The Sum of the square of a number and 34

The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is . The range of all real numbers x such that 2x − 5

lisov135 [29]

Solution for Part 1:

2x − 5 < 7 and 4x + 10 > 6 is called a compound inequality. To find the range we need to solve each of the inequality and range would be the values of x which will make both the inequality TRUE.

Solving inequality 2x - 5 < 7:

2x - 5 < 7 {adding 5 on both sides}

2x - 5 + 5 < 7 + 5 {Combining like terms in either side of inequality}

2x < 12 {Dividing 2 on both sides}

2x/2 < 12/2 {Simplifying fraction in either side of inequality}

x < 6

Solving inequality 4x + 10 > 6:

4x + 10 > 6 {Subtracting 10 on both sides of inequality}

4x + 10 - 10 > 6 -10 {Combining like terms on either side}

4x > -4 {Dividing by 4 on both sides}

4x/4 > -4/4 {Simplifying each fraction}

x > - 1

Range of 2x − 5 < 7 and 4x + 10 > 6 will be all the x value which satisfy both the inequality x < 6 and x > -1.

Conclusion Part 1:

The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is can be given by interval notation (-1, 6)

Solution for part 2:

2x − 5 < 7 or 4x + 10 > 6 is called a compound inequality. To find the range we need to solve each of the inequality and range would be the values of x which The solution is same as part 1, with a small difference.

Range of 2x − 5 < 7 or 4x + 10 > 6 will be all the x value which satisfy any one of the inequality x < 6 or x > -1.

Conclusion Part 2:

The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is can be given by interval notation (-∞, ∞)

Note:

(i) When two inequalities are joined by the word and, the solution of the compound inequality occurs when both inequalities are true at the same time. It is the overlap, or intersection, of the solutions for each inequality.

(ii) When the two inequalities are joined by the word or, the solution of the compound inequality occurs when either of the inequalities is true. The solution is the combination, or union, of the two individual solutions.

6 0

3 years ago

One watering system needs about three times as long to complete a job as another warning system when both systems operate at the

algol13

Answer:

One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.

Step-by-step explanation:

Given:

Both the system can complete the job = 9 minutes

We need find the time required by each system to do the job.

Solution:

Let the time required by another watering system to complete the job be 'x' mins.

Now given:

One watering system needs about three times as long to complete a job as another watering system.

Time required by one watering system = $3x$

Rate to complete the job by another watering system = $\frac{1}{x}\ job/min$

Rate to complete the job by One watering system = $\frac{1}{3x}\ job/min$

Rate at which both can complete the job = $\frac{1}{9}\ job/min$

So we can say that;

Rate at which both can complete the job is equal to sum of Rate to complete the job by another watering system and Rate to complete the job by One watering system.

framing in equation form we get;

$\frac{1}{x}+\frac{1}{3x}=\frac19$

Now taking LCM to make the denominator common we get;

$\frac{1\times3}{x\times 3}+\frac{1\times1}{3x\times1}=\frac19\\\\\frac{3}{3x}+\frac{1}{3x}=\frac19\\\\\frac{3+1}{3x}=\frac{1}{9}\\\\\frac{4}{3x}=\frac{1}{9}$

By Cross multiplication we get;

$4\times9 =3x\\\\3x =36$

Dividing both side by 3 we get;

$\frac{3x}{3}=\frac{36}{3}\\\\x=12\ min$

Time required by One watering system = $3x =3\times 12 =36\ min$

Hence One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.

6 0

3 years ago

What is the quotient of m and 7

finlep [7]

Answer:

m/7

Step-by-step explanation:

because m divided by seven is m/7 so that is the answer

4 0

3 years ago

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PLEASEEEE HELP ASAP , due today

Levart [38]

Answer:

circumference=>2πr

circumference= 119.32 cm

π = 3.14

r =?

119.32 = 2 × 3.14 × r

r = 119.32/6.28

r = 19 cm

so area = πr²

area = 3.14 × (19)²

area = 3.14 × 361

area = 1,133.54 cm²

3 0

2 years ago

each batch of mrs.claus toffee makes 14 pieces of toffee if the elves need 8 dozen pieces of toffee how many batches does mrs.cl

Radda [10]

Mrs Claus must make 7 batches

4 0

3 years ago

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