All categories

3 years ago

The sum of two consecutive even integers is at most seven more than half the sum of the next two consecutive even integers

1 answer:

7 0

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

You might be interested in

Which expression is equivalent to −1/ 12x−1 /3?

alexandr402 [8]

Answer:

$\frac{1}{12} (-x-4)$

Step-by-step explanation:

the expression we have is:

$-\frac{1}{12} x-\frac{1}{3}$

To find an equivalent expression, it would be helpful to express 1/3 so that it has a 12 in the denominator:

$\frac{1}{3}=\frac{4}{12}$

so we substitute this:

$-\frac{1}{12} x-\frac{4}{12}$

and now we have 1/12 in both terms :

$-\frac{1}{12}x-\frac{1*4}{12}$

so we can factor it (we take it out of each term: in the first we are left with -x and in the second with -4):

$\frac{1}{12} (-x-4)$

the equivalent expression is: $\frac{1}{12} (-x-4)$

5 0

3 years ago

Write the first five multiples of the number 16 in order.

timurjin [86]

Answer:

16,32,48,64 and 60

Step-by-step explanation:

How to find a multiple:

Choose a number you want to find a multiple for and multiply it by continuing whole numbers.

5 0

3 years ago

Read 2 more answers

I dont understand this

kirza4 [7]

Step-by-step explanation:

first u find the angles and then u use some low divide the length of triangle by sin of opposite angles

4 0

3 years ago

In the year 1995, there were 1200 students at pine elementary school. In the year 2010 there were 1500 students. Find the rate o

AnnZ [28]

The rate of change from 1995 to 2010 is 20 students per year and the linear function that models the data will be: $y=20x-38700$

Explanation

In the year 1995, there were 1200 students and in the year 2010, there were 1500 students.

If $x$ represents the year and $y$ represents the number of students, then two points in form of $(x,y)$ will be: $(1995, 1200)$ and $(2010, 1500)$

So, the rate of change or slope = (change in value of y / change in value of x) $=\frac{1500-1200}{2010-1995}= \frac{300}{15}=20$

Now, plugging slope $(m)$ = 20 and first point $(x_{1}, y_{1}) =(1995,1200)$ into point slope form of linear equation $y-y_{1} =m(x-x_{1})$ , we will get.....

$y-1200=20(x-1995)\\ \\ y-1200=20x-39900\\ \\ y= 20x-39900+1200\\ \\ y= 20x-38700$

4 0

3 years ago

PLEASE HELP!!!

Scilla [17]

You need the Law of Cosines here and you use it when you have 2 sides and an enclosed angle. The side across from the angle is the one we are looking for. The correct way to express the Law using what we have is the last choice above. Side RT is the unknown, and it is across from the angle that is enclosed between the 2 other sides.

3 0

3 years ago