How far will the truck travel on 120 litres of fuel?
Answer:
a：20 km
b：384
Step-by-step explanation:
a：
[tex] \frac{2.5}{ 8} = \frac{1}{x} [/tex]
[tex]x = 20[/tex]
b：
[tex] \frac{2.5}{8} = \frac{120}{y} [/tex]
[tex]y = 384[/tex]
Convert one three fifths to a percent find that percent of 30 Divide your answer by 25% of 16
Answer:
40%
Step-by-step explanation:
1 and 3/5 as a fraction is 8/5 which as a percent is 160%.
25% of 16 is 4
160%/4 = 40%
m(x)=−2(x−3)(x−9) solve for y-intercept
Answer:
(0, -54)
Step-by-step explanation:
We find the y-intercept by plugging in 0 for x:
[tex]y=-2(x-3)(x-9)\\y=-2(0-3)(0-9)\\y=-2*-3*-9\\y=6*-9\\y=-54[/tex]
According to the 2000 U.S. Census, 7 out of every 25 homes are heated by electricity. At this rate, predict how many homes in a community of 12,000 would be heated by electricity.a.6,725 homesb.3,100 homesc.3,360 homesd.4,020 homes
In 7/25 households, electricity is used for heating. By multiplying by 20,000. You'll receive 3,360. In light of this, the 2000 census indicates that 3,360 out of 12,000 houses use electricity for heating.
How many homes use electricity for heating in U.S. Census?Because we've already done it 7 out of every 25 residences are heated by electricity, according to the 2000 U.S. census.At this rate, we must determine how many residences in a 12000-person neighbourhood would be heated by electricity.Let x be the number of homes in a neighbourhood that would be heated by electricity.There being a direct variation
The result is that , A neighbourhood of 12000 people with 3360 dwellings that use electricity for heating. In 7/25 households, electricity is used for heating. By multiplying by 20,000. You'll receive 3,360. According to the 2000 Census, 3,360 dwellings out of 12,000 are heated by electricity.
[tex]$\frac{7}{25}=\frac{x}{12000}$[/tex]
[tex]$x={7 \times 12000}/{25}$$x=3360$[/tex]
As a result, 3360 households out of the 12000 in the community use electricity for heating.
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4. Find the value of each variable in the parallelogram.
Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.
A linear equation is precisely what?The algebraic equation y=mx+b stands in for a linear equation. The slope is m, and B is the y-intercept. The last phrase referred to a "simple formula with two elements" where both y and x are variables. Bivariate linear equations are calculations involving two variables. Here are a few examples: The outcomes are 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3. If the answer to a mathematical equation is in the form y=mx+b, where m denotes the slope and b the y-intercept, the equation is said to be linear.
Here,
Given :
According to parallelogram laws
adjacent side sum is 180 degree
=> 4y + 3x-18 = 180
=> 4y+3x = 162
and
2x+12+3z = 180
=> 2x + 3z = 168
and
=> 3x+3z = 162
=> x + z =54
=> z = 54-x
So,
2x + 3(54-x) = 168
=> 162 - 3x+2x =168
=> -x = 6
or x =-6
and
z = 60
and
y = 162 - 3x /4
=> y= 162 +18 /4
=> y =180/4
=> y = 45
Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.
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