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masha68 [24]
2 years ago
5

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

Mathematics
1 answer:
scoray [572]2 years ago
4 0

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

displaymath174

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:

displaymath192

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 .

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Please i need help on my math
Kamila [148]

Answer:

V = \pi (2.5)^2h

Step-by-step explanation:

The formula for the volume of a cylinder, is V = π r^2 h. It shows that the diameter is 5. But we need the radius. The radius is half of the diameter. So, 5/2. This gets you 2.5.

The equation is now:

V = π(2.5)^2h

This is the answer.

V = \pi (2.5)^2h

8 0
2 years ago
Match the values associated with this data set to their correct descriptions. {6, 47, 49, 15, 43, 41, 7, 36}
Brums [2.3K]

1st quartile: 11

median: 38.50000

3rd quartile: 45

<h3>According to the given information:</h3>
  • Order these numbers in increasing order: 6, 7, 15, 36, 41, 43, 47, 49
  • There is a 38.5 median (it is the mean of 36 and 41 - the pair of middle entries).
  • 6,7,15,36, or the left-most half of the data, make up the sample.
  • The median of the lower half is 11, which is the first quartile (it is the mean of 7 and 15 - the pair of middle entries).
  • 41, 43, 47, and 49, which are the data points in the upper half, are to the right of the median.
  • The median of the upper half is 45 in the third quartile (it is the mean of 43 and 47 - the pair of middle entries).
  • The biggest value deviates 10.5 from the median (49-38.5)

Measure descriptive statistics

1st quartile: 11

median: 38.50000

3rd quartile: 45

To know more about quartile visit:

brainly.com/question/8737601

#SPJ4

I understand that the question you are looking for is :

2 Drag the tiles to the boxes to form correct pairs. Match the values associated with this data set to their correct descriptions.  {6, 47, 49, 15, 43, 41, 7, 36} first quartile 38.5  median 11  third quartile 10.5 the difference of the largest value and the median 45

7 0
2 years ago
The table shows the type of super power students wish they had. Super power Students Flight 888 Super strength 101010 X-ray visi
pogonyaev

Answer:

the answer is A and B

Step-by-step explanation:

3 0
3 years ago
3=c/5+2... how do I solve for c??
expeople1 [14]
Primeiro Você IRA Dividir o c (APENAS Colocar 5 + 2 embaixo do c). Depois faça a soma 5 + 2 = 7. Então faça o mmc (mínimo múltiplo comum) entre 7 e 1(o 1 é invisível, mas continua estando embaixo do 3). Deu 7 o mmc. Transforme seus números em frações, com o denominador 7. Transforme os números em frações o 3 virá 21, pois você divide em baixo e multiplica em baixo, e o c continua normal, pois já estava em baixo de 7. Como é para descobrir uma incógnita você tira os denominadores e ficará 21 = c.

3 = c/5 + 2
3 = c/7
21/7 = c/7
21 = c
4 0
3 years ago
Read 2 more answers
How many are 5 raised to 4 ???​
Licemer1 [7]

Answer:

625

Step-by-step explanation:

5⁴ = 5x5x5x5 = 625

4 0
3 years ago
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