Answer:
48-x
Step-by-step explanation:
6(x-2) + 5(x+12)-12x
6x-12+5x+60-12x
6x+5x-12x-12+60
-x+48
What are the 5 ways to prove triangles similar?
Five different ways to prove the given triangles are similar is given by :
SAS, SSS, ASA, AA, and RHS.
Five different ways to prove triangles are similar is given by:
1. SAS (Side-Angle-Side) : If the corresponding sides of one triangle are in proportion to the other triangle and included angle is of equal measure.
2. SSS(Side-Side-Side): If the corresponding sides of one triangle are in proportion to the other triangle
3. ASA(Angle - Side- Angle) : If the two angles of one triangle are equal to the angles of other triangle and included side is in proportion.
4. AA( Angle-Angle) : If two adjacent angle of one triangle is equal to the measure of other triangle.
5. RHS(Right angle- Hypotenuse - side). If the hypotenuse and one of one right triangle are in proportion to another.
Therefore, five different ways to prove the given triangles are similar is given by : SAS, SSS, ASA, AA, and RHS.
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How do you find the median step by step?
The median is the exact middle number in a sequence or set of numbers.
Steps to find the median is given below:
Finding the Median in an Odd Set of Numbers:
Step 1: Sort your set of numbers from least to greatest. If they're scrambled, line them up, starting with the lowest number and ending with the highest number.
Step 2: Find the number that is exactly in the middle. This means that the median number has the same amount of numbers in front of it as it does behind it.
Finding the Median in an Even Set of Numbers
Step 1: Sort out your set of numbers from least to greatest. An even set of numbers is going to have two numbers exactly in the middle.
Step 2: Find the average of the two numbers in the middle. If 2 and 3 are both in the middle, so you need to add 2 and 3, then divide the sum by 2. The formula for finding the average of two numbers is (the sum of the two middle numbers) ÷ 2.
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17. एउटा वस्तुको अङ्कित मूल्यमा 20% छुट दिएपछि 13% भ्याट जोडेर रु. 18080 मा बिक्री गरियो भने उक्त वस्तुको अङ्कित मूल्य पत्ता लगाउनुहोस् । (Allowing 20% discount on the marked price of an article, the value of the article will be Rs. 18080 when a VAT of 13% is added, find its marked Ans: Rs. 20,000 price.)
Answer:
11111111111111111111
Which way is negative infinity?
Negative infinity is a concept that has no direction and function. It is the lowest possible number and is represented by the symbol "-∞".
Negative infinity is the lowest possible number, meaning there is no lower number than negative infinity. It is a concept that has no direction, meaning it is not a specific point on a number line. It is represented by the symbol "-∞", which can be thought of as a point before the beginning of the number line. Negative infinity is an abstract concept, but it is still used in mathematical operations. For example, if you have a set of numbers that contains negative infinity, then the sum of all the numbers in the set will be negative infinity. This is because negative infinity is the lowest possible number, so no matter how large the other numbers in the set are, the sum will always be lower than all of them.Negative infinity can also be used to represent undefined limits. For example, if you are looking at a graph of a function, and the y-axis goes to negative infinity, then the limit of the function at that point is undefined. This is because there is no lower number than negative infinity, so the limit cannot be determined.Negative infinity is a concept that can be confusing, but it is an important part of mathematics. It is used to represent the lowest possible number, as well as undefined limits. It is represented by the symbol "-∞" and has no direction.
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Solve the system of linear equations by substitution.
x=17-4y
y=x-2
Answer:
Step-by-step explanation
In the first equation
x=17-4y
In the second equation
We clear "x"
y=x-2
x=y+2
We ecuate "x"
x=17-4y=y+2
17-4y=y+2
15=5y
y=3
we substitute to find "x"
x=17-4y=17-4(3)=5
A diver leaps from the edge of a diving platform into a pool below. The figure shows the initial position of the diver and her position at a later time. At time t seconds after she leaps, the horizontal distance from the front edge of the platform to the diver's shoulders is given by xXt and the vertical distance from the water surface to her shoulders is given by t), where x(t) and yt) are measured in meters. Suppose that the diver's shoulders are 11.4 meters above the water when she makes her leap and that d0.8 and dar 3.6 9.8t for Os ts A, where A is the time that the diver's shoulders enter the water. image y0) Note: Figure not drawn to scale Question 1 (3 points) Find the maximum vertical distance from the water surface to the diver's shoulders. Question 2 (2 points) Find A, the time that the diver's shoulders enter the water Question 3 (2 points) Find the total distance traveled by the diver's shoulders from the time she leaps from the platform until the time her shoulders enter the water. Question 4 (2 points) Find the angle e. 0くθ 〈 π , between the path of the diver and the water at the instant the diver's shoulders enter the water.
A- The maximum vertical distance from the water surface to the diver’s
shoulders are 12.061 meters.
B- The time that the diver’s shoulders enter the water is 1.936 seconds.
C- The total distance traveled by the diver’s shoulders from the time
she leaps from the platform until the time her shoulders enter the water is 12.946 meters.
D- The angle, θ between the path of the diver and the water at the instant the diver’s shoulders enter the water is 1.519.
A-
[tex]\frac{dy}{dx} =0[/tex] only when [tex]t=0.36735[/tex]. Let [tex]b=0.36735[/tex]
The maximum vertical distance from the water surface to the diver’s
shoulders is y(b)=11.4 + [tex]\int\limits^b_0 \frac{dy}{dT} dt = 12.061[/tex] meters.
B-
[tex]y(A)=11.4+\int\limits^A_0 \frac{dy}{dt} dt = 11.4+3.6A- 4.9A^{2} =0[/tex]
when A= 1.936 seconds.
C-
[tex]\int\limits^A_0 {\sqrt{(\frac{dx}{dt} )^{2} + (\frac{dy}{dt} )^{2} } } \, dt = 12.946 m[/tex]
At time A, dy/dx = [tex]\frac{dy/dt}{dx/dt} | _{t=A} = -19.21913[/tex]
D- The angle between the path of the diver and the water is [tex]tan^{-1} (19.21913) = 1.518 or 1.519[/tex]
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Hodor combines 3 quarts of a 5% sugar solution and 2 quarts of an 8% sugar solution. How many additional quarts of a 12% sugar solution must be added to make a 10% sugar solution?
Katie needs 9.5 quartz of the 12% sugar solution to make the 10% sugar solution.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The volume of the 12% sugar solution required, 'X' for a given volume of the 8% sugar solution, 'Y' is;
X = (2·Y + 15)/2
When the volume of the 8% sugar solution, Y = 2 quartz, the volume of the 12% sugar solution required, X = 9.5 gallons
The data of the sugar solutions are;
The volume of 5% sugar solution Kate has = 3 quarts
The volume of the 12% sugar solution = X
Let 'Y' represent the volume of the 8% sugar solution, we have;
The volume of the resultant solution, Z = X + Y + 3
The concentration of the resultant solution = 10%
0.05 × 3 + 0.08·Y + 0.12·X = 0.1·(X + Y + 3)
Solving gives the relationship between the volume of the 12% sugar solution, 'X', and the 8% sugar solution, 'Y' in quartz, as follows;
X = (2·Y + 15)/2
When the volume of the 8% sugar solution, Y = 2 quartz, we have;
X = (2 × 2 + 15)/2 = 9.5 Quartz
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A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophia places a 11-foot tall pole to support the guy wire. After placing the pole, sophia measures the distance from the stake to the pole to be 4 ft. She then measures the distance from the pole to the tower to be 32 ft. Find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot, is 201 ft.
Refer to the diagram attached below for the given information
We have two similar right triangles, ΔABE and ΔCDE.
CD = 11 ft
DE = 4 ft
BD = 32 ft
Length of the guy wire (AE)
Since ΔABE ~ ΔCDE, therefore,
AB/CD = BE/DE (proportional sides)
Plug in the values:
AB/11 = (32 + 4)/2
AB/11 = 36/2
Cross multiply:
AB = (36 × 11)/2
AB = 198 ft
Apply Pythagorean Theorem to find AE:
AE = √(AB² + BE²)
AE = √(198² + 36²)
AE = 201 ft (nearest foot)
Therefore, the length of the guy wire, to the nearest foot is 201 ft.
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We have two similar right triangles, ΔABE and ΔCDE.
CD = 11 ft
DE = 4 ft
BD = 32 ft
Length of the guy wire (AE)
Since ΔABE ~ ΔCDE, therefore,
AB/CD = BE/DE (proportional sides)
AB/11 = (32 + 4)/2
AB/11 = 36/2
AB = (36 × 11)/2
AB = 198 ft
AE = √(AB² + BE²)
AE = √(198² + 36²)
AE = 201 ft (nearest foot)
What is the x and y intercept of y=3x-15 and is (2,-9) a solution
The x and y intercept of y=3x-15 is X intercept is 5, Y interceptis -15
How to find X intercept and Y intercept?To find X intercept substitute y=0
y=0
0=3x-15
3x=15
x=15/3
x=5
X intercept is 5 line cuts at (5,0)
To find Y intercept substitute x=0
y=3(0)-15
y=-15
Y interceptis -15 line cuts at (0,-15)
The distance on the axis from the origin where a line or a curve intersects the coordinate axis of the graph is known as the X and Y-intercept. The distance from the origin of a line or curve that cuts the x-axis at a point is known as the x-intercept, and the distance from the origin of a line or curve that cuts the y-axis at a point is known as the y-intercept.-c/m for the x-interceptc = y-interceptA line's equation has the general form axe + by + c = 0. Here, we change y to equal 0 and solve for x to obtain the x-intercept of the line. We then change x to equal 0 and solve for y in the same equation.To learn more about intercepts refer to:
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The matrix below is named E. Create a matrix that is 5E. Now what is the element
at e12?
4 -6 -7
12 3 4
five plus eight times nine
In the parallelogram below,
x = [? ]
3x+7
75x-17
Answer:
x=12
Step-by-step explanation:
3x+7 = 5x-17
-2x=-24
x=12
Hope this helps you can thank me if this helps and 5 star if you dont mind :)
Answer:
x=12
Step-by-step explanation:
The two sides must be equal in length
3x+7 = 5x-17
Subtract 3x from each side
3x-3x+7 = 5x-3x-17
7 = 2x-17
Add 17 to each side
7+17 = 2x-17+17
24 = 2x
Divide each side by 2
24/2 = 2x/2
12 =x
You are planning on installing a security system at your home. For Safety First Security, you can get monitoring for $2 a day with a one-time set-up fee of $150. For Home Safety Security, you can get
monitoring for $1.50 a day with a one-time set-up fee of $200. Using substitution, find the number of days for which both companies would cost the same.
Step-by-step explanation:
a one-time set-up fee of $200. so that's one day a one-time set-up fee of $150. and that's day 2Is base times height divided by 2?
The base is the length of one of the triangle's sides, and the height is the distance from that side to the triangle's opposite corner.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Here,
The base of the triangle is the length of one of its sides, and the height is the distance from that side to the triangle's opposite corner.
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How many integers are there between 100 and 999?
898 integers in that range excluding 100 and 999
There are 900 integers between 100 and 999, inclusive.
Numbers between 999 and 100 inclusive: 999 - 99 = 900
If you want to know the number of integers between 100 and 999, but not including either 100 or 999, then there are 898 integers in that range.
What is an integers number:
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that consists of the following:
Positive Numbers: If a number is greater than zero, it is considered positive. For instance, 1, 2, 3, etc.
Negative numbers are those that are less than zero. For instance: 1, 2, 3, etc.
Zero is described as being neither a positive nor a negative number. A whole number, that is.
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Is 5 a high standard deviation?
Yes, 5 is the high standard deviation which is considered very good.
What is a standard deviation evaluation?A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a low or a high standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points seem to be close to the mean.85 persons responded to my survey about their capacity to carry out specific duties.
The responses are rated on a Likert scale of 1 to 5:
2 = Poor, 1 = Very Poor, 2 = Poor, 4 = Good, 3 = Average, 5 = Very GoodIts standard deviation is 0.54 and the mean score is 2.8.To know more about the standard deviation, here
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Is AAA a triangle congruence theorem?
A triangle AAA does not satisfy congruence theorem. Triangle denoted by AAA refers a triangle having three equal side lengths and three equal angles.
what is congruence theorem?Congruence theorem is developed based on two triangles which have equal corresponding side lengths and equal corresponding angles.
what are the criteria for satisfying congruence theorem?there are four criteria in where one or more criteria needed to satisfy. if two triangles have all three equal side lengths and equal corresponding angles then they satisfy congruence theorem. if two triangles have 2 equal side lengths and angle between sides are equal, they satisfy congruence theorem. If two triangles have equal two angles along
with equal similar side length, they satisfy congruence theorem.
hence, the triangle mentioned in the question is not congruent.
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Answer:
FALSE
Step-by-step explanation:
The angles can be the same, but the lengths of the sides can differ.
Hi can someone answer this
Answer:
first one and second one
Step-by-step explanation:
x + y is lesser or equal to 20
20 being the max amount of hours he can work in one week and x and y being hours he works
second one because they can earn at least 300 dollars, not less than, but x+Y must still be less than 20 though
The last step mentioned in building equations to solve real-world problems is to check your answer by substituting it into the original equation. Another way to check your answer is to use estimation and to make sure the answer is reasonable for the situation. In the problem above, are all of the solutions reasonable for the given situation? Why or why not?
Graphing, substitution, and elimination are the three techniques used to solve systems of equations.
What is meant by linear equation ?There is only one way to know the unknown variable X. As a result, d has a value of 1. To find an equation, we must know the variable(s) that are missing as well as any associated known variable(s).
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The first-degree equations are linear equations. This is the formula for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.Anything connected to a line is said to be linear.
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How do you draw a SSS triangle?
We need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.
What is the SSS triangle condition?Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
We u can move, flip, twist, and turn these triangles to produce the same effect.
When relocated, they are parallel to one another.
Two triangles are deemed similar by the SSS test for triangle resemblance if their third sides are proportionate to one another.
Therefore, we need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.
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Which would cost more: 15 trips to Boston or 11 trips to New York? Explain
Answer:
I think 11 trips to New York because it's a popular tourist attraction.
The table describes the quadratic function p(x).
x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2
The equation of the quadratic function is (c) f(x) = 3(x - 1)² - 2
How to determine the equation of the quadratic function?From the question, we have the table of values that can be used in our computation:
A quadratic equation is represented as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
From the graph, we have the vertex to be
(h, k) = (1, -2)
Substitute (h, k) = (1, -2) in f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 1)² - 2
Also, from the graph, we have the point (0, 1)
This means that
a(0 - 1)² - 2 = 1
So, we have
a(1) = 3
Divide both sides by 1
a = 3
Substitute a = 3 in f(x) = a(x - 1)² - 2
f(x) = 3(x - 1)² - 2
Hence, the equation is f(x) = 3(x - 1)² - 2
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What is the mean of the following data set 4 8 11 12 13?
Answer:
9.6
Step-by-step explanation:
What is the mean of the following data set 4 8 11 12 13?
Mean: is the average of values so:
(4 + 8 + 11 + 12 + 13) / 5 = 9.6
What is the standard deviation of the data given below 10 28 13 18 29 30 22 23 25 and 32?
Hence, the standard deviation of the given data is 7 .
10 28 13 18 29 30 22 23 25 32
Here is the total number of observations n are 10
total= 10 +28+ 13+ 18+ 29+ 30+ 22+ 23+ 25+ 32 = 230
mean (μ) = total/n
= 230/10
= 23
Xi Xi-μ (Xi-μ)²
10 10-23=-13 169
28 28-23=5 25
13 13-23=-10 100
18 18-23=-5 25
29 29-23=6 36
30 30-23=7 49
22 22-23=-1 1
23 23-23=0 0
25 25-23=2 4
32 32-23=9 81
Use the formula to calculate the standard deviation.
√1/n*∑ (Xi-μ)² =√1/10*490
= √49
=7
Hence, the standard deviation of the given data is 7 .
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How do you find the factor of a root?
Answer:
Step-by-step explanation:
you can use the zero-product property to find the roots of a factored equation. After you factor a polynomial into its different pieces, you can set each piece equal to zero to solve for the roots with the zero-product property.
6. From the menu, select the correct
approximation.
If the expression
√24 × √10
represents the area of a rectangle, then
the approximate area of the rectangle is
60 square units
15 square units
8 square units
120 square units
The approximate area of the rectangle as per the options will be equal to 15 square units. Hence, option B is correct.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the amount of unit squares which completely encompass the surface of a compact figure.
The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given information in the question,
Let the length is given as, l = √24 and,
The width is given as, w = √10
Use the formula of area of rectangle,
A = lw
A = √24 × √10
A = 4.89 × 3.16
A = 15.45 ≈ 15 square units.
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One of the solutions to the quadratic equation x - 12x – 45 = 0 is x = -3 Which statement is true? Select all that apply. (Check Screenshot)
Answer:
1st and 3rd 4th
graph of f(x) = x² - 12x-45 has an x-intercept at x = -3
-3 is a zero of the function f(x) = x²-12x- 45
x + 3 is a factor of x² - 12x-45
Steps:
other solution is (x - 15) or x = 15
x² - 12x-45
2 numbers that when multiplied give -45 & when added give -12 are -15 & 3
(x-15) (x+3)
"zero" is a fancy way for asking for the answer or root
imaginary number is i which is √-1 so
if you have √-9 = √9 * √-1 = 3i
if you have √-20 = √4 * √-1 * √5 = 2i√5
.
Is the equation 3x² 11x 10 0 a quadratic equation?
Yes , the equation 3x² + 11x + 10 = 0 is a quadratic equation and the roots are x = -5/3 and x = -2
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
3x² + 11x + 10 = 0 be equation (1)
Now , the equation is of the form ax² + bx + c = 0 , where the value of a = 3 , b = 11 and c = 10
So , the coefficient a is has the variable x² and equation 3x² + 11x + 10 = 0 is a quadratic equation
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
Substituting the values in the equation , we get
x = [ -11 ± √ ( ( 11 )² - 4 ( 3 ) ( 10 ) ) ] / 2 ( 3 )
On simplifying the equation , we get
x = [ -11 ± √ ( 121 - 120 ) ] / 6
x = ( -11 ± 1 ) / 6
So , the two roots of the equations are
x = ( -11 - 1 ) / 6 and
x = ( -11 + 1 ) / 6
x = -2 and
x = -5/3
Therefore , the values of x are -5/3 and -2
Hence , the roots of the quadratic equations are -5/3 and -2
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A car travels 210 miles in 3 hours and 45 minutes. How many miles does it travel per hour?
Answer: 56 miles per hour
Step-by-step explanation:
45 minutes = 0.75 hour
3 hours and 45 minutes = 3.75 hours
Takes 210 divided by 3.75 = 56 miles per hour
How do the base and height of the rectangle compare to the base and height of the parallelogram?
In Parallelogram: Area = base x height(perpendicular distance).
In rectangle: Area = base x height.
Explain some properties of the parallelogram?Parallelogram:
A parallelogram is a particular sort of polygon. It's a quadrilateral in which the opposite side pairs are parallel to one another.
Congruent sides are those when AB = DC.Congruent opposite angels are D = B.(A + D = 180°) Consecutive angles are supplementary.All angles are correct if just one of them is.A parallelogram's diagonals cut each other in half.A parallelogram can be divided into two congruent pieces along each diagonal.Area = base x height(perpendicular distance)
Rectangle:
A quadrilateral having four equal internal angles is a rectangle.A rectangle's opposing sides are equal as well as parallel to one another.Each vertex of a rectangle has a 90° internal angle.The total of a rectangle's internal angles is 360°.The diagonals cut each other in half.The diagonals are all the same length.Area = base(length) x height(width).
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What are the factors of 3x² 4x 4?
The factors of the quadratic equation 3x² -4x -4 are (3x + 2)(x - 2) .
The process of factoring the quadratic equation means expressing the given equation as the product of two linear factors.
The quadratic expression is given as 3x² -4x -4 ;
it can be written as ⇒ 3x² -6x +2x -4 ,...by using split the middle term method .
⇒ 3x(x - 2) + 2(x - 2) ..taking 3x common from first two terms and 2 common from the last two terms .
⇒ (3x + 2)(x - 2)
Therefore , the factors are (3x + 2)(x - 2) .
The given question is incomplete , the complete question is
What are the factors of the quadratic equation 3x² -4x -4 ?
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