31.10.2021

# 2x≥12 I can't figure this out

0

24.06.2023, solved by verified expert

Step-by-step explanation:

You can start by dividing both sides by 2, getting .

### Faq

Mathematics

Step-by-step explanation:

You can start by dividing both sides by 2, getting .

Mathematics

Question 1:

The first error occurred going from line 2 to line 3. It is wrong because 6 was multiplied by 2 while 4/4*(x-2)/3 was not.

The second error occurred going from line 5 to line 6. It is wrong because while taking -1 to the other side, it becomes +1, and -8 + 1 = -7, not -9.

Question 2:

Equations 1, 3 and 5 have the same solution 4 and equations 2 and 6 have the same solution 0.

-(7-4x)=9

4x-7=9

4x=9+7

4x=16

x=4

12 = -4(-6x-3)

12/-4 = -6x-3

-3 = -6x-3

-6x=0

x=0

5x + 34 = -2(1-7x)

5x + 34 = 14x - 2

9x - 36 = 0

9x = 36

x = 4

14 = -x + 8

x=8-14

x=-6

-8 = -x-4

x = -4 +8

x=4

x + 5 = -5x + 5

6x = 0

x = 0

Mathematics

Question 1:

The first error occurred going from line 2 to line 3. It is wrong because 6 was multiplied by 2 while 4/4*(x-2)/3 was not.

The second error occurred going from line 5 to line 6. It is wrong because while taking -1 to the other side, it becomes +1, and -8 + 1 = -7, not -9.

Question 2:

Equations 1, 3 and 5 have the same solution 4 and equations 2 and 6 have the same solution 0.

-(7-4x)=9

4x-7=9

4x=9+7

4x=16

x=4

12 = -4(-6x-3)

12/-4 = -6x-3

-3 = -6x-3

-6x=0

x=0

5x + 34 = -2(1-7x)

5x + 34 = 14x - 2

9x - 36 = 0

9x = 36

x = 4

14 = -x + 8

x=8-14

x=-6

-8 = -x-4

x = -4 +8

x=4

x + 5 = -5x + 5

6x = 0

x = 0

Mathematics
D. Y = -0.175x^2 - 3.786x + 121.119A. Y= 2x-2

Step-by-step explanation:

1. The data generally goes down to the right, so the peak of the curve will be to the left of the y-axis. That means the x-coefficient will have the same sign as the x^2 coefficient (negative). The values near the y-axis are large positive values, so the y-intercept is positive. The equation with these characteristics is the last one:

... D. Y = -0.175x^2 - 3.786x + 121.119

___

You can have your calculator or spreadsheet program write the regression equation for you. It will give you substantially the same result. (see the attachment)

______

2. For estimating a regression line through data of this sort, it often works well to use the extreme data points: (1.5, 1) and (7.5, 13). If you draw a line through these points, you find that it passes through several other points on the graph, and it has a negative y-intercept. The slope of the line is ...

... (change in y)/(change in x) = (13 -1)/(7.5 -1.5) = 12/6 = 2

... A. Y = 2x-2

Mathematics
D. Y = -0.175x^2 - 3.786x + 121.119A. Y= 2x-2

Step-by-step explanation:

1. The data generally goes down to the right, so the peak of the curve will be to the left of the y-axis. That means the x-coefficient will have the same sign as the x^2 coefficient (negative). The values near the y-axis are large positive values, so the y-intercept is positive. The equation with these characteristics is the last one:

... D. Y = -0.175x^2 - 3.786x + 121.119

___

You can have your calculator or spreadsheet program write the regression equation for you. It will give you substantially the same result. (see the attachment)

______

2. For estimating a regression line through data of this sort, it often works well to use the extreme data points: (1.5, 1) and (7.5, 13). If you draw a line through these points, you find that it passes through several other points on the graph, and it has a negative y-intercept. The slope of the line is ...

... (change in y)/(change in x) = (13 -1)/(7.5 -1.5) = 12/6 = 2

... A. Y = 2x-2

Mathematics

(-1,2)

Step-by-step explanation:

Shown in picture below:

Mathematics

(-1,2)

Step-by-step explanation:

Shown in picture below:

Mathematics

The solution for x – y = - 3 and 2x + y = 12 by solving linear systems by substitution is (x, y) = (3, 6)

Solution:

Given, two system of equations are x – y = - 3 ⇒ (1)

And 2x + y = 12 ⇒ (2)

We have to solve the given system of equations by substitution method.

Now, we can write (1) as x – y = - 3 ⇒ x = y – 3

Then, substitute x value in (2)

(2) ⇒ 2(y – 3) + y = 12

⇒ 2y – 6 + y = 12

⇒ 2y + y = 12 + 6

⇒ 3y = 18

⇒ y = 6

So, substitute y value in (1) ⇒ x – 6 = - 3

⇒ x = 6 – 3

⇒ x = 3

Hence, the solution of system of equations is (x, y) = (3, 6)

Mathematics

When you factor a number, you are writing the number as a product of two numbers. Usually (not always), the two numbers are smaller than the original and different from each other. For example, one way to factor 6 is to write it as 3*2 which says "3 times 2". Another example is to take a number like 32 and write it as 8*4.

The x is simply a placeholder for a number, so we can apply the same factoring rules to algebra as you've done in the past with regular numbers. Something like 9x is really a factorization of its own because it means 9 times x where x is some unknown number. If x were say x = 2, then 9x = 9*2 = 18.

We can rewrite 9x into 3*3x because 9 is the same as 3*3. The +3 at the end of 9x+3 can be turned into 3*1.

So we go from this: 9x+3

To this: 3*3x+3*1

At this point, it might seem like we're just complicating something just for the fun of it. In reality, we're helping ourselves to factor out a common term of 3. Use the distribution rule to go from 3*3x+3*1 to 3*(3x+1). If you were to distribute the outer 3 back into each term, then you'd get 3*3x+3*1 = 9x+3 again. So in a way, you can think of it as distribution but in reverse. Factoring pulls things apart while distribution puts it back together. That's possibly one way to remember it.

So in the end, 9x+3 completely factors to 3*(3x+1). Note how we have a product of two expressions 3 and 3x+1

This might seem like a lot of steps but it's not that bad. Once you have enough practice, you'll be able to do this in one or two steps fairly easily. I'll let you practice the others on your own. They are similar to problem 1. If you still are stuck, then let me know and I'll update the solution.

Mathematics

The solution for x – y = - 3 and 2x + y = 12 by solving linear systems by substitution is (x, y) = (3, 6)

Solution:

Given, two system of equations are x – y = - 3 ⇒ (1)

And 2x + y = 12 ⇒ (2)

We have to solve the given system of equations by substitution method.

Now, we can write (1) as x – y = - 3 ⇒ x = y – 3

Then, substitute x value in (2)

(2) ⇒ 2(y – 3) + y = 12

⇒ 2y – 6 + y = 12

⇒ 2y + y = 12 + 6

⇒ 3y = 18

⇒ y = 6

So, substitute y value in (1) ⇒ x – 6 = - 3

⇒ x = 6 – 3

⇒ x = 3

Hence, the solution of system of equations is (x, y) = (3, 6)

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