The sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers
two consecutive even integers: n, n+2
next two consecutive even integers n+4, n+6
n+(n+2) >= 7+1/2(n+4 +n+6)
combine like terms
2n+2 >= 7 +1/2(2n+10)
distribute 1/2
2n+2 >= 7+n+5
2n+2>= n+12
subtract n from each side
n+2>= 12
subtract 2 from each side
n>10
4 integers : 10, 12 ,14, 16
Answer:
400/1000×100%
40% is the percent of decrease from 1,000 to 400.
Answer:
9/14.
Step-by-step explanation:
The probability is given as a fraction or percentage.
9:5 odds in favour of a horse winning means the horse will win 9 races for every 5 it does not win.
So the probability that this horse will win is 9/(9+5)
= 9/14.
Answer:
x³ - 3x² - 18x
Explanation:
Before we begin, remember the following:
xᵃ * xᵇ = xᵃ⁺ᵇ
Now, for the given:
To solve thus question, we will simply multiply each term from the first bracket by each term from the second bracket and then combine like terms to get the final answer.
This can be done as follows:
(x + 3)(x² - 6x)
x(x²) + x(-6x) + 3(x²) + 3(-6x)
x³ - 6x² + 3x² - 18x
x³ - 3x² - 18x
Hope this helps :)
Answer:
(a) width = (x - 1)
length = (7x - 6)
(b) Area = 350 cm²
Perimeter = 114 cm
Step-by-step explanation:
<h3><u>Part (a)</u></h3>
Given equation: 
⇒ a = 7, b = -13, c = 6
Find 2 two numbers that multiply to ac and sum to b: -6 and -7
Rewrite b as the sum of these 2 numbers:
Factorize the first two terms and the last two terms separately:
Factor out the common term (x - 1):
Therefore:
- width = (x - 1)
- length = (7x - 6)
<h3><u>Part (b)</u></h3>
Substitute the given value of x = 8 into the equations to find the area and perimeter:
![\begin{aligned}\textsf{Perimeter} & = 2(\sf width+length)\\& =2[(x-1)+(7x-6)]\\ & = 2[(8-1)+(7(8)-6)]\\ & = 2[7+(56-6)] \\& = 2(7+50)\\& = 2(57)\\ & = 114 \sf \:\: cm\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctextsf%7BPerimeter%7D%20%26%20%3D%202%28%5Csf%20width%2Blength%29%5C%5C%26%20%3D2%5B%28x-1%29%2B%287x-6%29%5D%5C%5C%20%26%20%3D%202%5B%288-1%29%2B%287%288%29-6%29%5D%5C%5C%20%26%20%3D%202%5B7%2B%2856-6%29%5D%20%5C%5C%26%20%3D%202%287%2B50%29%5C%5C%26%20%3D%202%2857%29%5C%5C%20%26%20%3D%20114%20%5Csf%20%5C%3A%5C%3A%20cm%5Cend%7Baligned%7D)
