The expression equivalent to the given expression 2(x -2)-5(2x -3) is
(2x-4-10x+15)
What is an expression?An expression in maths, a sentence with a minimum of two numbers or variables and at least one maths operation.
Given is an expression, 2(x -2)-5(2x -3)
Using distributive property,
a(b+c) = ab+bc
2(x -2)-5(2x -3) = 2x-4-10x+15
Hence, The expression equivalent to the given expression 2(x -2)-5(2x -3) is (2x-4-10x+15)
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Castel bought 5 writing utensils for a total of $8. Pens cost $1 and pencils cost $2. How many of each writing utensil did he buy?
Answer: 8 = 1x + 2y
Step-by-step explanation:
this could be multiple answers, is this a multiple-choice question? follow that equation to find the answer that fits.
I got the equation by these steps:
total money spent is $8, so you start with 8 =
you don't know the specific number of pens so make that x. the cost of pens is $1, so the total cost will be $1 times however many pencils are bought, ie 1x.
repeat that for pencils, replacing $1 with $2, and making pencils mean y. you get 2y.
now to find your answer, insert numbers into x and y until they equal 8.
possible answers:
x=4, y=1
x=2, y=2
x=0, y=4
All of the answers to the questions, this question makes no sense to me.
Answer:
(a) ∠HFE, ∠EFH
(b) FG, FE
(c) F
Step-by-step explanation:
You want the different names for the angles shown, and for their parts.
This question is about naming bits of geometry. Here, you're mainly naming rays and combinations that form angles. A ray is always named by naming its end point first, then another point on the ray. An angle is formed by two rays with a common end point.
(a) ∠2An angle can be named by naming rays that form it (with the vertex in the middle of the name), by naming the vertex alone (if that is unambiguous), or by using a designator, such as ∠2.
Angle 2 is made from rays FH and FE, so can be named either of ...
∠HFE∠EFHIf ray FG were not present, it could also be named angle F, the name of the vertex point.
(b) ∠GFEThe 3-letter angle name tells you the names of the sides. The end point of each ray must be named first in the ray name. It is named in the middle of the angle name.
FGFE(c) ∠1The vertex of angle 1 is the point that is also the vertex of angle 2:
F1) In a sample of 25 iPhones, 12 had over 85 apps downloaded. Construct a 90% confidence interval for the population proportion of all iPhones that obtain over 85 apps.
Assume z0.05 = 1.645.
a) 0.48 ± 0.16
b) 0.48 ± 0.09
c) 0.29 ± 0.15
d) 0.29 ± 0.16
we calculated confidence interval = 0.48±0.16
what is confidence interval?confidence interval represents the accuracy of a particular estimation.
what is proportion of sample?
proportion of population is the ratio of random sample to the total available sample.
Given, size of samples that means number of total iPhones, n = 25
size of random samples that means iPhone with 85 downloaded apps, p= 12,
critical value for 90% confidence interval z* = 1.65
proportion of samples, p^ = p/n = 12/25 =0.48
finally, confidence interval = p^±z*[√{p^(1-P^)/n}]
0.48±1.65[√{0.48(1-0.48)/25}]
hence, the confidence interval = 0.48±0.16
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Assuming that the annual rate of inflation averages 4% over the next 10 years, the approximate costs С of goods or services during any year in that decade will be modeled by C(t) = P(1.04)’. where t is the time in years and P is the present cost. The price of an oil change for your car is presently $23.95. Estimate the price 10 years from now.
By using the provided formula of inflation, the answer is $35.35.
What do you mean by inflation?The rate at which consumer prices for a variety of products and services are increasing is known as inflation.
What are the ways for measuring inflation?The common ways followed are:
The Consumer Price Index (CPI)CPI, less food and energy.Personal Consumption Expenditures (PCE)Personal Consumption Expenditures excluding food and energy or “Core PCE”[tex]C(t) = P(1.04)^{t}[/tex]
P= $23.95
t=10
The estimated price is [tex]23.95*(1.04)^{10}[/tex]
=$35.35
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Answer that shows work and is correct gets brainliest!! Pls help! 100 points
a) Using conditional probability, the likelihood that a driver purchases oil, given that he or she purchases gasoline is 5.62%.
b) Based on conditional probability, the chance that a driver purchases gasoline, given that he or she purchases oil is 71.43%.
What is conditional probability?Conditional probability is the likelihood or chance of an event or outcome occurring, based on a previous event or outcome that occurs.
Conditional probability considers two events occurring relatively.
The formula for conditional probability is intersection probability divided by base probability.
The percentage (proportion) of drivers who stop at a gas station to buy gasoline = 89%
The probability of buying both gasoline and oil = 5%
The percentage (probability) of purchasing oil = 7%
a) The probability that a driver purchases oil, given that he or she purchases gasoline = the probability of buying both gasoline and oil/the probability of stopping and buying gasoline.
= 5.62% (0.05/0.89).
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b) The probability that a driver purchases gasoline, given that he or she purchases oil = the probability of buying both gasoline and oil/the total probability of those who purchase oil.
= 71.43% (0.05/0.07 x 100).
Question:Of the drivers who stop at a gas station, 89% purchase gasoline, and 5% purchase both gasoline and oil. A total of 7% purchase oil.
(a) What is the probability that a driver purchases oil, given that he or she purchases gasoline? Round your answer to the nearest hundredth.
b) What is the probability that a driver purchases gasoline, given that he or she purchases oil? Round your answer to the nearest hundredth.
What is the range of h?
A)All real numbers greater than or equal to -7
B)All real numbers greater than or equal to -3
C)All real numbers greater than or equal to 41
D)All real numbers
The range of h of the given function table is; A)All real numbers greater than or equal to -7
What is the range of the function?The range of a function is defined as the set of all possible output values for which the function is valid.
From the given function table, we can see the following coordinates;
(-3, 18)
(-1, 8)
(2, -7)
(3, -12)
(4, 17)
(6, -27)
Now, from the above coordinates, we can see that the maximum value of h(x) is 17 while the minimum value is -27.
Looking at the options, the only one that fits the available range of the function is option A.
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his question is about filling in the blanks in the derivation of the first and second barycentric interpolation formulas. recall that the j-th lagrange polynomial is defined as
A variation on Lagrange polynomial interpolation is called barycentric interpolation. Second, just use Newton interpolation formula to assess p(x) for each x.
Why is the Lagrange interpolation theorem important?The Lagrange interpolation theorem can be used to create a polynomial that traverses a specified set of points and takes particular values at random locations. This theorem provides the approximate formula for the nth degree polynomials to the function f if a variable f (x) is available at discrete places xi, I = 0, 1, 2,... (x).
What is the LaGrange theorem's conclusion?The Lagrange theorem extrapolates well-known mathematical principles like the statement that a line is uniquely specified by two points, the knowledge that the quadratic function polynomial is completely determined by three points, and so forth.
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help I’ll mark brainliest
The value of expression 9 1/2k - [7 + 3 1/4k] without parentheses is 25 / 4 k - 7.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
9 1/2k - [7 + 3 1/4k]
Simplify the above expression and convert mixed fractions into improper fractions,
19 / 2 k - [7 + 13 / 4k]
19 / 2 k -[(28 + 13 k) / 4]
(38k - 28 -13k) / 4
(25k - 28) / 4
25 / 4 k - 7
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Identify the slope of the line through points (3,4) and (-4,-5).
a. -9/7
c. 0
b. -1
d. 9/7
A
D
B
C
Answer:
b) D => d. 9/7
Step-by-step explanation:
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (-5 - 4)/(-4 - 3)
→ m = (-9)/(-7)
→ [ m = 9/7 ]
Hence, the slope is 9/7.
Help pls I don’t understand
The missing length and the missing angle are approximately 40.447 and 20.034°.
How to determine the length of missing side and the measure of the missing angle
In this question we have a geometric system formed by a equilateral triangle divided into two triangles by a line segment. The missing sides and angles can be found by means of algebra properties, Euclidean geometry and trigonometry.
First, obtain the missing side by taking approach of properties for equilateral triangles:
y = 46 - 16
y = 30
Second, find the length of line segment by law of cosine:
l = √(46² + 16² - 2 · 46 · 16 · cos 60°)
l ≈ 40.447
The missing length is approximately 40.447.
Third, the measure of the missing angle by law of sine:
16 / sin x = 40.447 / sin 60°
sin x = (16 / 40.447) · sin 60°
sin x = 0.343
x ≈ 20.034°
The missing angle is approximately 20.034°.
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In Problems 1–6, use the method of undetermined coefficients to find a general solution to the system x′1t2 =
Ax1t2 + f1t2, where A and f1t2 are given
Answer:hi
Step-by-step explanation:
Sandra has 50 beads to make into 6 rings. Each ring will use the same number of beads. Sandra divides to see how many beads she can use in each ring.
Answer:
8 beads per ring.
Step-by-step explanation:
50/6 = 8.333..
Since you cannot have less than half of a ring, the answer is 8.
What happens to y = x| when the slope is changed to a negative?
Answer:
If the slope of a line is negative, it means that the line is sloping downward from left to right. In other words, as the value of x increases, the value of y decreases. This is in contrast to a positive slope, where as the value of x increases, the value of y also increases. So, if the slope of the line y = x is changed to a negative value, the line will still have the same general shape, but it will be flipped upside-down and will slope downward from left to right
Question 1:
Find the percent of change to the nearest tenth of a percent for Centerville
Question 2:
Which town had the greatest percent of change
Question 3:
What was the percent of change? (From your answer in Part B) Do Not Include 'Increase' or 'Decrease.' Round to the nearest whole percent.
Answer:
Sorry just trying to get points
Step-by-step explanation:
Simplify the expression.
8x-4y-8
-2xy5
Write your answer without negative exponents.
On solving the problem of expression we can say that , the answer is 5x + 9.A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
What is an Expression in Math?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6. Complex riddles are solved using mathematical expressions. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6. Complex riddles are solved using mathematical expressions.
[tex]3x + 2 - 3x + 7 + 5x = 5x + 9[/tex]
Group the like terms
[tex]3x - 3x + 5x + 2 + 7[/tex]
now adding similar elements: 3x - 3x + 5x = 5x
[tex]5x + 2 + 7[/tex]
and add the numbers: 2+7=9
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NO LINKS!! Please help me with the Domain and Range and Functions Part 4bb
Domain - the set of possible x-coordinates of a function.
Range - the set of possible y-coordinates of a function.
Question 32
Domain is:
x ∈ (- 6, 6), both ends exclusive as open circles.Range is:
y ∈ (-6, 2], the -6 is excluded as open circle, the 2 is included as part of the graph.This is a function as it passes the vertical line test.
Question 33Domain is:
x ∈ (- 5, 6], one end is open circle and the other is closed circle.Range is:
y ∈ (-1, 5], the -6 is excluded as open circle, the 2 is included as part of the graph.This is a function as it passes the vertical line test.
Answer:
32.a) Domain: (-6, 6)
32.b) Range: (-6, 2]
32.c) Function: Yes
33.a) Domain: (-6, 6]
33.b) Range: (-1, 5]
33.c) Function: Yes
Step-by-step explanation:
Definitions
An open circle indicates the value is not included in the interval.A closed circle indicates the value is included in the interval.An arrow shows that the function continues indefinitely in that direction.Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 32From inspection of the graph, the endpoints of the continuous curve are:
(-6, 0) and (6, -6)As the endpoints are open circles, the x-values are excluded from the domain. Therefore, the domain in interval notation is:
Domain: (-6, 6)The smallest y-value is y = -6 and the greatest y-value is y = 2.
y = -6 is excluded from the range since it is the y-value of the open circle endpoint, whereas y = 2 is included in the range. Therefore, the range in interval notation is:
Range: (-6, 2]The graph is a function as is each input (x-value) is related to exactly one output (y-value).
Question 33From inspection of the graph, the endpoints of the continuous line are:
(-6, -1) and (6, 5)As the graph is a straight line, the x and y values of the endpoints are the x and y values of the domain and range.
As the (-6, -1) endpoint is an open circle, the values are excluded from the domain and range.
As the (6, 5) endpoint is a closed circle, the values are included in the domain and range.
Therefore, the domain and range in interval notation are:
Domain: (-6, 6]Range: (-1, 5]The graph is a function as is each input (x-value) is related to exactly one output (y-value).
A seed has a 54% probability of growing into a healthy plant. 7 seeds are planted.What is the probability that the number of plants that grow is exactly 1?
The probability of growing seed exactly one is 0.0033.
What is probability?The probability of a seed not growing is 0.46, because if it has a 54% chance of growing, then 100% - 54% to find the odds that it will not grow, which is 46%.
The probability of 7 seeds growing is equivalent to asking what the probability is of a seed growing and another seed growing and another seed growing and another seed, and so on until I say a total of 7seeds. The point is that "and" in probability means to multiply.
To calculate the likelihood of seven seeds growing,
(0.46)(0.54)⁷
Probability = 0.0033
Probability = 0.0033 x 100
= 0.33%
Therefore probability of growing exactly one seed is 0.0033.
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A simple random sample of 500 individuals provides 250 Yes responses. a. What is the point estimate of the proportion of the population that would provide Yes responses (to 2 decimals)? b. What is your estimate of the standard error of the proportion (to 4 decimals)? c. Compute the 95% confidence interval for the population proportion (to 4 decimals).
a) The point estimate of the proportion of the population that would provide Yes responses is; 0.50
b) The estimate of the standard error of the proportion is; 0.0224
c) The 95% confidence interval for the population proportion is; CI = (0.4569, 0.5431)
How to calculate the confidence interval?a) The point estimate of proportion in a sample of n out of which x belongs to the favorable event is;
p^ = x/n
Thus, we are given; x = 250 and n = 500
p^ = 250/500
p^ = 0.5
b) The standard error is defined as a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. It is given by the formula;
S = √(p^(1 - p^)/n)
Plugging in the relevant values gives;
S = √(0.5(1 - 0.5)/500)
S = 0.0224
c) A confidence interval is defined as the mean of your estimate plus and minus the variation in that estimate. The confidence interval is given by the formula;
CI = p^ ± z√(p^(1 - p^)/n)
where z is z-score at confidence level
z at 95% confidence level = 1.96
Thus;
CI = 0.5 ± 1.96√(0.5(1 - 0.5)/500)
CI = 0.5 ± 0.04312
CI = (0.4569, 0.5431)
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find the slope of the line that passes through T(-2,11) U(3,11)
Answer:
Step-by-step explanation:
use equation [tex]\frac{y2-y1}{x2-x1}[/tex] to calculate the slope, in this case the slope would be [tex]\frac{11-11}{3-(-2)}=\frac{0}{6} =0[/tex]
The slope would be 0 for the line,
another way we can tell the slope is 0 is that we can see the two sets of coordinates are on the y=11, they just have different x coordinates.
But the equation above shows the complete work and supported the answer.
Answer:
Slope (m) = 0
Step-by-step explanation:
Given coordinates,
→ T(-2, 11)
→ U(3, 11)
Formula we use,
→ Slope = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (11 - 11)/(3 -(-2))
→ m = (0)/(3 + 2)
→ m = 0/6
→ [ m = 0 ]
Therefore, the slope is 0.
Find the equation of the exponential function represented by the table below:
The equation of the exponential function represented by the table will be:
[tex]f(x) = 2(4)^{x}[/tex]
An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
We know the equation of exponential function such as
[tex]f(x) = ab^{x}[/tex]
Put x=0, and y=2 in the function
[tex]2 = ab^{0} \\2 = a[/tex]
Also x=1, and y=8 in the function
[tex]8 = 2b^{1} \\b = 4[/tex]
Thus,
[tex]f(x) = ab^{x} \\f(x) = 2(4)^{x}[/tex]
Therefore, the equation of the exponential function represented by the table will be:
[tex]f(x) = 2(4)^{x}[/tex]
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True or false equation 2/3 - 1/6=1/3
Answer:
False
Step-by-step explanation:
2/3 - 1/6 = 3/6
The table gives the temperature (in °F) in five cities at 6 a.m. on the same day. Use the table to answer the questions. City Buffalo Phoenix Memphis Houston Fairbanks Temperature (°F) -13 83 45 64 -24 (a) How much higher was the 6 a.m. temperature in Houston than in Buffalo? °F higher (b) By noon, the temperature in Buffalo had risen by 19 °F. What was the temperature there at noon? °F
Temperature at 6 a.m. was:
Houston = 64 °F,Buffalo = - 13 °F.The difference is:
64 - (-13) = 64 + 13 = 77 °FPart BTemperature in Buffalo at noon was 19 °F greater:
- 13 + 19 = 19 - 13 = 6 °FHELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ITS DUE IN 15 MINS
Answer:
[tex]2 x 3^{2} x 7[/tex]
Step-by-step explanation:
The answer is 2 × 3 × 3 × 7 which is 2 x 3^2 x 7
You want to format a 64GB USB disk to use it in Windows. Which file system should you use? FAT FAT32 ONTFS
Answer: FAT32
you're welcome :D
Answer:
use fat32
FAT32 is regarded as the default file system for external drives, especially the removable USB flash drives and SD memory cards. It's the most compatible file system that can be used on major devices and operating systems like Windows and macOS. So, the advantage of using FAT32 is portability.
However, FAT32 has some disadvantages, or let's say limitations as well. First and foremost, if you use a single file over 4GB in size, you'll need to convert FAT32 to NTFS or exFAT; What's more, due to the manufacturers' specifications, FAT32 can only be used to format drives between 2GB and 32GB, and that's why native tools on Windows have that limit, too. When you try to format a USB drive over 32GB in Windows Explorer, there is no "FAT32" option at all.
Determine probability of selecting at least 1 marble that is not red
The probability of selecting at least one marble that is not red is given as follows:
1.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.Considering a success as selecting non-red marbles, the values of these parameters are given as follows:
N = 4, n = 2, k = 3.
The probability of at least one not red is given as follows:
P(X > 0) = 1 - P(X = 0).
In which:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,4,3,2) = \frac{C_{3,0}C_{1,2}}{C_{4,2}} = 0[/tex]
Hence the probability is of:
P(X > 0) = 1 - P(X = 0) = 1 - 0 = 100%.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Stefano owns a restaurant where his customers create their own pasta dishes. The customer chooses exactly one type of noodle, sauce, vegetable, and meat. The following table shows the options available to customers.
Create your own pasta
Noodle options Spaghetti, Penne, Linguine
Sauce options Tomato, Rosa, Alfredo
Vegetable options Mushroom, Onion, Green pepper, Tomato
Meat options Steak, Beef, Sausage, Chicken, Bacon
How many different pasta dishes can customers create
The number of different pasta dishes the customers can create are 180.
Define combination.According to its definition, a combination is "An arrangement of objects where the order in which the objects are selected is irrelevant." The phrase "Selection of things" denotes a situation in which the chronological order of events is irrelevant.
Given,
Number of noodle options = 3.
Number of sauce options = 3.
Number of vegetable options = 4.
Number of meat options = 5.
To find the number of possible combinations we need to take the total number of each option and multiply them together as there is no repetition allowed.
Possible combinations = 3×3×4×5
= 180
Thus, the number of pasta dishes created = 180.
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a coach took his team out for pizza after their last game. there were 14 players so they had to sit in smaller groups at different tables. six players sat at one table and got 4 small pizzas to share equally. the other 8 players sat at a different table and got 6 small pizzas to share equally. afterwards one of the players said it wasnt fair because some kids got more pizza do u agree?
Yes, it wasn't fair because some kids got more pizza.
What is simplest form of a fraction?
When the numerator (top) and denominator (bottom) of the fraction do not have any common factors, the fraction is said to be in its simplest form. For instance, 1/2 is the most basic version of 6/12.
Given that, there were 14 players.
Six players sat at one table and got 4 small pizzas to share equally.
Applying unitary method,
Thus each players got 4/6 part of a pizza.
= 2/3 [ Divide denominator and numerator by 2]
The other 8 players sat at a different table and got 6 small pizzas to share equally.
Each players got 6/8 part of a pizza.
= 3/4 [Divide denominator and numerator by 2]
Now compare 2/3 and 3/4:
The LCM of the denominators 3 and 4 is 12.
Multiply 4 with denominator and numerator of 2/3:
(2×4)/(3×4) = 8/12
Multiply 3 with denominator and numerator of 3/4:
(3×3)/(4×3) = 9/12
Therefore, 9/12 > 8/12
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Your neighbor is digging a hole in his back yard for an in-ground swimming pool. The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep. If his pickup truck can haul one cubic meter, how many trips will it take him to haul all of the dirt away?
(please show work)
There are 896 trips will it take him to haul all of the dirt away.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep.
Now,
Since, The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep.
And, His pickup truck can haul one cubic meter.
Hence, Number of trips will it take him to haul all of the dirt away will be;
⇒ 16 × 7 × 8 / 1
⇒ 896
Thus, Number of trips = 896
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On the coordinate plane below, draw a line through C point ths is parallel to AB.
Based on your drawing write equation of line that passes through point C and is parallel to AN. Your equation should be in the form y = mx + b. Desribe how you determined the equation.
Answer:
y = 2/3x -7
see the attachment for a graph
Step-by-step explanation:
You want the equation and graph of a line through point C(6, -3) parallel to the line shown through points A(-3, 3) and B(3, 7).
SlopeYou can count the grid squares to see that the slope of line AB is 2 units up for each 3 units to the right. The line through C will have the same slope:
m = rise/run = 2/3
Y-interceptThe line drawn with that slope through point C will cross the y-axis at y = -7. This value is the "b" in the slope-intercept equation for the line:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 2/3x -7
Graph
A graph of the line is shown in the attachment.
Factor the greatest common factor: 12a³b + 8a²b² - 20ab³.
O4ab(3a + 2ab - 5b²)
O 4ab(3a² + 2ab - 5b²)
O4a²b(3a³b-2a²b² - 5ab³)
O4a²b(3a² + 2ab - 5)
Greatest common factor (GCF): 12a³b + 8a²b² - 20ab³. = 4ab(3a² + 2ab - 5b²) that is option 2
Describe GCF.A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. Since four is the biggest, we refer to the GCF of 12, 20, and 24 as four.
There are two stages to get the GCF since 12a3b + 8a2b2 - 20ab3. contains both integers and variables (HCF). Find GCF for the variable component first, then for the numeric part.
How to locate GCF
1. Find the GCF for the 12, 8, 20 numerical portion.
2. Calculate the GCF for the variable component (a3b, a2b2, and ab3).
3. Add the values together and multiple them
Find the common factors for the numerical part: 12 ,8,20 is
factors of 12 -1,2,3 ,4,6,12
factors of 8 - 1,2,4,8,
factor of 20 - 1,2,4,5,10,20
the common factor will be 1,2,4
so GCF = 4
Next, find the common factors for the variable part: a³b , ,a²b² ,ab³.
the common factors will be ab
so GCF = ab
for the equation 12a³b + 8a²b² - 20ab³.
4ab is common , if we take 4ab common then remaining parts are
12a³b = 3a²
8a²b² = 2ab
20ab³. = 5b²
greatest common factor: 12a³b + 8a²b² - 20ab³. = 4ab(3a² + 2ab - 5b²)
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