Solve by using substitution and graph.
X = 3y + 2
5x - 15y = 10
Answers
This system of equations has been solved graphically and by using substitution: it has infinitely many solutions.
How to graph the solution to this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x = 3y + 2 ......equation 1.
5x - 15y = 10 ......equation 2.
By substituting equation into equation 2, we have the following:
5(3y + 2) - 15y = 10
15y + 10 - 15y = 10
15y - 15y = 10 - 10 (infinitely many solutions)
Based on the graph (see attachment), we can logically deduce that the given system of equations has infinitely many solutions.
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Related Questions
given a two-dimensional pore geometry of packed squares as below, plot the porosity as a function of the averaging length scale. the black grains are separated by a distance equal to the grain size in the x and y directions. use a square as the averaging volume and the edge of the square as the averaging length scale. what is the representative elemental volume?
Answers
Porosity calculated as ratio of pore to total vol. Plot of porosity vs averaging length scale (edge of square used for averaging). Rep. elemental vol = vol of square used for averaging.
The porosity as a function of the averaging length scale can be calculated as follows:
Define the pore geometry: A two-dimensional pore geometry of packed squares is given, with black grains separated by a distance equal to the grain size in the x and y directions.Select the averaging volume: The averaging volume is defined as a square.Determine the porosity: The porosity is calculated as the ratio of the pore volume to the total volume of the material. In this case, the pore volume is the volume between the black grains and the total volume is the volume of the material.Plot the porosity as a function of the averaging length scale: The averaging length scale is defined as the edge of the square used for averaging. The porosity can be calculated for various values of the averaging length scale and plotted as a function of the averaging length scale.Representative elemental volume: The representative elemental volume is the volume of a single element (e.g. a square in this case) used in the averaging calculation. In this case, the representative elemental volume is equal to the volume of the square used for averaging.Learn more about geometry :
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using diagonals from a common vertex, how many triangles could be formed from the polygon pictured below tiiip
Answers
5 triangles could be formed from the polygon pictured.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The given figure is an irregular heptagon (7 unequal sides).
Now,
Taking a common vertex A we can draw the triangles as given below.
We see that,
There are 5 triangles that can be drawn.
Thus,
5 triangles can be formed.
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EX I: Calculate the sector area below.
Answers
The sector area for the figure below is 268.19.
What is area of a sector?The quantity of space included within the sector's perimeter is referred to as the sector's area in a circle. A sector always starts at the circle's center. The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle. The sector of a circle that most often symbolizes half of a circle is a semicircle.
The area of sector is given by the formula:
A = (pi)r² × α/360
where, r is the radius and α is the angle of the sector.
Substituting the value of r and α in the formula we have:
A = pi (16)² × 120/ 360
A = 268.19
Hence, the sector area for the figure below is 268.19.
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susan can pick 4 lbs of coffee beans in an hour or gather 2 lbs of nuts. tom can pick 2 lbs of coffee beans in an hour or gather 4 lbs of nuts. each works 6 hrs per day. if they only pick coffee, what is the maximum amount of coffee the two can gather in a day? if they only pick nuts, what is the maximum amount of nuts the two can gather in a day? write the answer as x lbs, y lbs.
Answers
Answer:
see below
Step-by-step explanation:
Susan
4lbs of coffee
2lbs of nuts
Tom
2lbs of coffee
4lbs of nuts
6 hrs per day.
if only coffee x = (4+2)*6=36lbs
if only nuts y = (4+2)*6=36lbs
- sports the distance between each base on a baseball infield is 90 feet. the third baseman throws a ball from third base to point p. to the nearest foot, how far did the player throw the ball?
Answers
The distance between the third base and the player is 150 feet.
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle of 90°. The sides of a right triangle (say a, b, and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
In the diagram attached, we can see the locations of the 1st base, 2nd base, 3rd base, and Home plate.
Since these four points form a square of which diagonals are equal in size.
So if we find the distance between the 1st and 3rd base that will be equal to the distance between the Home plate to the second base.
To find the nearest distance,
By applying "Pythagoras' Theorem"
[tex]nearest \ distance =\sqrt{120^2+90^2}\\\\=\sqrt{22500}\\\\=150\ feet.[/tex]
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Grade 8 math please help. I’m trying to sleep
Answers
The set of points for which y is a function of x is given as follows:
B.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
For set B in the context of this problem, we have that:
The input of -3 is mapped to an output of 3.The input of -2 is mapped to an output of 2.The input of -1 is mapped to an output of 1.The input of 1 is mapped to an output of -1.As there are no repeated inputs, this is the set that represents y as a function of x.
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The line representing the equation part of the constraint 7x1 + 4x2 28 goes through the following two points a. (4,0) and (7,0)b. (0,4) and (7,0) c. (4,0) and (0,7) d. (0,4) and (0,7) e. none of the above
Answers
The line representing the equation part of the constraint 7x1 + 4x2 28 goes through the following two points e. none of the above.
The equation of a line can be represented as y = mx + b, where m is the slope of the line and b is the y-intercept. The line representing the equation of a constraint, such as 7x1 + 4x2 = 28, would be a straight line in a two-dimensional graph.
The points given in the options a, b, c, and d are pairs of x and y coordinates. To determine if any of these points lie on the line representing the constraint equation, we would need to substitute the x and y values into the equation and see if the equality holds.
For example, for option a, if we substitute x = 4 and y = 0 into the equation, we get 7 * 4 + 4 * 0 = 28, which is not true. Hence, none of the given points in the options lie on the line representing the constraint equation.
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8 cm
7cm
6 cm
What is the surface area, in cm², of the figure?
Answers
Answer:
Here you have
Step-by-step explanation:
8 x 7 x 6 = 336 cm²
Please help >_<
If t = <2, -10> and v = <-3, −1> find t + v.
A. <-1, -11>
B. <-1, -9>
C. <5, -11>
D. <5, -9>
Answers
The correct option regarding the addition of vectors t and v is given as follows:
A. <-1, -11>.
How to add the vectors?The standard notation of a vector is given as follows:
<x,y>.
In which:
x is the horizontal component of the vector.y is the vertical component of the vector.To add two vectors, we add the elements at the same component.
Then the addition of vectors t and v is given as follows:
t + v = <2, -10> + <-3, - 1> = <2 - 3, -10 -1> = <-1, -11>.
From the result obtained above, the correct option in the context of this problem is given by option A.
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the mean (average) of 6, 9 and 18 is equal to the mean (average) of 12 and $y$. what is the value of $y$?
Answers
Answer:
y = 10
Step-by-step explanation:
[tex]\displaystyle \frac{6+9+18}{3}=\frac{12+y}{2}\\ \\\frac{33}{3}=\frac{12+y}{2}\\ \\11=\frac{12+y}{2}\\ \\22=12+y\\\\10=y[/tex]
3
6+9+18
=
2
12+y
3
33
=
2
12+y
11=
2
12+y
22=12+y
10=y
answer: 10=y
Please help me with this science/math question. I'll tell you the instructions.
We're basically combining science and math.
The letters are elements of the periodic table.
Element's can start with uppercase and lowercase letters together (Sr)
It can just be uppercase to (O)
If both of the letters are capital, they aren't symbols TOGETHER, their separate meaning they have their own element.
So we have the numbers next to the elements symbols (except for 2)
The starting values of each element is one, and we multiple the number that is after the element symbol, not before it.
Once you multiply the element and the number next to it, the element now has a new value, for example
Sr3.
Sr's value is 1.
1x3=3
Sr's new value is 3.
For the parenthesis, both element symbols are capital, which mean they don't belong to the same element, they have different elements. The number 4 isn't after the element symbol P so we don't multiply 4 and P. We multiply 4 and O because 4 is after O.
After we multiply each element's value, we multiply 2 (outside the parenthesis)
We multiply 2 x P which is 2
Then we multiply 2 x 4 since O's new value is 4 because we multiplied it. We'll get 8.
We can't forget about 2 (2 is the starting number from the equation) We multiply the whole equation by 2.
Now this is the part I need help on. I must add the TOTAL number of atoms from each I element. Please help me with this!!! I'd really appreciate it! (tell me step by step as well)
Answers
The number of atoms in the compound will be 54 atoms.
How to calculate the number of atomsChemistry's fundamental building block is an atom. It is the smallest fraction of matter into which electrically charged particles cannot be released. It is also the smallest piece of substance with chemical element-like characteristics.
The number of atoms in 2 Sr3(PO4)2 can be determined by counting the number of each type of atom present in the compound. In 2 Sr3(PO4)2, there are:
2 x 3 = 6 Sr atoms
2 x 2 x 4 = 16 P atoms
2 x 2 x 8 = 32 O atoms
So, there are a total of 6 + 16 + 32 = 54 atoms in 2 Sr3(PO4)2.
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Victor has saved $89.25 for the bicycle that he wants .the bicycle cost $129.85
Answers
The model used by Victor in the linear equation is incorrect,
How to identify Linear Equation Models?The parameters are that;
Victor saved: $89.25
Cost of the bicycle = $129.85
Thus, to find the amount extra that he will need to purchase the bicycle, the equation model should be;
$89.25 + x = $129.85
This can be expressed in words as;
The amount of money he already has saved + the amount of money he still requires = the total price of the bike.
An equation that correctly represents this problem can show the sum of the amount of money he already has and the amount of money he needs equals the total cost of the bicycle
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Complete question is;
Victor has saved $89.25 for the bicycle that he wants. The bicycle costs $129.85. Victor writes the equation below to help him determine the additional amount that he needs to solve to have enough to buy the bicycle.
89.25 + 129.85 = x
Does Victor's equation correctly model the problem?
What is the slope of the line that contains the points (7, -1) and (6, - 4)?
Answers
Answer:
-1/-3 s the slope
Step-by-step explanation:
(7,-1) and (6,-4)
-4-(-1)=-3
6-7=-1
so -1/-3 is the slope
the manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of his car and its make (foreign or domestic). a car was randomly selected from the lot. given that the car selected was a domestic car, what is the probability that it was older than 2 years?
Answers
The probability that the car selected was a domestic car and older than 2 years is 0.63 or 63%.
Probability is a mathematical concept that quantifies the likelihood or chance of an event occurring. It is a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between, probabilities reflect the degree of certainty that an event will occur, with values closer to 1 indicating a higher likelihood of occurrence and values closer to 0 indicating a lower likelihood.
The probability of an event is calculated by taking the ratio of the number of favorable outcomes to the total number of possible outcomes.
domestic car older than 2 years/total domestic cars = (28 + 12 + 23)/100 = 63/100 = 0.63 = 63%
Therefore, the probability of selecting a car that is less than 2 year given that it is a domestic car is 0.63 or 63%.
*The problem seems incomplete, attached might be the complete version of it.
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Sales : 1,253.70 commision : 18.6%
Answers
The commission earned on the sale of $1253.70 is $233.20
What is commission?A fee paid to an agent or employee for transacting a piece of business or performing a service is called commission.
Given that, there is a commission of 18.6% on the sale of $1253.70
Therefore,
The commission earned = 1253.70 × 18.6%
= 1253.70 × 18.6 / 100
= 233.20
Hence, the commission earned on the sale of $1253.70 is $233.20
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Calculate the sum of the partial sequence.
[tex]\sum_{n=1}^{75} (12n-9)[/tex]
Answers
The required sum of the given partial sequence is 33525.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The sum of the partial sequence.
[tex]= \sum_{n=1}^{75}12n - 9[/tex]
[tex]= \sum_{n=1}^{75}12n - \sum_{n=1}^{75} 9\\= 34200-675\\=33525[/tex]
Thus, The required sum of the given partial sequence is 33525.
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What is the slope of the graphed line?
O
I
5/2
O
O
5/2
O
7/2
10
9
8
7
6
5
4
31
21
1
1 2 3
4
5
6
7
8
9 10
Answers
Answer:
Step-by-step explanation:
OK YOU ARE GOOD OH AND IT
5/8
There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.
Several trials are performed with the results shown in the table. What is the experimental probability of randomly drawing a green marble?
Red Blue Green
10 12 28
What is the experimental probability of randomly drawing a green marble?
What is the theoretical probability of randomly drawing a green marble?
What would you expect to happen if more trials of the experiment are performed? Explain your reasoning using complete sentences.
Answers
The probability of randomly drawing a green marble form the bag would be = 12/25
What is probability?Probability is defined as the expression that show the possible outcome of an event.
The number of red marbles = 5
The number of blue marbles = 8
The number of green marbles = 12
The total number of marbles = 5+12+8 = 25
Therefore the probability of randomly drawing a green marble = 12/25
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when there are an even number of observations, and the observations are in order from smallest to largest, the median is... multiple choice question. the last observation the average of the two middle observations the first observation the middle observation average of the first and last observation.
Answers
When there are an even number of observations, and the observations are in order from smallest to largest, the median is:The average of the two middle observations.
The median is a measure of central tendency that is commonly used for data sets with an odd number of observations. When there are an even number of observations, the median is defined as the average of the two middle observations. This provides a representative value that splits the data set in half, with half of the observations having values lower than the median, and half having values higher.
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Dominick’s grandfather gave him $300 to start his college savings account. Dominick’s grandfather also gives him $75 each month to add to the account. Dominick’s mother gives him $40 each month, but has been doing so for 3 fewer months than Dominick’s grandfather. Write a simplified expression for the amount of money Dominick has received from his grandfather and mother after m months.
Answers
Simplified expression for the amount is 5(36+23m) .
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
Step 1: Form an equation for the amount of money Troy has received after m months.
If the total months that Troy's grandfather has given him money is m, then the number of months that Troy's mother has given him money is m - 3.
⇒ Total amount in account = 300 + 75m + 40(m - 3)
= 300 + 75m + 40m-120
=180 + 115m
=5(36+23m)
Hence, Simplified expression for the amount is 5(36+23m) .
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write an exponential expression for the value of each investment. do not evaluate
can someone please help me on number 27 i kind of understand it but i don’t really understand where you have to do the fraction part :)
Answers
The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
y = a (1 ± r)ˣ
The rate is 6% for 20 years semiannually. Then the rate is given as,
r = 0.06 / 2
r = 0.03
Then the time is given as,
x = 20 (2)
x = 40
Then the exponential function is given as,
A = $2000 × (1 + 0.03)⁴⁰
A = $2000 × (1.03)⁴⁰
A = $2000 × 3.262
A = $6524.1
The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.
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Every matrix transformation is a linear transformation.a. Trueb. false
Answers
True , Every matrix transformation is a linear transformation.
Is there a linear transformation for every matrix operation?
Despite the fact that every linear transformation is a matrix transformation, not all linear transformations are matrix transformations.
Because of this, it's possible that we'll encounter a linear transformation in which we're unable to locate a matrix to carry out the mapping.
What alteration does matrix entail?
In a two-dimensional or three-dimensional space, the transformation matrix converts one vector into another vector, which may be comprehended geometrically.
Stretching, squeezing, rotation, reflection, and orthogonal projection are some of the often utilized transformations.
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The figure is made up of a semicircle and a triangle.
Find the area of the figure.
Use
�
=
3.14
π=3.14
Answers
The area of the figure made up of a semicircle and a triangle is 63.25 ft²
How to solve an equation?An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.
The figure is made up of a semicircle and a triangle.
The semicircle has a diameter of 10 feet. Hence:
Area of semicircle = (1/2) * π * diameter²/4
Substituting:
Area of semicircle = (1/2) * π * 10²/4 = 39.25 ft²
The triangle has a base of 8 ft and height of 6 ft. hence:
Area of triangle = (1/2) * base * height
Substituting:
Area of triangle = (1/2) * 8 ft * 6 ft = 24 ft²
The area of the figure = Area of triangle + Area of semicircle
Area of figure = 24 ft² + 39.25 ft² = 63.25 ft²
The area of the figure is 63.25 ft²
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Please help me with this
Answers
The value of the variable, x is 45 degrees
How to determine the valueWe have that the polygon is one with eight sides, that is, it is a regular octagon.
To determine the interior angle, we have
(n - 2) 180
n is the number of sides
(8-2)180
1080 degrees
Now, divide it by the number of sides
1080/8 = 135 degrees
Note that angles on a straight line is equal to 180
Then,
x + 135 = 180
Collect like terms
x = 180 -135
subtract the values
x = 45 degrees
Hence, the value is 45 degrees
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Which fraction is not equivalent to 2/6?
Use the graph to answer the questions:
What does (6, 120) represent?
What ordered pair describes the unit rate?
Use cross multiplication to solve for y
Answers
Answer:From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have
x = dozen
y = cookies
This means that
(3, 36) means 3 dozens required 36 cookies
What ordered pair describes the unit rate?
Using the ordered pair in (a):
The unit rate of the pair (3, 36) is 36/3 = 12.
This means that for every 1 dozen change, there is a corresponding 12 cookies change
Step-by-step explanation:
Solve the inequality -8 < 32.
-8x < 32
?
on both sides. ?
the inequality.
Answers
x>-4 is the solution of the inequality -8x < 32
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is -8x < 32
Minus eight times of x less than thirty two.
We need to solve for x which is a variable.
Divide both sides by 8
-x<4
x>-4
Hence, x>-4 is the solution of the inequality -8x < 32
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Please help asap!! Try ur best <3 • will give u brainliest
Answers
The solution of the system of equation is , x= -4 & y= -8.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
from the given graph we get,
one line is passing through the points (0,10) , ( 4,28)
so, the equation of the line can be,
4y= 18x + 40
and, second line is passing through the points (0,8) , (1,12)
so, the equation of the line can be,
y= 4x+8
solving the equations we get,
x= -4
y= -8
Hence, The solution of the system of equation is , x= -4 & y= -8.
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a frustum of cone is filled with ice cream such that the portion above the cone is a hemisphere. define the variables di
Answers
The total volume of the ice cream is -4.76 cubic inches.
The volume of the frustum of a cone can be calculated as follows:
V = (1/3) × π × h × (r1² + r2² + r1 × r2), where r1 and r2 are the radii of the top and bottom base of the cone.
And the volume of a sphere can be calculated as follows:
V = (4/3) × π × r³, where r is the radius of the sphere.
To calculate the total volume of the ice cream, we need to subtract the volume of the cone from the volume of the sphere.
Let's first calculate the radii of the top and bottom base of the cone.
r1 = (di/2) = (1.25/2) = 0.625 in.
r2 = (d0/2) = (2.25/2) = 1.125 in.
Now, we can estimate the volume of the cone.
V_cone = (1/3) × π × h × (r1² + r2² + r1 × r2)
= (1/3) × π × 2 × (0.625² + 1.125² + 0.625 × 1.125)
= 6.45 cubic inches.
Next, let's calculate the radius of the sphere.
r_sphere = (di/2) = (1.25/2) = 0.625 in.
And finally, we can calculate the volume of the sphere.
V_sphere = (4/3) × π × 0.625³
= 1.69 cubic inches.
So, the total volume of the ice cream is given by:
V_ice_cream = V_sphere - V_cone
= 1.69 - 6.45
= -4.76 cubic inches.
Note: Since the volume of the cone is larger than the volume of the sphere, the total volume of the ice cream will be negative, indicating that it is not possible to fill a frustum of a cone with ice cream in the manner described.
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--The given question is incomplete; the complete question is
"A frustum of a cone is filled with ice cream such that the portion above the cone is a hemisphere. Define the variables di=1.25 in., d0=2.25 in., h=2 in., and determine the volume of the ice cream."--
write the number as a quotient of integers to show that it is rational300=
Answers
The number 300 can be written as 300/1 as a quotient of integers to show that it is rational.
A rational number is a number of the form p/q, where q not equal to 0 and p and q must be co-primes.
To write a number in the form of quotient of integer, we write it as , where p/q.
Here, 300 can be written as 300/1 or 600/2 .
But we should also take care that p and q must be co-primes.
Co-primes are the pairs of numbers that have only one common factor which is 1.
So, 300 can be written as 300/1
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Evaluate: (1) 3p +5(2q+p)+3p-6q
(2) Z+8-6(z-2a)+5z
Answers
The values are evaluated to give;
1. 11p + 4q
2. -12a + 8
What is an algebraic expression?An algebraic expression is an expression that is composed of terms, coefficients, variables, factors and constants.
From the information given, we have that;
3p +5(2q+p)+3p-6q
expand the bracket, we get;
3p + 10q + 5p + 3p - 6q
collect and add the like terms
11p + 4q
Then,
Z+8-6(z-2a)+5z
expand the bracket
z + 8 - 6z - 12a + 5z
collect and add the like terms
-12a + 8
Hence, the expression are 11p + 4q and -12a + 8
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