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andrey2020 [161]
3 years ago
12

1. Which point on the axis satisfies the inequality y

Mathematics
2 answers:
Alina [70]3 years ago
5 0
1.) C - (1, 0)
2.) A - 4
3.) C - 1
4.) D - (1, 1)
5.) D
grigory [225]3 years ago
3 0

Answer:

1) Point (1,0) -----> see the attached figure N 1

2) The value of x is 4

3) I quadrant

4) (1,1)

5)  y>-5x+3

Step-by-step explanation:

Part 1)

we know that

If the point satisfy the inequality

then

the point must be included in the shaded area

The point (1,0) is included in the shaded area

Part 2)

we have

x-2y\geq 4

see the attached figure N 2

we know that

The value for x on the boundary line and the x axis is equal to the x-intercept of the line x-2y= 4

For y=0

Find the value of x

x-2(0)= 4  

x=4

The solution is x=4

Part 3)

we have

x\geq 0 -----> inequality A

The solution of the inequality A is in the first and fourth quadrant

y\geq 0 -----> inequality B

The solution of the inequality B is in the first and second quadrant

so

the solution of the inequality A and the inequality B is the first quadrant

Part 4) Which ordered pair is a solution of the inequality?

we have

y\geq 4x-5

we know that

If a ordered pair is a solution  of the inequality

then

the ordered pair must be satisfy the inequality

we're going to verify all the cases

<u>case A)</u> point (3,4)

Substitute the value of x and y in the inequality

x=3,y=4

4\geq 4(3)-5

4\geq 7 ------> is not true

therefore

the point (3,4) is not a solution of the inequality

<u>case B)</u> point (2,1)

Substitute the value of x and y in the inequality

x=2,y=1

1\geq 4(2)-5

1\geq 3 ------> is not true

therefore

the point  (2,1) is not a solution of the inequality

<u>case C)</u> point (3,0)

Substitute the value of x and y in the inequality

x=3,y=0

0\geq 4(3)-5

0\geq 7 ------> is not true

therefore

the point  (3,0) is not a solution of the inequality

<u>case D)</u> point (1,1)

Substitute the value of x and y in the inequality

x=1,y=1

1\geq 4(1)-5

1\geq -1 ------> is true

therefore

the point  (1,1) is  a solution of the inequality

Part 5) Write an inequality to match the graph

we know that

The equation of the line has a negative slope

The y-intercept is the point (3,0)

The x-intercept is a positive number

The solution is the shaded area above the dashed line

so

the equation of the line is y=-5x+3

The inequality is  y>-5x+3

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the total attendance at a concert in a theater hall was 1500, of this total 400 were children,850 were women , and the remaining
AleksandrR [38]

<u>Answer:</u>

Below!

<u>Step-by step explanation:</u>

<u>We know that:</u>

  • 400 + 850 + m = 1500

<u>Solution of Question A:</u>

<u>Percent of children: Total children/Total attendance</u>

  • => 400/1500
  • => 4/15
  • => 0.27 (Rounded to nearest hundredth)
  • => 0.27 x 100
  • => 27%

<u>Hence, the percent of children is about 27%.</u>

<u>Solution of Question B:</u>

<u>Percent of women: Total women/Total attendance</u>

  • => 850/1500
  • => 85/150
  • => 17/30
  • => 17/30 x 100
  • => 17/3 x 10
  • => 170/3
  • => 56.67%

<u>Hence, the percent of women is 56.67%.</u>

<u>Solution of Question C:</u>

  • 400 + 850 + m = 1500
  • => 1250 + m = 1500
  • => m = 1500 - 1250
  • => m = 250

<u>Percent of men: Total men/Total attendance</u>

  • => 250/1500
  • => 1/6
  • => 0.17 (Rounded to nearest hundredth)
  • => 0.17 x 100
  • => 17%

<u>Hence, the percent of men is about 17%</u>

Hoped this helped.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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