We can use zero product property in a series of steps to find the quadratic equation by factoring.
In mathematics, the zero product property states that if A and B are mathematical expressions, and AB = 0, then A = 0 or B = 0.
The steps that we use to solve a quadratic equation by factoring are as follows:
1- Put the equation in the form ax² + bx + c = 0, where a, b, and c are constants.
2- Factor ax² + bx + c.
3- Use the zero product property to set each factor equal to 0.
4- Solve each of the resulting equations for x.
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A peron took a loan of R 150000for tw year at the rate of 10% annual compound interet To reduce interet and loan partly he paid R 85000 at the end of firt year
a) Now how many rupee hould he have to pay at the end of econd year to clear hi debt
b) If he had paid the loan only at the end of econd year how much le or more interet hould have to be paid?
Therefore, if the borrower had paid the loan just at the end of the second year, he would have owed R 167250. The additional interest due would be R 167250 - 150000 = R 17250.
a) To calculate the amount of money that the person would have to pay at the end of the second year to clear his debt, you can use the formula for compound interest:l,
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the person took a loan of R 150000 for 2 years at an annual interest rate of 10%. He paid R 85000 at the end of the first year. So, the new principal at the beginning of the second year is P = 150000 - 85000 = 65000.
So, A = P(1 + r/n)^(nt)
A = 65000(1 + 0.1)^2
A = 65000*1.1^2
A = 73,650
So, the person should have to pay R 73650 at the end of the second year to clear his debt.
b) If the person had paid the loan only at the end of the second year, the interest would have been calculated on the original principal of R 150000 for 2 years. So,
A = P(1 + r/n)^(nt)
A = 150000(1 + 0.1)^2
A = 150000*1.1^2
A = 167250
So, the person would have had to pay R 167250 if he had paid the loan only at the end of the second year. Therefore, he would have to pay more interest of R 167250 - 150000 = R 17250.
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Find the single transformation that is equivalent to
• reflection in x= -1
followed by
• reflection in x=2
You may use a grid to help you.
(3 marks)
It’s a translation by:
(—)
As a result, there is just one transformation from shape A to shape B: dilate A by 1/2, followed by a 180 degree rotation.
Explain about the single transformation?A drastic change in shape or appearance is called a transformation. An crucial occasion, such as receiving your driver's licence, enrolling in college, or getting married, might change the course of your life. Extreme, dramatic change is what we refer to as transformation.
When we move a figure in any direction, we say that we are translating. Flipping a figure over a line is what is meant by reflection. Rotation is the process of rotating a figure around a point by a specific amount. When we dilate a figure, it is enlarged or shrunk.
By multiplying the original shape by a scale factor, we can change the size of the shape and make it bigger or smaller. This type of modification is called an expansion.
A shape can be transformed by shifting its location and size.
Shape A can only be transformed into shape B by rotating 180 degrees and enlarging it by half.
Based on the figure, we can:
Shape A's side lengths are twice as long as Shape B's side lengths.
After dilatation, shape A can be rotated 180 degrees to imprint onto shape B.
The range of dilatation from shape A to shape B is thus:
Scale = 1/2
As a result, there is just one transformation from shape A to shape B: dilate A by 1/2, followed by a 180 degree rotation.
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Answer:
Step-by-step explanation:
i don't know
do not bother answering with these answers I have already checked none of them have the correct answer
bye children
write an equation for a degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and has a y-int at 5..
The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:
y = -5/12(x - 3)(x - 2)²(x + 1)³.
How to define the polynomial?The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.
The zeros of the function, along with their multiplicities, are given as follows:
Zero at x = 3 with a multiplicity of 1.Zero at x = 2 with a multiplicity of 2.Zero at x = -1 with a multiplicity of 3.Then the linear factors of the function are given as follows:
(x - 3).(x - 2)².(x + 1)³.The function is then defined as:
y = a(x - 3)(x - 2)²(x + 1)³.
In which a is the leading coefficient.
When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:
5 = -12a
a = -5/12
Hence the polynomial is:
y = -5/12(x - 3)(x - 2)²(x + 1)³.
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What are the zeros of p x )= 5 x2?.
The zeros of function p(x) = 5 - x² are x = √5 and x = -√5
Consider given polynomial function.
p(x) = 5 - x²
We know that the zeros of a function are the values of the variable of the function that makes the function value equal to 0.
To find the zeros of function p(x), we need to equate p(x) to zero then solve it for x.
⇒ p(x) = 0
⇒ 5 - x² = 0
⇒ 5 - x² - 5 = 0 - 5 ....(subtract 5 from each side of equation)
⇒ -x² = -5
⇒ x² = 5 ......(multiply both the sides by -1)
⇒ x = ±√5 .........(taking square-root of both the sides)
Thus x = √5 and x = -√5 are zeros.
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The complete question is:
What are the zeros of p(x) = 5 - x²?.
If a parabola's focus is at (-1,-1) and directrix is at y = 7, what is the general form of the equation representing this
parabola?
0x² 2x+16y
49 = 0
O x² - 2x + 2y² + 16y - 47 = 0
O x² + 2x + 16y - 47 = 0
Ox²-47-0
A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.
What is Parabola?A parabola is formed by cutting a right circular cone in half along a plane perpendicular to the cone's generator. It is a locus of a moving point whose separation from the focus is equal to its separation from a stationary line (directrix)
Fixed point is called focusFixed line is called directrixIn general, if the directrix is parallel to the y-axis in the standard equation of a parabola is given as: y2 = 4axIf the parabola is sideways i.e., the directrix is parallel to x-axis, the standard equation of a parabola becomes, x2 = 4aythe equation of a parabola can also be y2 = -4ax and x2 = -4ay if the parabola is in the negative quadrants.To know more about Parabola refer to:
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A line passes through (5,3) and has a slope of 3. Find a second point on the line.
Answer:
(1, -9)
Step-by-step explanation:
The slope-intercept formula of a line is: y = mx + b
m = slope
b = y-intercept
We know one point already.
3 = 3(5) + b
3 = 15 + b
3 - 15 = 15 - 15 + b
-12 = b
So now we know the formula: y = 3x - 12
We can plug in 1 as x to find another point
y = 3(1) - 12
y = 3 - 12
y = -9
What is the ratio for cos?.
The cosine function (also known as the cos function) in triangles is the ratio between the neighbouring side and the hypotenuse.
The complement of sine and one of the three primary trigonometric functions, cosine is one of the three basic trigonometric functions.
The cosine of a right triangle is the ratio between the lengths of the adjacent side and the longest side, or hypotenuse.
Adjacent Side/Hypotenuse = cos theta
If the ratio between the side and hypotenuse is known, the cos inverse function can be used to calculate the angle of any right-angled triangle. The symbol for the cos inverse is [tex]cosx^{-1}[/tex].
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The cosine function (also known as the cos function) in triangles is the ratio between the neighbouring side and the hypotenuse.
The complement of sine and one of the three primary trigonometric functions, cosine is one of the three basic trigonometric functions.
The cosine of a right triangle is the ratio between the lengths of the adjacent side and the longest side, or hypotenuse.
Adjacent Side/Hypotenuse = cos theta
If the ratio between the side and hypotenuse is known, the cos inverse function can be used to calculate the angle of any right-angled triangle. The symbol for the cos inverse is .
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the area of the bottom of a triangular upright prism is 4 cm2 and the areas of the sides are 9 cm2, 10 cm2 and 17 cm2. calculate the volume of the prism
To calculate the volume of a triangular prism, you need to know the base area and the height. In this case, the base area is given as 4 cm^2, and the areas of the sides are given as 9 cm^2, 10 cm^2 and 17 cm^2.
To find the volume of the prism, you can use the formula:
Volume = Base Area x Height
Since we don't know the height of the prism, we can use the area of the sides to find the height.
To find the height, we need to use the formula of area of the triangle.
Area = (1/2) x b x h
let's use the area of one side (for example 9cm^2)
9cm^2 = (1/2) x b x h
we can divide both sides by (1/2) x b
h = (2 * 9cm^2) / b
Now we have the height of the triangular prism, so we can use that to find the volume.
so the volume of the triangular prism = Base Area x Height = 4cm^2 x ( (2 * 9cm^2) / b) = 72/b cm^3
As we don't know the value of b, we can't find the exact volume of the prism.
Answer:
12 cm³
Step-by-step explanation:
Conditions:
a * h = 9 cm
b * h = 10 cm
c * h = 17 cm
S = 4 cm²
To calculate the area on three sides, we use the Heron formula:
[tex]S = \sqrt{p * (p-a) *(p-b)*(p-c)[/tex]
where "p" is the semi-perimeter:
[tex]p = \frac{(a+b+c)}{2}[/tex]
Let's express the sides in terms of the height:
a = 9/h
b = 10/h
c = 17/h
Then the semiperimeter will be:
p = (9/h+10/h+17/h) : 2 = 36/h : 2 = 18/h
Substituting the values into the Heron formula:
4 = √(18/h * (18/h - 9/h) * (18/h - 10/h) * (18/h - 17/h))
4² = 18/h * (18/h - 9/h) * (18/h - 10/h) * (18/h - 17/h)
16 = 18/h * 9/h * 8/h * 1/h
16 = 1296 / h^4
h^4 = 1296 / 16 = 81
h = 3 cm
Now we can calculate the volume of the pyramid:
V = S * h = 4 cm² * 3 cm = 12 cm³
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The following data give the ditribution table of total houe hold expenditure (in<) of manual work in the city
then,find thye average expenditure which i done by the maximum number of manual worker
The average expenditure which I did by the maximum number of the manual worker is 1847.826
We note that the maximum frequency for the class 1500–2000 is 40. As a result, it belongs to the modal class.
The class interval with the most data points, or what we may refer to as the highest frequency, inside a collection of data is called the modal class.
The class that will include the mode is known as the modal class. The modal class may be determined using the formula I0 I 0 + (f1−f02f1−f0−f2)h ( f 1 − f 0 2 f 1 − f 0 − f 2 ) h
l=1500,h=500,f=40,f
1=24, and f 2=33
∴Mode=(l+ 2f−f1/2f−f2f−f 1 )×h
Mode=1500+ 40−24 / 80−24−33×500
⇒Mode=1500+ 16/23 ×500
=1847.826
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The numbers 630 and 1248 written as the products of their prime products
Answer: The prime factorization of 630 is 2 x 3 x 5 x 7.
The prime factorization of 1248 is 2^4 x 3 x 7.
So, 630 can be written as 2 x 3 x 5 x 7 and 1248 can be written as 2^4 x 3 x 7
In general, to find the prime factorization of a number, you can divide the number by the smallest prime number (2) and continue dividing by prime numbers until the quotient is a prime number. Then divide that quotient by the next smallest prime number, and so on, until the quotient is 1.
Step-by-step explanation:
distance driven vs time spent in a car
which one is the independent variable?
Distance Driven is the IV
How do you write a quotient as a complex number?.
To see the Polar form and Rectangular form of quotient as a complex number.
Polar numbers can be written in two different forms: rectangular and polar. Rectangular complex numbers are given by a + bi, where a represents the real part of the complex number and b represents the imaginary part of the complex number. Polar complex numbers are given by its absolute value,
r = [tex]\sqrt{x^{2} +y^2}[/tex] and the argument, θ, which can then be determined through the following relations:
x = rcosθy = rsinθ[tex]z=re^i^\theta[/tex]
If the complex numbers are in polar form, then the quotient is given by:
[tex]\frac{z_1}{z_2}=\frac{r_1e^i^\theta_1}{r_2e^i^\theta_2}[/tex] [tex]= \frac{r_1}{r_2}e^i^(^\theta_1^-^\theta_2^)[/tex]
If the complex numbers are in rectangular form, then you will have to use the complex conjugate to remove the complex number in the denominator:
[tex]\frac{a_1+b_1i}{a_2+b_2i}[/tex] [tex]=\frac{(a_1+b_1i)(a_2-b_2i)}{(a_2+b_2i)(a_2-b_2i)}[/tex].
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ANSWER QUICK I WILL MAKE U BRAINLIEST
Answer: 1) 1,500 2) 36 3) 15 4) 8,400
Step-by-step explanation: Hope it helps!
y=_x + _
what is the slope?
PLS HELP!!!
Answer:
Step-by-step explanation:
y= 1/4x + 2.5
Joseph measured a city park and made a scale drawing. The scale he used was 6 centimeters = 7 meters. What scale factor does the drawing use?
The scale factor used in the scale drawing which has the scale of 6 centimeters = 7 meters is 116.667
How to get the scale factorScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
For the scale drawing with a scale of scale of 6 centimeters = 7 meters
the units are converted to be same, using the conversion unit of
100 cm = 1 m
x cm = 7 meters'
solving for x
x = 700 cm
hence the scale of the drawing is 6 cm = 700 cm, we solve for the scale factor
6 cm = 700 cm
1 cm = scale factor
solving for the scale factor
scale factor = 700 / 6
= 350 / 3
the factor is 116.667
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Is √ 144 a perfect square?.
Yes. 144 is a perfect square. It is a perfect square of 12. The integer that can be expressed as the square of another integer is called as a perfect square.
A number is said to be a perfect square if its square root is an integer. It means that a perfect square is an integer's product with itself. It is also defined as the second exponent of an integer. A number squaring a whole number is a perfect square. A perfect square can be determined by the prime factorization method. Prime factorization is defined as the process of writing all numbers as a product of prime. Through prime factorization we can determine the square root. Every integer has its prime factorization.
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What is the y-intercept of Y =- 4x 6?.
The y-intercept of the equation y = -4x-6 is (0, -6).
Equation: y = -4x - 6
The y intercept of a graph is the point where the graph intersects the y-axis. We know that the x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.
Use the slope-intercept form to find the slope and y-intercept.
The slope-intercept form is
y = mx + b, where m is the slope and b is the y-intercept.
y = mx + b
Find the values of m and b, using the slope-intercept equation.
Now, using this information,
y = −4x − 6
y = mx + c
m → slope
the slope is −4 and
y−intercept would be (0,−6).
Thus, the y-intercept is (0, -6).
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Which jam recipe has more strawberry flavor?
Recipe A
3 cups strawberries
1/2 cup sugar
Recipe B
5 cups strawberries
1 cup sugar
Answer:
recipe A
Step-by-step explanation:
I think it's recipe A cause it contain 3 cups of strawberries and there is lots of sugar so. A lot of sugar makes the recipe flavourful
in my opinion it might be that
You have 2 eggs timers, a 7 min and a 4 min timer. You want to boil a 9 minute egg. How can you do it exactly?
Answer:
You start your first timer, and let it run out, then either let the second timer run for 2 minutes, then take the eggs out.
Step-by-step explanation:
What does the distance between two points represent?.
The distance between two points in a two-dimensional coordinate system represents the length of the shortest path between those two points. This length is also called the Euclidean distance, it is a measure of the straight-line distance between two points.
In other words, it is the length of the line segment connecting the two points. It is calculated using the distance formula which is derived from the Pythagorean theorem, it is calculated as the square root of the sum of the squares of the differences of the coordinates of the two points.
The distance between two points is always a positive value and it is a scalar quantity, it does not have any direction associated with it. It is a measure of the separation between two points, regardless of the direction of the line connecting them.
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Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. A. C. B. D. Please select the best answer from the choices provided a b c d.
The reduced row-echelon form of the augmented matrix for the system of equations is: 1 0 0 1 | 8, 0 1 0 -2 | -2, 0 0 1 0 | 0. This means that the first equation is reduced to x_1 + x_4 = 8, the second equation is reduced to x_2 - 2x_4 = -2, and the third equation is reduced to x_3 = 0.
Step 1: Subtract 2 times row 1 from row 2 to get row 2 in the form [0 1 0 -2 | -2].
Step 2: Divide row 2 by -2 to get row 2 in the form [0 1 0 1 | 8].
Step 3: Subtract 3 times row 2 from row 1 to get row 1 in the form [1 0 0 1 | 8].
Step 4: Subtract 4 times row 2 from row 3 to get row 3 in the form [0 0 1 0 | 0].
Step 5: The reduced row-echelon form of the augmented matrix for the system of equations is now: [1 0 0 1 | 8], [0 1 0 -2 | -2], [0 0 1 0 | 0]. This means that the first equation is reduced to x_1 + x_4 = 8, the second equation is reduced to x_2 - 2x_4 = -2, and the third equation is reduced to x_3 = 0.
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Which of the following is equal to the rational expression when x -2 or 3? A. B. C. D.
The solution to the given rational expression is (x+3)/(x-3). The correct answer would be an option (C).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The rational expression is given in the question, as follows:
(x²+5x+6)/(x²-x-6)
The above expression can be rewritten in the form of factors,
(x+3)(x+2)/(x-3)(x+2)
These are simplified by canceling similar numerator and denominator components, and we get:
(x+3)/(x-3)
This is the solution to the given expression.
Hence, the correct answer would be option (C).
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The question seems incomplete, the complete question would be as:
Which of the following is equal to the rational expression when x ≠ -2 or 3? (x²+5x+6)/(x²-x-6)
A. (x+3)/(x-2)
B. (x+2)/(x-3)
C. (x+3)/(x-3)
D. (x-3)/(x+3)
You have been asked to find the value of f(-5) for the function
f(x)=3x2 -2x+5
Which of the following options is NOT a possible way to evaluate that function and find the correct answer?
Substitute (-5) wherever there is an x and solve using a calculator
Graph the equation and find the y-value of the ordered pair when x=-5
See what x is when y=-5
Graph the equation and look at the table to find the y-value when x=-5
Answer: The option that is NOT a possible way to evaluate the function and find the correct answer is
See what x is when y=-5
Explanation:
In the function f(x) = 3x^2 - 2x + 5, x is the input variable and y is the output variable. To find the value of f(-5), we need to substitute -5 wherever there is an x in the function and then solve the resulting expression. This is the first option.
The second and forth options are also correct ways to evaluate the function, they involve graphing the equation and finding the y-value of the ordered pair when x=-5.
But the third option is not the correct way, because it is asking to find x when y=-5, but in the given function the y is unknown, so it is not possible to find x when y=-5.
Step-by-step explanation:
if the simple interest on $5000 for 2 years is $700, then what is the interest rate
1. Find the length of each leg.
R
Q
30⁰
4
60%
P
Answer:
QP = 2
QR = 2√3
Step-by-step explanation:
This is a special right triangle with angle measures as follows:
30° - 60° - 90°
And side lengths represented with:
x - x√3 - 2x respectively to angle measures.
The side length that sees angle measure 90, hypotenuse, is given as 4 so the legs would be:
2 and 2√3
What does a 360 angle look like?.
A 360-degree angle can be visualized as a full rotation or circle, and it is often used to measure angles in a circular context.
A 360-degree angle is a complete rotation and is equivalent to one full circle. It is often represented as a circle with a line that goes from the center of the circle to the outer edge, marking the angle.
When looking at a 360-degree angle, it can be divided into four quadrants: the top right, top left, bottom left, and bottom right. Each quadrant is 90 degrees or one-fourth of the total angle. This division is useful when analyzing or measuring angles in different sections of a circle.
In terms of visual representation, imagine a clock face with the numbers 1-12. The clock face is a 360-degree angle, with each number representing a 30 degree increment. The hour hand of the clock would rotate around the face, completing a full rotation and reaching the starting point at the 12 o'clock position, completing a 360 degree angle.
In other words, a 360 degree angle can be visualized as a full rotation or circle, and it is often used to measure angles in a circular context. It can also be divided into smaller sections for analysis or measurement purposes.
Therefore, A 360 degree angle can be visualized as a full rotation or circle, and it is often used to measure angles in a circular context.
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What is an expression of more than two algebraic terms?.
An expression of more than two algebraic terms is called Polynomial.
Polynomial:
Polynomials are made up of two terms: poly (meaning "many") and nominal (meaning "terms"). A polynomial is defined as an expression consisting of variables, constants, and exponents combined by mathematical operations such as addition, subtraction, multiplication, and division (not division by a variable). Based on the number of terms in the expression, it is classified as monomial, binomial, and ternary. Examples of constants, variables, and exponents are:
Constant: For example: 1, 2, 3, etc.variables: Example: g, h, x, y, etc.Exponent: Example: 5 in x5, etc.Polynomials can be classified by degree and power. Based on the number of terms, there are three main types of polynomials:
MonomialBinomialTrinomial.Learn more about Polynomial:
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Two step equation that equals 13
This equation can be solved using the addition and subtraction property of equality, x + 7 = 13.
What is an equation?An equation is an expression containing an equal sign that states the equality of two mathematical expressions. It is a statement that two expressions have the same value. Equations often involve variables, which are placeholders for unknown numbers. An equation contains at least one operation, such as addition, subtraction, multiplication, or division. Equations are used in a variety of mathematical applications, from basic algebra to more advanced topics such as calculus.
Subtract 7 from both sides to isolate x.
x + 7 - 7 = 13 - 7
x = 6
Therefore, the two step equation that equals 13 is x + 7 = 13.
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What is the maximum value of log x by x?.
The maximum value of log(x)/ x is 1/e.
The function given is f(x) = log(x)/ x
As base is not mentioned assuming that the base is e.
To find maximum value, let us find the critical point of this function equating its first derivative to 0.
d/dx (f(x) = log(x)/ x) = ( 1 - log(x))/ x²
So d/dx (f(x)) = 0 when 1 - log(x) = 0
That is log(x) = 1
So x = e
f''(x) = (2log(x) - 3)/ x³
f''(e) = (2log(e) - 3)/ e³ = -1/e³ < 0
So at x = e, f(x) is maximum.
Thus maximum value of f(x) is at x = e
f(e) = log(e)/ e = 1/e
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How do you solve systems by elimination with multiplication?.
The process of solving systems by elimination with multiplication for the equation is explained below.
In math the term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign.
Here we need to write down the steps to solve systems by elimination with multiplication.
Here the first steps id to out the equations in Standard Form.
And then here we need to determine which variable to eliminate.
Finally we have to Multiply the equations and solve.
And this process that allows us to multiply both sides of an equation by the same constant while still having an equivalent expression.
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