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Naddika [18.5K]
3 years ago
14

(25 points!!!!) draw the graph of the area bounded by these inequalities

Mathematics
1 answer:
Stels [109]3 years ago
3 0

Step-by-step explanation:

To draw the graph, follow these steps:

  1. Graph the lines using points from the equations. (the blue line shown should be dotted, unfortunately I cannot do that in the program I used)
  2. Determine which direction the inequalities are correct.  
  3. Find the boundary given.

The three inequalities given form a triangle.

The first equation, y ≤ 2x + 5, has a y-intercept at (0, 5) and a point at (-2, 1).

The second equation, y < -3x + 10, has points at (3, 1) and (2, 4).

Use two points to draw the lines.

After the lines are drawn, determine which side of the line the inequality works on. You can do this by testing points that are not on the line.

I will test each inequality using (0, 1):

y ≤ 2x + 5

0 ≤ 2 + 5

<em>This is correct</em>, so the inequality for y ≤ 2x + 5 will be shaded towards (0, 1).

y < -3x + 10

0 < -3 + 10

<em>This is correct,</em> so the inequality for y < -3x + 10 will be shaded towards (0, 1).

0 ≤ 1

<em>This is correct</em>, so the inequality for 0 ≤ y will be shaded upwards towards (0, 1).

The end result of this graph is all three inequalities being shaded (inwards).

The solution is a triangle with points at (1, 7), (3.33333, 0), and (-2.5, 0).

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You want to solve 11% of what number is 22. Explain how you can solve that by using a proportion
Doss [256]
Write the first ratio as 11/100 and set it equal to 22/n.

since 11 x 2=22 you can multiply 100 x 2 and you'll get 200. 

*Check*: 11% of 200=22
3 0
3 years ago
Area=<br> Help me please!! Thanks :)
Savatey [412]

Answer:

80π

Step-by-step explanation:

Circle O with radius IO:

large radius = IO = 12 = R

Circle O with diameter JK

IJ = JK = KL = 2 × IO = 24

IJ = JK = KL = 24/3 = 8

small radius = 8/2 = 4 = r

The shaded area is a semicircle of radius 12 minus a semicircle of radius 4 plus two semicircles of radius 4.

That is the same as

1 semicircle of radius 12 plus 1 semicircle of radius 4

A = πR²/2 + πr²/2

A = π(12² + 4²)/2

A = 160π/2

A = 80π

8 0
2 years ago
I really extremely need help! I will give you 5 stars and branilest
Ivanshal [37]

Answer:

37.5%

Step-by-step explanation:

12\32 = 6\16=3\8 =0.375

=37.5%

7 0
2 years ago
Find the missing side.​
Vitek1552 [10]

Answer:

5

Step-by-step explanation:

This is a right triangle, but note that you only know the measurement of one angle, which is 90 degrees.

Use the following formula to solve:

a² + b² = c²

In which:

a & b = shorter sides

c = hypotenuse

Plug in the corresponding numbers to the corresponding variables:

(3)² + (4)² = ?²

Solve. Remember to follow PEMDAS. First, solve the exponents, then add:

(3)² = (3 * 3) = (9)

(4)² = (4 * 4) = (16)

9 + 16 = ?²

25 = ?²

Isolate "?". Root both sides:

√(25) = √(?²)

? = √25 = √(5 * 5) = 5

Your missing side's measurement is 5.

~

4 0
3 years ago
Read 2 more answers
Bryan and Jadyn had barbeque potato chips and soda at a football party. Bryan ate 4 oz of chips and drank 1 cup of soda for a to
Inga [223]

Answer:

1 oz of chips has 140 mg of sodium, and 1 cup of soda has 40 mg of sodium.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

x is the amount of sodium in 1oz of chips.

y is the amount of sodium in 1 cup of soda.

Bryan ate 4 oz of chips and drank 1 cup of soda for a total of 600mg of sodium.

This means that 4x + y = 600, also y = 600 - 4x

Jadyn ate 1 oz of chips and drank 4 cups of soda for a total of 300mg of sodium.

This means that:

x + 4y = 300

From the first equation, we have that y = 600 - 4x. So

x + 4(600 - 4x) = 300

x + 2400 - 16x = 300

15x = 2100

x = \frac{2100}{15}

x = 140

y = 600 - 4x = 600 - 4*140 = 40

1 oz of chips has 140 mg of sodium, and 1 cup of soda has 40 mg of sodium.

4 0
3 years ago
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