<u>Given</u>:
Let the 3 consecutive even integers be x, x + 2 and x + 4.
Given that the sum of the squares of the first and the second integers is 2 more than the third integer.
We need to determine the 3 consecutive integers.
<u>Value of x:</u>
From the given, the expression can be written as,
![x^2+(x+2)^2=2+(x+4)](https://tex.z-dn.net/?f=x%5E2%2B%28x%2B2%29%5E2%3D2%2B%28x%2B4%29)
Simplifying, we get;
![x^2+x^2+4x+4=2+x+4](https://tex.z-dn.net/?f=x%5E2%2Bx%5E2%2B4x%2B4%3D2%2Bx%2B4)
![2x^2+4x+4=x+6](https://tex.z-dn.net/?f=2x%5E2%2B4x%2B4%3Dx%2B6)
![2x^2+3x+4=6](https://tex.z-dn.net/?f=2x%5E2%2B3x%2B4%3D6)
![2x^2+3x-2=0](https://tex.z-dn.net/?f=2x%5E2%2B3x-2%3D0)
Factoring the middle term, we get;
![2x^2+4x-x-2=0](https://tex.z-dn.net/?f=2x%5E2%2B4x-x-2%3D0)
![2x(x+2)-1(x+2)=0](https://tex.z-dn.net/?f=2x%28x%2B2%29-1%28x%2B2%29%3D0)
![(2x-1)(x+2)=0](https://tex.z-dn.net/?f=%282x-1%29%28x%2B2%29%3D0)
![2x-1=0 \ or \ x+2=0](https://tex.z-dn.net/?f=2x-1%3D0%20%5C%20or%20%5C%20x%2B2%3D0)
![x=\frac{1}{2} \ or \ x=-2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D%20%5C%20or%20%5C%20x%3D-2)
Since, the fraction
is neither a even nor odd integer.
Thus, the value of x is -2.
<u>Consecutive integers:</u>
Substituting the value of x in the consecutive integers x, x + 2 and x + 4, we get;
![x=-2](https://tex.z-dn.net/?f=x%3D-2)
![x+2=-2+2=0](https://tex.z-dn.net/?f=x%2B2%3D-2%2B2%3D0)
![x+4=-2+4=2](https://tex.z-dn.net/?f=x%2B4%3D-2%2B4%3D2)
Thus, the 3 consecutive integers are -2, 0 and 2.
The percentage of the total cost of 23 separate tickets that George saves by buying a season ticket is 23%.
<h3>What are percentages?</h3>
A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As the cost of the separate ticket is £24, and there are a total of 23 games, therefore, the total cost of the 23 games separate ticket can be written as,
= £24 × 23
= £552
Now, the cost of the season ticket is £425, therefore, the percentage of the total cost of 23 separate tickets that George saves by buying a season ticket can be written as,
![\rm Percentage = \dfrac{\text{Total cost of 23 seperate ticket}-\text{Cost of season ticket}}{\text{Total cost of 23 seperate ticket}} \times 100\%](https://tex.z-dn.net/?f=%5Crm%20Percentage%20%3D%20%5Cdfrac%7B%5Ctext%7BTotal%20cost%20of%2023%20seperate%20ticket%7D-%5Ctext%7BCost%20of%20season%20ticket%7D%7D%7B%5Ctext%7BTotal%20cost%20of%2023%20seperate%20ticket%7D%7D%20%5Ctimes%20100%5C%25)
![\rm Percentage = \dfrac{552-425}{552} \times 100\% = \dfrac{127}{552} \times 100\% = 23\%](https://tex.z-dn.net/?f=%5Crm%20Percentage%20%3D%20%5Cdfrac%7B552-425%7D%7B552%7D%20%5Ctimes%20100%5C%25%20%3D%20%5Cdfrac%7B127%7D%7B552%7D%20%5Ctimes%20100%5C%25%20%3D%2023%5C%25)
Hence, the percentage of the total cost of 23 separate tickets that George saves by buying a season ticket is 23%.
Learn more about Percentages:
brainly.com/question/6972121
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Answer:
B. The solution is valid because all steps to solve the inequality for F are correct.
Step-by-step explanation:
F - 32 ≤ 0
Add 32 to both sides of the equation to have;
F -32 + 32 ≤ 0 + 32
F ≤ 0 + 32
F ≤ 32
It can be observed that to solve for F, the steps are correct. Thus the solution is valid. Therefore, the correct choice in the given question is the solution is valid because all steps to solve the inequality for F are correct.
Bill has spent 1/6 of an hour longer jogging than swimming.
Answer: y=x^8-x^7+x^6-x^5+x^4+x^3+x^2+3
Step-by-step explanation:
here is an example function that satisfies the requirement:
y=x^8-x^7+x^6-x^5+x^4+x^3+x^2+3
if you plug in x=0,
you get y= 3, which satisfies (0,3)
if you plug in x=1,
you get y = 1 - 1 + 1 - 1 + 1 + 1 + 1 + 3,
you get y=6, which satisfies (1,6)