The temperature increases by 1/4 degree per hour. If it is 75 degrees at'8 AM, at what time will the temperature be 79 degrees?

Answer:

  (n ≤ -3) ∪ (-1 ≤ n)

Step-by-step explanation:

I like to "unfold" the absolute value expression by copying the right-side expression to the left side (with the same comparison symbol) and negating its value. I do it this way because I find it easier to work the problem "all at once".

  -1 ≥ n +2 ≥ 1

Obviously, -1 ≥ 1 is not true, which means the solution to this inequality will be disjoint sections of the number line. A compound inequality of this nature is generally interpreted to mean the AND of the two inequalities. So, technically, this is an incorrect step. I choose to overlook that, and consider the expression to represent the two inequalities ...

  -1 ≥ n +2 . . . OR

  n +2 ≥ 1

Subtracting 2 from the above compound inequality gives ...

  -3 ≥ n ≥ -1

So, the solution is ...

  (n ≤ -3) ∪ (-1 ≤ n)

_____

Further explanation

The inequality symbol negates its content if that content is negative. So, the expression ...

  |n+2| ≥ 1

means ...

  ±(n +2) ≥ 1

This resolves to two cases:

  n +2 ≥ 1

and

  -(n +2) ≥ 1

The latter case is equivalent to ...

  n +2 ≤ -1

which can also be written as ...

  -1 ≥ n +2

A more technically correct solution process would identify the two cases and work them separately.

__

In the graph, the red shading (with the solid edge) shows the solution with respect to the numbers on the x-axis. If you were to graph this on a number line, you would put solid dots at -3 and -1, and shade the line to their left and right, respectively. The blue curve shows the absolute value, and the green line shows y=1, so you can see that the shaded areas correspond to the absolute value being greater than or equal to 1.

The vector magnitude is 10.29lb and the vector direction is 150.9⁰.

Vector:

As per the given question:

To find:

magnitude and direction=?

Solution:

Vector representation of the given value:

Calculating the vector magnitude:

Calculating the vector direction:

When

Let's solve the value for

lies in the second quadrant,

Find out more information about the angle here:

brainly.com/question/24797859

Answer:

$65 ≤ x ≤ $135

Step-by-step explanation:

Now, one should know the meaning of compound inequality. A compound inequality is an inequality that simply combines the two simple inequalities.

Now, in an inequality, three relations are performed, equal to, less than, and greater than. You can combine 'equal to' with 'less than' or 'greater than' according to the situation given.

Notice that in the given sign

≤

the value on the left side of the pointed side will be small or lesser than the value on the right side. Also notify that if inverted, like this ≥

The value of the left side will be greater. This means the value at the pointed side will always be smaller. The lower bar is a sign of equal to

if this is written

x ≤ 3

It means that x can be equal to three or any value less than 3 means 2,1,0,-1, etc.

Now in the question given, it is stated that money should be not less than $65 means it can either be $65 or more but not less than it. Let's assume 'x' as the amount required,

So one inequality is

$65 ≤ x

The second condition which is amount should be no more than $135, means it can be $135 or less, so inequality is

x ≤ $135

Remember that we use AND in the answer because both statements of inequality need to be fulfilled or satisfied.