Answer:
[tex]2000 \: and \: 9.[/tex]
[tex]it \: could \: be \: the \: sum \: of \: any \: two \: \\ positive \: integers \: so \: they \: are : \\ 2000 \: and \: 9[/tex]
Let's consider a much smaller value and work our way up to the factorial 2009!
Start with a+b = 2. The value 2 is the smallest right hand side possible since a > 0 and b > 0, so a = b = 1 is the smallest a,b possible.
The only solution to a+b = 2 is a = b = 1 as mentioned.
----------
Now move onto a+b = 3. We have two solutions:
a = 1, b = 2
a = 2, b = 1
-----------
Now move onto a+b = 4. We have three solutions
a = 1, b = 3
a = 2, b = 2
a = 3, b = 1
Note how 'a' counts up while b counts down. I have 'a' starting at the smallest value, and b is set to add with 'a', getting to the right hand side.
So 'a' counts up to 3, while b counts down from 3.
We cannot reach 4 since 0 is not allowed for a or b.
-------------
The conjecture is that a+b = k has k-1 positive integer solutions. A simple proof of this is to list out all solutions like so
a = 1, b = k-1
a = 2, b = k-2
a = 3, b = k-3
....
a = k-3, b = 3
a = k-2, b = 2
a = k-1, b = 1
Where k > 2
Going from 1 to k-1 is exactly k-1 items. It's similar to how {1,2,3,..,m} has m different integers in it. Replace m with k-1 and you have the same idea.
This confirms there are k-1 solutions listed above.
The last step is to simply replace k with 2009! and we have 2009! - 1 different ordered pair solutions
Since the factorial 2009! is so massive, it's best to not expand this out using a calculator. Many calculators would produce "overflow", or similar, if you tried to compute the factorial 2009!
12. Bob thought of a number, added 5, multiplied
by 3 and took away 5 to give an answer of 10.
What was the starting number?
Answer:
0
Step-by-step explanation:
Say the number was x.
3(x+5)-5=10
3(x+5)=15
x+5=5
x=0
Which list shows the numbers in order from greatest to least?
0.6, 0.453, 0.563, 0.4
0.4, 0.453, 0.563, 0.6
0.6, 0.563, 0.453, 0.4
0.563, 0.6, 0.453, 0.4
Answer:
c
Step-by-step explanation:
its really simple it's c
Write the sentence as an inequality. A number x is less than 7 and greater than 3
The inequality as per the given statement will be equal to 3 < x < 7.
What is inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the information in the question,
Let the number is x.
x is less than 7.
x < 7 and,
x is greater than 3,
So, x > 3
So, it can be written in combined form as:
3 < x < 7
To know more about Inequality:
https://brainly.com/question/28823603
#SPJ2
There are two different maps of California. The scale on the first map is 1 cm to 20 km. The distance from Fresno to SanFrancisco is 15 cm.The scale on the second map is 1 cm to 100 km.What is the distance from Fresno to San Francisco on the second map? Explain your reasoning.b
Answer:
1500km
Step-by-step explanation:
1cm=100km
15•100=1500km
-2/9 ÷ 1/2 as a fraction
Answer:
-4/9
Step-by-step explanation:
-2/9*2/1
-4/9
Answer:-4/9
Step-by-step explanation:used a caculator
-1+10x^3+x^2
−1+10x
3
+x
2
Answer:
=20x3+2x2−2
Step-by-step explanation:
Let's simplify step-by-step.
−1+10x3+x2−1+10x3+x2
=−1+10x3+x2+−1+10x3+x2
Combine Like Terms:
=−1+10x3+x2+−1+10x3+x2
=(10x3+10x3)+(x2+x2)+(−1+−1)
=20x3+2x2+−2
After completing the fraction division 8 divided by StartFraction 1 Over 6 EndFraction, Patel used the multiplication below to check his work. StartFraction 1 Over 48 EndFraction times 6 = StartFraction 1 Over 48 EndFraction times StartFraction 6 Over 1 EndFraction = StartFraction 6 Over 48 EndFraction = StartFraction 1 Over 8 EndFraction Which is the most accurate description of Patel's work? Patel found the correct quotient and checked his work using multiplication correctly. Patel found the correct quotient but checked his work using multiplication incorrectly. Patel found an incorrect quotient but checked his work using multiplication correctly. Patel found an incorrect quotient and checked his work using multiplication incorrectly.
Answer:
Patel found an incorrect quotient and checked his work using multiplication incorrectly.
Step-by-step explanation:
After completing the fraction division 8 divided by StartFraction 1 Over 6 EndFraction, Patel used the multiplication below to check his work.
Correct calculation
8 ÷ 1/6
= 8 × 6/1
= 48
Check:
1/6 * 48
= 48 / 6
= 8
Patel's calculation
1/48 * 6
= 1/48 * 6/1
= 6/48
= 1/8
Patel found an incorrect quotient and checked his work using multiplication incorrectly.
Answer:
D on edge
Step-by-step explanation:
have a great day :)
hope this helps :)
2. What is the equation in slope-intercept form of the line that passes through the given points in
the table?
x
2
3
y
-1
-4
Answer:
3y= -1 + 2x -4
Step-by-step explanation:
cause.... COOCHIEMAN
Estimate the square root of 19 to the nearest tenths place
Find the distance between (8,-4,7) and (8,5,3)
Answer:
sqrt(97)
Step-by-step explanation:
Since the x for both of the points are the same, we can reduce the problem to "find the distance between (-4, 7) and (5, 3)".
To do that, we can use the Pythagorean theorem, where (change in x)^2+(change in y)^2 = (distance)^2:
(5-(-4))^2+(3-7)^2=d^2
(9)^2+(-4)^2=d^2
81+16=d^2
97=d^2
d=sqrt(97).
I have 4 and 11/12 . how much do i need to add to get 6 and 1/2
Answer:
= 1 7/12
Step-by-step explanation:
6 1/2 - 4 11/12 =
6 6/12 - 4 11/12 =
5 18/12 - 4 11/12 =
=1 7/12
To check if the answer is right or wrong, you can add 1 7/12 to 4 11/12
4 11/12 + 1 7/12 = 5 18/12 = 6 6/12 = 6 1/2
Hope this helps and pls do mark me brainliest if you can:)
Hong needs to memorize words on a vocabulary list for Spanish class. He has memorized 30 of the words, which is five-sixths of the list. How many words are on the list?
Someone help ASAP!!!
Pleaseee
Answer: C
Step-by-step explanation:
A slide is when you slide it over and a flip is when you flip it around
the answer is C because it said slide than flip across
−2(x+1/4)+1=5 PLEASE HELP
Answer:
x = -2 1/4
Step-by-step explanation:
-2(x + 1/4) + 1 = 5
-2x - 1/2 + 1 = 5
-2x + 1/2 = 5
-2x = 5 - 1/2
-2x = 4 1/2
-x = 2 1/4
x = -2 1/4
Hope this helps!
Let me know if I'm wrong :)
Look at the following graph and determine the slope of the line. AY 10 7 5 3 2 1 х 1 2 3 4 5 6 7 8 9 8 9 10
Answer:
I believe the slope is 2/3.
if your highway gas mileage is 26 and you take a trip that is 600 miles how much gas will you use
OMG i dont remember to find square roots
can someone please explain why 5√ 5 is equal to √ 125
15 pts and brainliest!
Answer:
5
Step-by-step explanation:
√125 / 5= √25 since 125 / 5 =25
√25 = 5
Answer:
5x25
Step-by-step explanation:
since its 5 you multiply it by 5 and then multiply why you got to another 5
PLEASE HELP, MARKING BRAINLIEST!!!!
These triangles are congruent by _____.
A. SAS
B. ASA
C. AAS
D. SSS
Answer:
ASA Postulate
Step-by-step explanation:
It's Angle-Side-Angle Postulate because you can see two clearly congruent angles, two clearly congruent sides attached to that angle, and the angle connected to that line is congruent to the other triangles corresponding angle because they're vertical angles.
Answer:
B. ASA
Step-by-step explanation:
We know that the angles in which the triangles are connected are equal to one another because the lines continue and do not bend so that is your first angle, then we see a red line on both triangles indicating that the sides are equal. That is your side, and finally there is a red curve in both corners of the triangle indicating the angles are equal. Therefore the triangle is congruent by ASA.
what is 1/2 x2/5 =
and 3/4 x 5/9 =
1/5
5/12
Step-by-step explanation:Hi there !
1/2 × 2/5 = 1×2/2×5 = 2⁽²/10 = 1/5
3/4 × 5/9 = 3×5/4×9 = 15⁽³/36 = 5/12
Good luck !
Answer:
1/5
5/12
Step-by-step explanation:
These are the answers because:
1) Whenever we multiply fractions, we have to multiply the numerator with the numerator and the denominator with the denominator.
2) In this case it would be:
1/2 x 2/5 = 1 x 2/2 x 5 = 2/10 = 1/5
3/4 x 5/9 = 3 x 5/4 x 9 = 15/36 = 5/12
Hope this helps! :D
Which one?
A. B. C. or D?
The answer is to the question is c.11
What's the difference between Direct and Inverse Proportion? Please explain
Answer: Direct means when x goes up y also goes up, inverse means when x goes up, y goes down and vice versa.
Answer:
Step-by-step explanation:
The answer is that with direct variation, the value and the quantity changes and goes according, either lower or higher, but with inverse variation, the value can go higher, and the quantity can go lower, and the quantity can go higher, but the value can be lower.
The City Zoo feeds its three giant pandas 181.5 pounds of bamboo shoots every day. Each panda is fed the same amount of bamboo. How many pounds of bamboo does each panda eat every day?
Group of answer choices
605 pounds
61.5 pounds
60.5 pounds
6.05 pounds
Answer:
60.5 pounds
Step-by-step explanation:
The total amount of pound is 181.5
And there are three pandas.
So 181.5 divide by 3 is 60.5
what is 11/12 plus (-7/12)? simplest form
Answer:
1/2
Step-by-step explanation:
11/12 + (-7/12) have the same denominator so you can leave it as is.
11/12+(-7/12) is the same as 11/12-7/12 which is equal to 6/12 which can be simplified to 1/2
Please Help, this is 20pts worth it.. Please Don’t waste my points.. please help..
Answer:
1. 7+62+5+4
2. 18+62+5
3.15+4+1
4.5 families
6. three
Step-by-step explanation:
f (x) = -43 +7
Using the function above, evaluate f (-2).
Which problem solving strategy would be best to solve this problem? Four people are in line at the movie theater. Jennifer is ahead of Jeanie. John is not first or last in line. Jarett is directly in front of Jennifer. Name the order in which the people are standing in line. A. guess, check and revise B. compute or simplify C. work backwards D. write an equation
Answer:
C. work backwards
Step-by-step explanation:
Given from the first statement of the question that that four people are in line. This is the result of the question, so the strategy required would be the work backwards.
Jennifer is ahead of Jeanie implies that Jeanie is somewhere behind Jennifer. Since John is neither the first or the last in the line, then he must be between Jeanie and Jennifer. And Jarett is directly in front of Jennifer, so that Jarett is the first in line. The arrangement goes thus:
Jeanie ⇒ John ⇒ Jennifer ⇒ Jarett
Answer:
The answer is C, work backwards.
Step-by-step explanation:
I really hope this helps.
URGENT QUESTION!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
2 + 2 = ______
Answer
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
2+2 = 4!!!
Hope this helps :)
In cross country, the team score is determined by the place each individual runner finishes. (For example, 1st place is one point, 16th place is 16 points, etc.) In their latest meet, the boys cross-country team scored 55 points. If there were five runners on the team and each runner finished one after another, what places did they come on? Explain your reasoning and support your answer. *
Answer:
Kindly check explanation
Step-by-step explanation:
Given that there were five rummers in the team;
Each runner finished one after the other
Total. Points scored =. 55
Let the positions of each runner be :
1sr runner = p
2nd runner =.p + 1
3rd runner =.p + 2
4th runner =.p + 3
5th runner =.p + 4
(1st + 2nd + 3rd + 4th +. 5th) runner = 55
(p + p + 1 + p + 2 + p + 3 + p + 4) = 55
5p + 10 = 55
5p = 55 - 10
5p = 45
p = 9
Hence,
1st runner = 9th
2nd runner = 9 + 1 = 10th
3rd runner = 9 + 2 = 11th
4th runner = 9 + 3 = 12th
5th runner = 9+ 4 = 13th
The deductions from Jennifer monthly pay are federal income tax (FIT) of $87, state income tax (SIT) of 2.5% of gross pay, city income tax (CIT) of 1.2% of gross, social security, and Medicare. Her monthly net pay is $3,982.22. Find Jennifer's monthly gross pay
Answer:
$4,225.6
Step-by-step explanation:
Jenifer had the following deductions from her monthly pay
Federal income tax of $87
State income tax of 2.5% of gross pay
City income tax of 1.2% of gross pay
Jennifer monthly pay is $3,982.22
Therefore jenifer monthly gross pay can be calculated as follows
Let x represent the gross pay
x = 3982.22 + 87 + 1.2/100x + 2.5/100x
x = 3982.22 + 87 + 0.012x + 0.025x
x =4069.22 + 0.037x
Collect the like terms
x - 0.037x = 4069.22
0.963x = 4069.22
Divide both sides by the coefficient of x
x = 4069.22/0.963
x = 4,225.6
Hence Jennifer monthly gross pay is $4,225.6
What is the scale factor of 12?
Scale factor: A number that enlarges/reduces a figure or shape
Greater than 1
Less than 1
Equal than 1
Need Help!!!!
Answer:
Equal to 1
Step-by-step explanation:
By using the exponential delta we can infer that the orthogonal is correct because the high order bits multivariate and are asymptomatic.