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2 years ago

What is the GCF of

Mathematics

2 answers:

Troyanec [42]2 years ago

7 0

$1.) 14b^2 - 35b^3=2\cdot7b^2-5b\cdot7b^2=7b^2(2-5b)\\\\2.) 18x^3y^2 + 42x^2y^3=3x\cdot6x^2y^2+7y\cdot6x^2y^2=6x^2y^2(3x+7y)\\\\3.) 12x^2 + 16y^2=4(3x^2+4y^2)\\\\4.) 3x^2 - 9xy + 12y=3(x^2-3xy+4)\\\\5.) 45x^3 - 60xy^2=3x^2\cdot15x-4y^2\cdot15x=15x(3x^2-4y^2)\\\\6.)36x^2+18x^3-6x+12x^4=6x(2x^3+3x^2+6x-1)$

$Ans.\ GFC:\ 1)\ 7b^2,\ 2)\ 6x^2y^2,\ 3)\ 4,\ 4)\ 3,\ 5)\ 15x,\ 6)\ 6x$

natima [27]2 years ago

6 0

$1.\\14b^2-35b^3\\GCF(14;35)=7\\GCF(b^2;b^3)=b^2\\14b^2-35b^3=7b^2(2-5b)\\\\2.\\18x^3y^2+42x^2y^3\\GCF(18;42)=6\\GCF(x^3y^2;x^2y^3)=x^2y^2\\18x^3y^2+42x^2y^3=6x^2y^2(3x+7y)$

$3.\\12x^2+16y^2\\GCF(12;16)=4\\GCF(x^2;y^2)=1\\12x^2+16y^2=4(3x^2+4y^2)\\\\4.\\3x^2-9xy+12y\\GCF(3;9;12)=3\\GCF(x^2;xy;y)=1\\3x^2-9xy+12y=3(x^2-3xy+4y)$

$5.\\45x^3-60xy^2\\GCF(45;60)=15\\GCF(x^3;xy^2)=x\\45x^3-60xy^2=15x(3x^2-4y^2)\\\\6.\\36x^2+18x^3-6x+12x^4\\GCF(36;18;6;12)=6\\GCF(x^2;x^3;x;x^4)=x\\36x^2+18x^3-6x+12x^4=6x(6x+3x^2-1+2x^3)$

$GCF:\\1)\ b^2;\ 2)\ 6x^2y^2;\ 3)\ 4;\ 4);\ 3;\ 5);\ 15x;\ 6)\ 6x$

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2) 4 6 2 3 If L= | 5 8 and M= 1 4 3 -2 -5 3 3 Find L-M -)) 2 4 8 A ) 3 4 5 2 3 B) 4 4 8 -5 6 9 o 6 12 -2 1 6 6 2 D) 9 12 1

Misha Larkins [42]

$\\ \sf\longmapsto L-M$

Put values

$\sf \left[\begin{array}{cc}\sf 4&\sf 6\\ \sf 5 &\sf 8 \\ \sf 3 &\sf -2\end{array}\right]-\left[\begin{array}{cc}\sf 2&\sf 3\\ \sf 1 &\sf 4 \\ \sf -5&\sf3\end{array}\right]$

Just substract corresponding terms

$\\ \sf\longmapsto \left[\begin{array}{cc}\sf 2 &\sf 3\\ \sf 4&\sf4\\ \sf 8&\sf -5\end{array}\right]$

Option B

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2 years ago

Find Mean, Median, mode and range. Round to the nearest tenth.

stiv31 [10]

Answer:

Mean = 26.24

Median = 27

Mode = 32

Range = 38

Step-by-step explanation:

Plotting the original data from leaf plot

$9,11,12,12,14,17,25,25,27,32,32,32,33,35,41,42,47$

Finding Mean:

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

$\mu=\frac{446}{17}$

= 26.24

Therefore, the range = 26.24.

Finding Median:

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

So, the median is 27 .

Finding Mode:

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

We see that the mode is 32.

Finding Range:

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

The lowest value is 9.

The highest value is 47.

The range = 47 - 9 = 38

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mojhsa [17]

since LM=LN there values are same which is given as 5.5 cm and MN =7cm

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