hannahgracew12
28.10.2019 •
Mathematics
G(x)=27x^3+125
find factors of the binomial g(x).
a. g(x)= (3x+5)(9x^2+15x+25)
b. g(x)= (3x-5)(9x^2+15x+25)
c. g(x)= (3x+5) (9x^2-15x+25)
d. g(x)= (3x-5)(9x^2-15x+25)
Solved
Show answers
More tips
- C Computers and Internet Dynamically Assigned IP Address: What Is It and How Does It Work?...
- H Health and Medicine Angina: Causes, Symptoms, and Treatment...
- C Computers and Internet How to Learn to Type Fast?...
- F Food and Cooking Delight for Gourmets: How to Prepare Liver Pate...
- S Style and Beauty How to braid friendship bracelets?...
- H Health and Medicine Mercury Thermometer Danger: What to do when a thermometer breaks?...
- F Food and Cooking Which Calamari Salad is the Most Delicious?...
- S Society and Politics 10 Tips for Boosting Your Self-Esteem...
- F Food and Cooking The Most Delicious and Simple Fish in Batter Recipe...
- H Health and Medicine What is Autism? Understanding the Basics of This Neurodevelopmental Disorder...
Answers on questions: Mathematics
- M Mathematics Seven times the first number plus 6 times the second number equals 36. Three times the first number minus ten times the second number is 28. What are the two numbers?...
- M Mathematics If a = 45°, what dose b equal?...
- M Mathematics Help me with math pls 20 pints show work !...
- M Mathematics alonso brings $21 to the market to buy eggs and avacofoes. he notices the store sells avacodos in bags of 3 for 5$...
- M Mathematics Name a point thats is not on Plane R...
- M Mathematics СУК В ГРЯЗИ XDDDDDDDDDDDDD...
- M Mathematics The ages of three friends are consecutively one year apart. Together, their ages total 66 years. Which equation can be used to find the age of each friend (where...
- M Mathematics X(2+4^2-5-3x) use the distribute property to write an equivalent expression in standard form...
- M Mathematics Most tennis rackets have 110 square-inch head, plud or minus 25 inches. write and solve an absolute value equation to determine the least and greatest possible sizes...
- M Mathematics What is the non-perfect square root of 9.6...
Ответ:
The answer to your question is: (3x + 5)(9x² - 15x + 25)
Step-by-step explanation:
Data
G(x) = 27x³ + 125
This is a sum of cubes
Process
27x³ + 125 = (3x)³ + (5)³ = (3x + 5)(9x² - 15x + 25)
Ответ:
since each ball has a different number and if no two pairs have the same value there is going to be 14∗14 different sums. Looking at the numbers 1 through 100 the highest sum is 199 and lowest is 3, giving 197 possible sums
For the 14 case, we show that there exist at least one number from set {3,4,5,...,17} is not obtainable and at least one number from set {199,198,...,185} is not obtainable.
So we are left with 197 - 195 options
14 x 14 = 196
196 > 195
so there are two pairs consisting of one red and one green ball that have the same value
As to the comment, I constructed a counter-example list for the 13 case as follows. The idea of constructing this list is similar to the proof for the 14 case.
Red: (1,9,16,23,30,37,44,51,58,65,72,79,86)
Green: (2,3,4,5,6,7,8;94,95,96,97,98,99,100)
Note that 86+8=94 and 1+94=95 so there are no duplicated sum
Step-by-step explanation:
For the 14 case, we show that there exist at least one number from set {3,4,5,...,17} is not obtainable and at least one number from set {199,198,...,185} is not obtainable.
First consider the set {3,4,5,...,17}.
Suppose all numbers in this set are obtainable.
Then since 3 is obtainable, 1 and 2 are of different color. Then since 4 is obtainable, 1 and 3 are of different color. Now suppose 1 is of one color and 2,3,...,n−1 where n−1<17 are of the same color that is different from 1's color, then if n<17 in order for n+1 to be obtainable n and 1 must be of different color so 2,3,...,n are of same color. Hence by induction for all n<17, 2,3,...,n must be of same color. However this means there are 16−2+1=15 balls of the color contradiction.
Hence there exist at least one number in the set not obtainable.
We can use a similar argument to show if all elements in {199,198,...,185} are obtainable then 99,98,...,85 must all be of the same color which means there are 15 balls of the color contradiction so there are at least one number not obtainable as well.
Now we have only 195 choices left and 196>195 so identical sum must appear
A similar argument can be held for the case of 13 red balls and 14 green balls