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attashe74 [19]
2 years ago
6

John wants his friends to figure out what number he is thinking of. He gives them three clues: It is a whole number. The number

divided by 2 is greater than 9 and less than 13. The sum of its prime factors is 9. A. What are the possible numbers that John could be describing?
Mathematics
1 answer:
Sedbober [7]2 years ago
5 0

Answer:

11 and 12

Step-by-step explanation:

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Which of the following number lines and solution sets show the values of r that make the inequality -2r+3<9 true
scoray [572]

Answer:

"Solving'' an inequality means finding all of its solutions. A "solution'' of an inequality is a number which when substituted for the variable makes the inequality a true statement. When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality.

Step-by-step explanation:

Example 1:

Consider the inequality

displaymath173

The basic strategy for inequalities and equations is the same: isolate x on one side, and put the "other stuff" on the other side. Following this strategy, let's move +5 to the right side. We accomplish this by subtracting 5 on both sides (Rule 1) to obtain

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after simplification we obtain

displaymath175

Once we divide by +2 on both sides (Rule 3a), we have succeeded in isolating x on the left:

displaymath176

or simplified,

displaymath177

All real numbers less than 1 solve the inequality. We say that the "set of solutions'' of the inequality consists of all real numbers less than 1. In interval notation, the set of solutions is the interval tex2html_wrap_inline187 .

Example 2:

Find all solutions of the inequality

displaymath189

Let's start by moving the ``5'' to the right side by subtracting 5 on both sides (Rule 1):

displaymath190

or simplified,

displaymath191

How do we get rid of the ``-'' sign in front of x? Just multiply by (-1) on both sides (Rule 3b), changing " tex2html_wrap_inline201 " to " tex2html_wrap_inline203 " along the way:

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or simplified

displaymath193

All real numbers greater than or equal to -1 satisfy the inequality. The set of solutions of the inequality is the interval tex2html_wrap_inline205 .

Example 3:

Solve the inequality

displaymath207

Let us simplify first:

displaymath208

There is more than one route to proceed; let's take this one: subtract 2x on both sides (Rule 1).

displaymath209

and simplify:

displaymath210

Next, subtract 9 on both sides (Rule 1):

displaymath211

simplify to obtain

displaymath212

Then, divide by 4 (Rule 3a):

displaymath213

and simplify again:

displaymath214

It looks nicer, if we switch sides (Rule 2).

displaymath215

In interval notation, the set of solutions looks like this: tex2html_wrap_inline227 .

4 0
2 years ago
How did Wilson believe conquered empires should be treated?
Veseljchak [2.6K]

Answer:

Their people deserved to determine their own political futures.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Pls help me. will give brainliest if correct!!
baherus [9]
The answer is 12.206556

6 0
3 years ago
You want to buy a tent in the shape of a pyramid. The rectangular base is 35 square feet, with a height of 4 feet. What is the v
marin [14]

Answer:

46.67 cubic feet

Step-by-step explanation:

The formula for volume of a pyramid is

V = (1/3)Bh      where B is the area of the base, and h is the height.

We are givne B = 35 and h = 4.  Plug those values in and simplify...

V = (1/3)(35)(4)

 

  V = (1/3)(140)

       V = 140/3

             V = 46 2/3 cubic feet, which is 46.666667, or 46.67 rounded to the nearest hundredth

7 0
3 years ago
TSolve the system of equations below by graphing. What is the solution rounded to the nearest tenth? (–1.1, 3.2) (0.2, 2.8) (0.7
igor_vitrenko [27]

Answer:  Answer:The solution to the given system of equations is (2.8,0.1)

Step-by-step explanation: I got it correct on the Unit Test

4 0
3 years ago
Read 2 more answers
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