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2. Which of the following systems of inequalities represents the graph?

Rom4ik [11]

Answer:

Option: D is the correct answer.

D) –2x + y ≥ 4

x + y < 2

Step-by-step explanation:

We are asked to find the linear inequality that represents the following graph.

Clearly from the graph we could observe that one line is dotted and the other is solid line.

i.e. one inequality is strict while the other is a inequality with equality sign.

Dashed line:

It passes through (0,2) and (2,0).

Hence, the equation of line is:

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

As the shaded region is towards the origin.

Hence, the inequality will be:

x+y<2.

Solid line:

The line passes through (-2,0) and (0,4).

hence equation of line is:

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

i.e

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

Now, as the shaded region is away from the origin hence the inequality which will be used is:

$-2x+y\geq 4$

Hence, option: D is the correct answer.

D. –2x + y ≥ 4

x + y < 2

8 0

3 years ago

Read 2 more answers

7) Find EC 16 E- B D С 49 30

lana66690 [7]

Answer:

EC = 35

Step-by-step explanation:

The whole entire line measures 49

DB measures 30

49 - 30 = 19 or ED

But we’re looking for EC so…

19 + 16 = 35

EC = 35

3 0

3 years ago

Six is less than or equal to the sum of a number n and 15

Debora [2.8K]

Answer:

6(less than or equal sign) n+15

Step-by-step explanation:

the less than or equal sign is a less than sign with one line under it

6 0

3 years ago

A goat and a cow together weigh 190 kg 640 g. The weight of the goat is 59 kg 720 g. Find the weight of the cow

AVprozaik [17]

Answer: 130 kg 920 g

Step-by-step explanation:

Given

The weight of the goat is 59 kg 720 g

The combined weight of goat and cow is 190 kg 640 g

Suppose, the weight of the cow is x kg

We know, 1 kg=1000 g

Converting weight into kg

Goat weight

$=59+0.720\\=59.720\ kg$

Total weight

$=190+0.640\\=190.640\ kg$

Then, the cow weight is given by

$\Rightarrow 190.640-59.720\\\Rightarrow 130.920\ kg\ \text{or}\ 130\ kg\ 920\ g$

7 0

2 years ago

Margot has 21 1/2 pounds of flour 8 pounds of butter and 18 1/2 ponds of sugar to make shortbread cookies if she makes 12 batche

adell [148]

Answer:

4 pounds of ingredients are used in each batch.

Step-by-step explanation:

Amount of flour = $21\frac{1}{2}pounds = \frac{43}{2}pounds$

Amount of butter = 8 pounds

Amount of sugar = $18\frac{1}{2}pounds= \frac{37}{2} pounds$

So, the total amount of all ingredients will be: $(\frac{43}{2}+\frac{37}{2}+8)pounds = (\frac{43+37+16}{2}) pounds= \frac{96}{2} pounds = 48 pounds$

Given that, she makes 12 batches of cookies using all the ingredients.

Thus, the amount of ingredients used in each batch $=\frac{48}{12} pounds = 4 pounds$

5 0

3 years ago