Kevin bought 6 hectograms of cheese selling for $9 per kilogram.

find three consecutive odd integers such that the sum of the smallest number and middle number is 27 less than 3 times the large

katrin2010 [14]

A generic odd number can be written as

$2k+1,\quad k \in \mathbb{Z}$

Since there is an odd number every two numbers, three consecutive odd numbers will be

$2k+1,\quad 2k+3,\quad 2k+5$

Now let's make up the equations: the sum of the first two is

$(2k+1)+(2k+3)$

And 27 less than 3 times the largest is

$3(2k+5)-27$

These two must be the same, so we have

$(2k+1)+(2k+3)=3(2k+5)-27 \iff 4k+4 = 6k+30-27 \iff 4k+4=6k+3$

Subtracting 4k and 3 from both sides gives

$1=2k \iff k=\dfrac{1}{2}$

Which means that the problem has no solution.

To confirm this hypothesis, we can observe that, on the left hand side, we have the sum of two odd numbers, which is even

On the right hand side, we have an odd number, multiplied by 3 (still odd), take away 27 (still odd).

So, the left hand side is even, and the right hand side is odd. They can't be the same number.

7 0

3 years ago

The intersection of the two lines, shown in the image below, creates special angle relationships between angles 1,2,3,

levacccp [35]

Answer:

3 and 4

1 and 3

Step-by-step explanation:

This is because these are vertical angles so anything on one side is the same on the other in these words Congruent. Good luck.

5 0

3 years ago

Which expression is equivalent to 4(3+5)-3.94?

kondor19780726 [428]

Answer:

4(3+5)-3.94

4(8)-3.94

32 - 3.94

what do you mean by . multifaction or decimal

Step-by-step explanation:

3 0

3 years ago

I need help on #4 I do not know how to do it.

mr Goodwill [35]

25 is the answer to question 4 traveld by a passenger in one full rotation

3 0

3 years ago

Use elimination <br> I NEED IT HURRY

Vera_Pavlovna [14]

Answer:

(5,-2)

Step-by-step explanation:

The given system is:

$3x+2y=11$

$2x+6y=-2$

Both equations are in the same form. That form being standard form, $ax+by=c$ .

We need one of the variable columns to contain opposite terms (we will add if this is the case) or same terms (we will subtract if this is the case).

To do this we will either need to multiply both equations or one equation.

I really like the column with the variable $y$ right now because the least common multiple of 2 and 6 is 6 and 6 is already a coefficient of one of the $y$ variables.

So This means I will need to either choose to multiply the first equation by 3 or -3. It is your choice or mine in this case.

I'm going to choose to multiply the first equation by -3.

This will give me my system as:

$-9x-6y=-33$

$2x+6y=-2$

I will now add the equations. This is method is called elimination because in this step one of the variables get eliminated.

$-7x+0y=-35$

$-7x+0=-35$

$-7x=-35$

$x=\frac{-35}{-7}$

$x=5$

So now we can find the $y-$ coordinate using of the initial equations along with $x=5$ .

I choose $3x+2y=11$ along with the $x=5$ :

$3(5)+2y=11$

$15+2y=11$

$2y=11-15$

$2y=-4$

$y=\frac{-4}{2}$

$y=-2$

So the solution is (5,-2).

Let's confirm the answer through a check.

I will plug our "solution" into both equations.

If both equations render true, then the "solution" is confirmed and I will refer to it as just a solution without the quotation.

$3x+2y=11$ with $(x,y)=(5,-2)$ :

$3(5)+2(-2)=11$

$15+(-4)=11$

$11=11$ is true.

$2x+6y=-2$ with $(x,y)=(5,-2)$ :

$2(5)+6(-2)=-2$

$10+(-12)=-2$

$-2=-2$ is true.

Since both equations ended up being true, (5,-2) is the solution of the system.

6 0

3 years ago