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lys-0071 [83]
3 years ago
9

Solve the system of inequalities 1-12y<:3y+1; 2-6y>4+4y

Mathematics
1 answer:
ICE Princess25 [194]3 years ago
8 0

For 1 - 12y < 3y+1;        y > 15

For 2 - 6y  >  4  +  4y;   y  <  -0.2

The given inequalities are:

1  -  12y < 3y  +  1

2 - 6y  >  4  +  4y

For 1  -  12y < 3y  +  1:

1  -  12y < 3y  +  1

Collect like terms

-12y  -  3y  <  1  -  1

-15y    <   0

Multiply both sides by -1

-1(-15y)   >  0(-y)

15y    >   0

Divide both sides by 15

y   >  0/15

y   >   15

For 2 - 6y  >  4  +  4y

Collect like terms

-6y  - 4y  >  4  -  2

-10y   >   2

Multiply both sides by -1

-1(-10y)   <  2(-1)

10y   <  -2

y  <  -2/10

y  <  -0.2

Learn more here: brainly.com/question/11316045

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The quotient of the sum of 2t and 2, twice the cube of s
natali 33 [55]

Answer: \frac{2t+2}{2s^3}

Step-by-step explanation:

Since you did not indicate what you need to do, I assume that you have to write an expression using the sentence given in the problem.

In order to solve this exercise, it is importat to remember the following information:

1. The quotient is the result of a division.

2. The sum is the result of an addition.

3. The word "twice" indicates a multiplicatio by 2.

4. The word "cube" indicates an exponent 3.

Then, keeping on mind the explained above and the data given in the exercise, you know that:

-The sum of 2t and 2 can be expressed as:

2t+2

- Twice the cube of s can be expressed in the following form:

2s^3

Therefore, you can dermine that "the quotient of the sum of  2t and 2 and twice the cube of s" is represented with the following expression:

\frac{2t+2}{2s^3}

O

8 0
3 years ago
List the following elements in proper set notation. Place the elements in numerical order within the set. 0, 1, 123, 4, 34
forsale [732]

Answer:

{0, 1, 4, 34, 123}

Step-by-step explanation:

{0, 1, 4, 34, 123}

8 0
3 years ago
What is the equation of a line that passes through the points (0,5) and (4,8)?
nikdorinn [45]
A linear function has the form y=mx+b
if you insert the point (0,5) in this you receive:
5=m*0+b
5=b
(remember b is the distance to the x axis at x=0, so you can read it directly of)

To get m you insert (4,8) and the previous b:
8=m*4+5
3=4m
3/4=m

your line is: y=3/4x+5

(also this question is a duplicate of #3469085 by you :) )

7 0
3 years ago
5. As two boats are coming to the end of a race, a top view of their positions is
Dafna1 [17]

The distance of the boat on the right to the finish line is 297.29 m and the distance of the boat on the left to the finish is 294.11 m, so the boat on the left will reach the finish line faster.

<h3>How do you know which boat will reach the finish line faster? </h3>

The image shows two triangles of which we know an angle and the value of the opposite leg. Therefore, we can perform a mathematical operation to know the value of the hypotenuse of these triangles, which would be the distance of the boats to the goal as shown below.

h = hypotenuse

  • Right Boat

Sen 22° =  \frac{110 m}{h}

h = \frac{110 m}{ Sin 22}

h = \frac{110 m}{0.37}

h = 297,29 m

  • Left boat

Sen 20° = \frac{100}{h}

h = \frac{|00 m}{ Sin 20}

h = \frac{100 m}{0.34}

h = 294,11 m

According to the above, the distance of the boat on the left is less, so it can be inferred that this boat will reach the finish line faster.

Learn more about triangles in: brainly.com/question/2269348

8 0
2 years ago
(0.3d-1.5)/3 1/3=0.84:7/15
Anika [276]

Answer:

  d = 25

Step-by-step explanation:

Perhaps you want to solve for d:

  (0.3d -1.5)/(3 1/3) = 0.84/(7/15)

Change the division by a fraction to multiplication by its inverse.

  (0.3d -1.5)·(3/10) = (0.84)·(15/7)

  0.09d -0.45 = 1.8 . . . . . . . . . . . . simplify

  d - 5 = 20 . . . . . . . . . . . . . . . . . . divide by 0.09

 d = 25 . . . . . . . . . . . . . . . . . . . . . add 5

_____

Grouping symbols help show what is being divided by what. Especially where mixed numbers are involved, parentheses help show that the number 3 1/3 is not supposed to be interpreted as the product of 3 and 1/3.

4 0
3 years ago
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