Please help me I don't get it

Which system of inequalities is represented by the graph?

alexgriva [62]

Answer:

$\left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.$

Step-by-step explanation:

The diagram shows shaded region which boundary is bounded with two lines.

<u>Equation of the 1st line:</u>

This line passes through the points (-6,0) and (0,-6), so its equation is

$\dfrac{x-(-6)}{0-(-6)}=\dfrac{y-0}{-6-0}\\ \\\dfrac{x+6}{6}=\dfrac{y}{-6}\\ \\y=-x-6$

<u>Equation of the 2nd line:</u>

This line passes through the points (-2,0) and (0,4), so its equation is

$\dfrac{x-(-2)}{0-(-2)}=\dfrac{y-0}{4-0}\\ \\\dfrac{x+2}{2}=\dfrac{y}{4}\\ \\y=2x+4$

The origin belongs to the shaded region, so it must satisfy both inequalities, so

$-0-6=-6\le 0\Rightarrow$ correct inequality is $-x-6\le y$

$2\cdot 0+4=4\ge 0\Rightarrow$ correct inequality is $2x+4\ge y$

Note that signsare with notion "or equal to" because lines are solid.

Answer:

$\left\{\begin{array}{l}-x-6\le y\\ \\2x+4\ge y\end{array}\right.\Rightarrow \left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.$

7 0

3 years ago

Three consecutive integers have a sum of 48 find the integers?

zavuch27 [327]

The sum of three consecutive integers is three times the middle one: if we call the middle one $x$ , the three numbers are

$x-1,\ x,\ x+1$

So, their sum is $x-1+x+x+1 = 3x$

Which is three times the middle one.

So, if the sum of three consecutive intergers is 48, the middle one must be 48/3 = 16.

So, the three numbers are 15, 16 and 17

6 0

3 years ago

6th grade math If Bob has 14,023 memes and each meme gains a profit of $3 how much money will Bob get if he posts all his memes?

trapecia [35]

Answer:

Lol, okay Bob will get $42,069 if he posts all his memes! Man, where can I get a job like that?!

14,023 x 3 = 42,069

6 0

3 years ago

Read 2 more answers

In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police

Lyrx [107]

Answer:

Option 3 - 4 miles

Step-by-step explanation:

Given : In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station. The distance between the library and the police station is 5 miles.

To find : How far apart are the police station and the fire station?

Solution :

Let the distance between police station and fire station be 'x'.

The distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station.

i.e. $2x-3$

The distance between the library and the police station is 5 miles.

i.e. $2x-3=5$

$2x=5+3$

$2x=8$

$x=4$

Therefore, The police and fire stations is 4 miles apart.

So, Option 3 is correct.

3 0

3 years ago

Read 2 more answers

What does a standard deviation of 0 indicates ?

DIA [1.3K]

What does a standard deviation of 0 indicates 0.

4 0

2 years ago