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bulgar [2K]
3 years ago
9

Which system of inequalities is represented by the graph?

Mathematics
1 answer:
alexgriva [62]3 years ago
7 0

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.

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Robin has a certain number of dimes in his pocket. If the dimes were pennies, he would have $1.08 less than he has now. How many
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Answer:

Robin will have 12 dimes in his pocket.

Step-by-step explanation:

Since;

D = One dime = $0.1

P = One penny = $0.01

Amount to have less = $1.08

From the above, when a dime is changed to a penny, the amount held by Robin will decrease by $0.09. That is,

Decease in holding = D - P = $0.1 - $0.01 = $0.09

Therefore, we have:

Number of dimes = Amount to have less / Decease in holding = $1.08 / $0.09 = 12 dimes

Therefore, Robin will have 12 dimes in his pocket.

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2 years ago
The tempeture of chicken soup is 192.7 degrees F. As it cools the tempeture of the soup decreases 2.3F per minute.
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Answer:

Step-by-step explanation:

To find the answer to Part A, we can turn this into a simple equation:

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135.2 = Answer to Part A.

Now, onto Part B. We can use <u>another</u> equation!

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Now, we must solve the given equation, first by taking 100.7 from each side:

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We are now left with: 92 - 2.3x = 0 - we must now add 2.3x to 2.3x and 0, giving us this:

92 = 2.3x, which is equivalent to 920 = 23x, if that is what you prefer to solve.

To give us our missing value (x), we can divide 920 by 23, giving us: x = 40. This is the answer to Part B: 40 minutes.

I hope this was really helpful! Tell me if you need any more help.

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2 years ago
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Which of the following must be true?
IgorLugansk [536]

Answer:

A

Step-by-step explanation:

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