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3 years ago

Solve the inequality and find the solution set. y-6 ≥12

1 answer:

4 0

The first step for solving this inequality is to move the constant to the right side by adding its opposites to both sides. This will look like the following:
y - 6 + 6 ≥ 12 + 6
Eliminate the opposites on the left side.
y ≥ 12 + 6
Lastly,, add the numbers on the right side together to get your final answer.
y ≥ 18
Let me know if you have any further questions.
:)

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When 1 is subtracted from three- tenths of the number, the result is equal to one-fifth of a number. What is the number

Bas_tet [7]

Based on the given mathematical statement, it can be rewritten into a mathematical equation to simplify and to be solved easily. The statement, "When one is subtracted from three-tenths of a number" corresponds to the equation, 3x/10 - 1, that is assuming the number is represented by the variable x. This is equal to one-fifth of the number. In other words,
3x/10 - 1 = x/5
x = 10

8 0

3 years ago

The sum of three consecutive integers is 90. Find the three numbers by letting x

Law Incorporation [45]

Answer:

x = 28

Step-by-step explanation:

let us take three consecutive numbers be (x + 1), (x + 2) and (x + 3)

Now,

The sum of three consecutive integers is 90

i.e.,

(x + 1) + (x + 2) + (x + 3) = 90

x + 1 + x + 2 x + 3 = 90

3x + 6 = 90

3x = 90 - 6

3x = 84

x = 84/3

x = 28

x = 28Thus, The value of x is 28

<h2>VERIFICATION:</h2>

(x + 1) + (x + 2) + (x + 3) = 90

(28 + 1) + (28 + 2) + (28 + 3) = 90

28 + 1 + 28 + 2 + 28 + 3 = 90

90 = 90

8 0

3 years ago

Read 2 more answers

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Alexandra [31]

Answer: y-axis.

Explanation:

The equation r = 3 - 4 sin θ may be graphed using cartesian coordinates (i.e. x and y) or polar coordinates.

The logical way is to graph in polar coordinates. I did it using a graphing software and obtained the attached graph.

Also, I attached the graph in cartesian coordinates.

Here you have a table that you can build by your self and use the pairs to draw the graph (either cartesian or polar coordinates).

 θ (rad) r = 3 - 4 sin θ 

0 3 
π/8 2.61731657 
 π/4 2.29289322 
3π/8 2.07612047
 π/2 2
 5π/8 2.07612047 
3π/4 2.29289322 
7π/8 2.61731657 
π 3 
9π/8 3.38268343 
5π/4 3.70710678 
11π/8 3.92387953 
3π/2 4 
13π/8 3.92387953 
7π/4 3.70710678 
15π/8 3.38268343 
2π 3 

In both of the attached graphs you can see that the left side is equal to the right side, but the upper side is not equal to the bottom side.

Therefore, the graph is symmetric about the y-axis.

7 0

3 years ago

Read 2 more answers

A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $22. The total cost to re

Cloud [144]

Answer:

The cost to rent each chair and each table are $1.5 and $8.75 respectively

Step-by-step explanation:

Let x represent 1 chair

Let y represent 1 table

Therefore

3x + 2y = 22 ------------(1)

5x + 6y = 60 ------------(2)

Multiply (1) by 5 and (2) by 3

15x + 10y = 110 ----------(3)

15x + 18y = 180 ------------(4)

Subtract (3) from (4)

8y = 70

Divide through by 8

y = $8.75

Substitute y = 8.75 in (1)

3x + 2y = 22

3x + 2(8.75) = 22

3x + 17.5 = 22

Collect like terms

3x = 22 - 17.5

3x = 4.5

Divide through by 3

x =$1.5

6 0

3 years ago

Mrs. Solar is remodeling a house and is looking for a contractor to do the work. She is getting quotes from 3 different contract

andrezito [222]

#b. The equation y = 50x + 200 represents the total cost that the contractor will charge for x hours of work.
#c. (1, 250); (2, 300); (3, 350)

6 0

3 years ago