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3 years ago

Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?

Mathematics

1 answer:

AveGali [126]3 years ago

6 0

Answer:

1) The inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

2) The test point (0,0) satisfies both of the inequalities in the system represented by the graph.

Step-by-step explanation:

Given : A graph showing a system of inequalities.

We have to find the system of inequality.

For line 1)

The points that cut the x and y axis are (1,0) and (0,-4)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute, we get,

$m=\frac{-4-0}{0-1}=4$

Slope is 4.

Thus, equation becomes y = 4x + c

For c put (0,-4) in the above equation , we have,

-4 = 4(0) + c ⇒ c = -4

Thus, equation becomes y = 4x - 4

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = 4x - 4 becomes 0 = - 4 is satisfied when 0 > -4

thus, the inequality becomes y ≥ 4x - 4

Since, the line is a solid so it will take up equality sign too.

For line 2)

The points that cut the x and y axis are (1.5,0) and (0,-1.5)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute, we get,

$m=\frac{-1.5-0}{0-1.5}=1$

Slope is 1.

Thus, equation becomes y = x + c

For c put (0,-1.5) in the above equation , we have,

-1.5 = (0) + c ⇒ c = - 1.5

Thus, equation becomes y = x - 1.5

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = x - 1.5 becomes 0 = -1.5 is satisfied when 0 > - 1.5

thus, the inequality becomes y ≥ x - 1.5

Since, the line is a solid so it will take up equality sign too.

Thus, the inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

Also, The test point (0,0) satisfies both of the inequalities in the system represented by the graph.

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From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. Wha

Ede4ka [16]

Answer:

D. 2/7

Step-by-step explanation:

The probability is calculate as a division between the number of ways in which Andrew will be selected and karen will not and the total ways in which they can select 4 people from a group of 8 volunteers.

The number of ways in which they can select 4 people from a group of 8 volunteers can be calculated using:

$nCk=\frac{n!}{k!(n-k)!}$

Where nCk give as the number of ways in which we can form groups of k elements from a group of n elements.

So, if we replace n by 8 and k by 4, we get:

$8C4=\frac{8!}{4!(8-4)!}=70$

Then, there are 70 ways to select 4 people from a group of 8 volunteers.

At the same way, the number of ways in which Andrew will be selected and karen will not can be calculate replacing n by 6 and k by 3 in the same equation as:

$6C3=\frac{6!}{3!(6-3)!}=20$

We replace n by 6 because from the 8 volunteers, Andrew is going to be selected and Karen will not, so, the people that affect the result are just the 6 remaining volunteers. Also, k is equal to 3 because Andrew is already selected and we just need to select 3 more people.

Finally, the probability is:

$P=\frac{20}{70} = \frac{2}{7}$