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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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There are 5 different pairs of gloves, where left and right are distinguishable. Select 4 of the 10 gloves. (a) How many are the

zlopas [31]

Answer:

(a) How many are there to select 2 pairs of gloves?

10 ways

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

130 ways

Step-by-step explanation:

For the above questions we apply that combination formula

(a) How many are there to select 2 pairs of gloves?

There are 5 pairs of gloves according to the question above, hence:

5C2 = 5!/2! × (5 - 2)!

= 5!/2! × 3!

= 5 × 4 × 3 × 2 × 1/2 × 1 × 3 × 2 × 1

= 10 ways.

Therefore, there are 10 ways to select 2 pairs of gloves

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

i) A way to select 4 gloves out of 10 gloves =

10C4 = 10!/4! ×(10 - 4)!

= 10!/ 4! × 6!

= 210 ways

ii) In order for 2 of the 4 gloves selected to be a pair, note that we have 5 pairs of gloves hence:

5 × 2⁴

= 80 ways.

Therefore, the number of ways which we can select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.) = 210 ways - 80 ways

= 130 ways

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A bag with 5 pound of potatoes costs $3.20. How much do 12 pounds of potatoes cost at the same rate?

Temka [501]

Answer:

$7.68

Step-by-step explanation:

You must find the rate first, so in order to do that you divide the price by the quantity which is

3.20/5

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Discuss circumstances under which it is preferable to use relative frequency distributions instead of frequency distributions?

Mrac [35]

Answer:

The relative frequency distributions would be more preferable to use when we want to measure the weight of a particular category or also when we want to compare different categories of data within a table. Moreover, relative frequency is often used for the probability calculations.

Step-by-step explanation:

Frequency distribution:

A frequency distribution simply tells us how many times an event has occurred or in other words, it is the rate of occurrence.

Relative frequency distribution:

On the other hand, the relative frequency tells us the fraction of how many times an event has occurred with respect to the total number of trials.

For example:

Consider a bag of marbles having marbles of different colors. We randomly pick marbles from the bag and got the following results.

Event | Frequency

Red | 2

Blue | 4

Green | 6

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The frequency of Red marbles is 2 which means that the red marble came up two times. Similarly, the blue marble came up four times.

The relative frequency of red marble is 2/15 = 0.133 = 13.3%

The relative frequency of green marble is 6/15 = 0.40 = 40%

This means that the green marbles came up 40% of the time.

When relative frequency distributions is preferred?

The relative frequency distributions would be more preferable to use when we want to measure the weight of a particular event or also when we want to compare different categories of data within a table. Moreover, relative frequency is often used for the probability calculations.

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