Every odd whole number can indeed be written as the difference of two squares, leveraging the fact that the difference between the squares of consecutive integers is an odd number.
The question whether every odd whole number can be written as the difference of two squares is of arithmetical and algebraic interest. The answer is yes, every odd whole number can be expressed as such. For example, consider the odd whole number 7. This number can be expressed as 4^2 - 3^2, which simplifies to 16 - 9, giving us 7. Generally, for any odd whole number n, we can find whole numbers x and y such that n = x^2 - y^2. This is because we can write n = (m+1)^2 - m^2, where m is an integer. Essentially, m can be taken as (n-1)/2 which ensures that m and m+1 are consecutive integers, hence their squares differ by an odd number, which is n.
You purchasing 220 airline ticket you have a discount code to receive 10% off there is a 10.5% service charge and how much do you pay for your ticket
I need the answer for #4 a&b
Choose the correct description of the graph of the compound inequality 3x + 1 > 10 and 4x alt= 20.
amanda read 15 pages of her 150-page book in 2 hours. At this rate, how long will it take her to read the entire book?
A pitcher contains 1 3/4 quarts of milk. How many fluid ounces of milk does the pitcher contain ?
1 3/4 quarts is equivalent to 56 fluid ounces. This conversion is done by first converting the mixed fraction to an improper fraction, and then multiplying by 32, which is the number of ounces in one quart.
Explanation:The subject of your question is Mathematics, specifically a unit conversion problem. You want to convert 1 3/4 quarts of milk to fluid ounces. We know that there are 32 fluid ounces in one quart. So, to convert quarts to fluid ounces, we multiply the number of quarts by 32:
For 1 3/4 quarts:
1. First, convert the mixed fraction to an improper fraction: (1 * 4) + 3 = 7/4 quarts
2. Multiply by 32(our conversion factor from quarts to fluid ounces): (7/4) * 32 = 56
So, 1 3/4 quarts is equal to 56 fluid ounces.
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What is the first step in simplifying the expression 11x-2-3(1-7x)^2+(x+1)
Answer with Step-by-step explanation:
We are given a expression:
[tex]11x-2-3(1-7x)^2+(x+1)[/tex]
We have to determine the first step in the solution of the above expression.
First step will be to solve the term [tex](1-7x)^2[/tex]
We will firstly square the term 1-7x
[tex]11x-2-3(1-7x)^2+(x+1)\\\\=11x-2-3(1+49x^2-14x)+(x+1)\\\\=11x-2-3-147x^2+42x+x+1\\\\=-147x^2+54x-4[/tex]
Hence, First step is:
solve the term [tex](1-7x)^2[/tex]
What factor makes the number true
solve the system by the elimination method? -5x-2y=2 6x-2y=24
emilys meal costs 32.75 and darren's meal costs 39.88. emily treats darren by paying for both meals, and leaves a 14 percent tip. find the total cost
82.80
32.75+39.88=72.63
72.63x1.14=82.7982 rounds to 82.80
if cosA=2/5, find the value of 4+4 tan^2A
Answer:
25
Step-by-step explanation:
Given the functions f(x) = − 4x − 1 and g(x) = 2x + 4, which operation results in the smallest coefficient on the x term?
Answer: addition
Step-by-step explanation:
If you select a card at random, what is the probability of getting:A number smaller than 5 (counting the ace as a 1)?
4 Aces, 4 2's, 4 3's 4 4's
= 16 cards total out of 52 cards
so probability would be 16/52 which reduces to 4/13
the probability of selecting a card smaller than 5 is [tex]\ = \frac{2}{5} \).[/tex]
Step 1
To calculate the probability of selecting a card with a number smaller than 5 (considering the ace as 1), we need to determine how many cards meet this condition and divide it by the total number of cards in the deck.
There are 4 suits in a standard deck of cards, each with cards numbered from 1 to 10 (excluding face cards).
For each suit, the numbers smaller than 5 are 1, 2, 3, and 4.
Step 2
So, for each suit, there are 4 cards smaller than 5.
Since there are 4 suits, the total number of cards smaller than 5 is [tex]\(4 \times 4 = 16\).[/tex]
Step 3
The total number of cards in the deck is [tex]\(4 \times 10 = 40\)[/tex], considering 4 suits with 10 cards each.
Therefore, the probability of selecting a card smaller than 5 is [tex]\( \frac{16}{40} = \frac{2}{5} \).[/tex]
What is 871 rounded to the nearest ten
Rounding 871 to the nearest ten gives us 870.
We have,
To round 871 to the nearest ten, we look at the ones digit, which is 1.
If the ones digit is 5 or greater, we round up to the next ten.
If the ones digit is less than 5, we round down to the previous ten.
In this case, the ones digit is 1, which is less than 5.
Therefore, we round down.
Rounding 871 to the nearest ten gives us 870.
Thus,
Rounding 871 to the nearest ten gives us 870.
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-Question Worth 50 Points-
At the city park there were 15 blue jays, 6 cardinals, and 9 mockingbirds.
For each of the following questions set up a proportion equation and solve for the unknown.
1. If there were 6 mockingbirds, how many cardinals would there be at the park?
2. If there were 5 blue jays, how many cardinals would there be at the park?
3. If there were 20 cardinals, how many mockingbirds would there be at the park?
eight cheerleaders set a goal of selling 424 boxes of cards to raise money. after two weeks, each cheerleader has sold 28 boxes. how many boxes more must each cheerleader sell?
Solve the quadratic equation y2 - 5y = -4 by factoring.
Solve for x:
x + 4.5 = -17.75
Please help!
1. Write the square of 6
2. Write the number of terms in 6x + 3y
3. Simplify 3x + 2y + y + 4x
Help me out on this kne
The cost, in dollars, to rent a kayak is proportional to the number x of hours you rent the kayak. It costs $27 to rent the kayak for 3 hours. Write an equation that represents y.
There are 20 people in Susan’s class. Each person gives a card to everyone else in the class. How many cards were exchanged?
describe the steps you used to solve the equation and find the amount of carries allowance. linear equation: 1/4a+1/3a+8=22
1/4a + 1/3a +8 =22
1st step add like terms:
1/4a +1/3a = 3/12a +4/12a = 7/12a
7/12a +8 =22
2nd step subtract 8 from each side:
7/12a = 14
3rd step divide both sides by 7/12 to get a:
a = 14 / 7/12
a = 24
Answer:
.
Step-by-step explanation:
1/4a + 1/3a +8 =22
1st step add like terms:
1/4a +1/3a = 3/12a +4/12a = 7/12a
7/12a +8 =22
2nd step subtract 8 from each side:
7/12a = 14
3rd step divide both sides by 7/12 to get a:
a = 14 / 7/12
a = 24
In a board game, negative number cards represent moving backward and positive number cards represent moving forward. For example, Nuha drew a card with 4 and moved forward 4 spaces.
Rags draws a card with 0.
What does 0 represent in the board game?
Choose 1 answer:
A: Not moving any spaces
B: The number of spaces she moved on her last turn.
C: Losing all points.
Unit rate 117 points in 13 minutes
Answer: 9 points per minute.
Step-by-step explanation:
Hi, answer this question we have to calculate the unite rate in points per minute; by dividing the number of points (117) by the number of minutes.
Mathematically speaking:
117 points / 13 minutes = 117/13= 9 points per minute
So, the unit rate is 9 points per minute.
Feel free to ask for more if needed or if you did not understand something.
Find the LCM of n^3 t^2 and nt^4.
A) n 4t^6
B) n 3t^6
C) n 3t^4
D) nt^2
Answer:
The correct option is C.
Step-by-step explanation:
The least common multiple (LCM) of any two numbers is the smallest number that they both divide evenly into.
The given terms are [tex]n^3t^2[/tex] and [tex]nt^4[/tex].
The factored form of each term is
[tex]n^3t^2=n\times n\times n\times t\times t[/tex]
[tex]nt^4=n\times t\times t\times t\times t[/tex]
To find the LCM of given numbers, multiply all factors of both terms and common factors of both terms are multiplied once.
[tex]LCM(n^3t^2,nt^4)=n\times n\times n\times t\times t\times t\times t[/tex]
[tex]LCM(n^3t^2,nt^4)=n^3t^4[/tex]
The LCM of given terms is [tex]n^3t^4[/tex]. Therefore the correct option is C.
Answer: C) n 3t^4
Step-by-step explanation:
Definition : The least common multiple (LCM) of any two expressions is the smallest expression that is divisible by both expressions.
Given expressions : [tex]n^3 t^2 \text{ and } nt^4[/tex]
Factorization form of [tex]n^3 t^2 \text{ and } nt^4[/tex] will be :
[tex]n^3 t^2 =n\times n\times n\times t\times t[/tex]
tex]nt^4 =n \times t\times t\times t\times t[/tex]
The least common multiple of [tex]n^3 t^2 \text{ and } nt^4[/tex] :
[tex]n^3 t^2 =n\times n\times n\times t\times t\times t\times t=n^3t^4[/tex]
Hence, the LCM of [tex]n^3 t^2 \text{ and } nt^4=n^3t^4[/tex]
Thus , the correct answer is option C).
A circuit board manufacturer can produce 2,000 boards per hour. How many days will it take to produce 16,500 if the company has a 10 hour work shift? How many days will it take to produce 16,500?
Answer:
it will take less than one day.
Step-by-step explanation:
A circuit board manufacturer can produce 2,000 boards per hour.
If the company has a 10 hour work shift.
manufacturer can produce in one day = 2000 × 10 = 20,000
To produce 16,500 boards, they need time = 16,500 ÷ 2000 = 8.25 hours
The company will take to produce 16,500 boards in 8.25 hours less than one day.
what is 65% of 300!???
Find the greatest common factor of 25x^2 and 20b^4
a cabbage palmetto has a height of 80 feet. what is the approximate height of the tree in meters?
need help like last time do the same thing