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3 years ago

Twice the sum of a number and 5 is equal to three times the difference of the number and 7. Find the number.

Mathematics

1 answer:

Alexandra [31]3 years ago

5 0

Step-by-step explanation:

Let the required number be x.

According to the given information:

$2(x + 5) = 3(x - 7) \\ \\ \therefore \: 2x + 10 = 3x - 21 \\ \\ \therefore \: 10 + 21 = 3x -2x \\ \\ \therefore \: 31 = x \\ \\ \huge \red { \boxed{\therefore \: x = 31}}$

Hence the required number is 31.

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A 75.0 W bulb is connected to a

FromTheMoon [43]

Answer:

161

Step-by-step explanation: 110^2/75

8 0

3 years ago

Use decimals and fractions in the same equation showing the Commutative Property. Repeat for the Associative Property.

Anna71 [15]

For Commutative Property of Addition

Let us take a decimal number $2.14$ and a fraction $\frac{5}{20}$

Now, according to the Commutative property of Addition:

For any two numbers $a$ and $b$ :

$a+b = b+a$

So, for $2.14$ and $\frac{5}{20}$

Let us add

$2.14+\frac{5}{20} = \frac{214}{100} +\frac{5}{20}$

$=\frac{214}{100} + \frac{5 \times 5}{20 \times 5} \\ \\=\frac{214}{100} + \frac{25}{100} \\ \\= 2.14 + 0.25 \\ \\ = 2.39$

Also,

$\frac{5}{20} + 2.14 = \frac{5}{20} + \frac{214}{100}$

$= \frac{5 \times 5}{20 \times 5} +\frac{214}{100} \\ \\= \frac{25}{100} + \frac{214}{100} \\ \\= 0.25 + 2.14 \\ \\ = 2.39$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Commutative Property of Addition is satisfied.

For Associated Property of Addition

Let us take two same decimal numbers $2.14$ , $7.25$ and a fraction $\frac{5}{20}$

Now, according to the Associated property of Addition:

For any three numbers $a$ , $b$ and $c$

$a + (b+c) =(a+b) + c$

So, for $2.14$ , $7.25$ and $\frac{5}{20}$

The Left hand side:

$a + (b+c)$

$2.14 + (7.25 + \frac{5}{20}) = 2.14 + (\frac{725}{100} + \frac{5 \times 5}{20\times 5})$

$= 2.14 + (\frac{725}{100} + \frac{25 }{100})$

$= 2.14 + (\frac{750}{100} )$

$= \frac{214}{100} + \frac{750}{100}$

$= \frac{964}{100}$

$=9.64$

The Right hand side:

$(a + b )+c$

$(2.14 + 7.25 )+ \frac{5}{20}= ( 9.39 ) + \frac{5 }{20}$

$= 9.39 + \frac{5 \times 5 }{20 \times 5}$

$= 9.39 + \frac{25}{100}$

$= 9.39 + 0.25$

$= 9.64$

Thus,

$(2.14 + (7.25 + \frac{5}{20} )= (2.14 + 7.25 )+ \frac{5}{20}$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Associative Property of Addition is satisfied.

8 0

3 years ago

What is the estimate of 215% of 18.

Vsevolod [243]

215% of 18
You must change 215% into a decimal by multiplying by 100 which is 2.15
Then you multiply them
2.15×18=38.7
Then you estimate to the nearest whole number
38.7⇒39
You answer is 38.7
Your answer is 39 estimated

5 0

3 years ago

Read 2 more answers

How do you find the domain and range of a function and write it in set notation? What is the process of finding it? Tips and tri

DerKrebs [107]

Answer:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis

Step-by-step explanation:

plz forgive me if my answer is wrong

7 0

3 years ago

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Explain why the graph below does not represent a direct variation

Nitella [24]

Answer:

C. The line does not go through the origin.

Step-by-step explanation:

We have been given a straight line graph that doesn't pass through origin (0,0) and has y-intercept at (0,3).

Now we need to decide why that graph doesn't represent a direct variation.

We know that graph represents variation when it passes through origin. But since given graph doesn't passes through origin so it doesn't represent the direct variation.

Correct choice is :

<u>C. The line does not go through the origin.</u>

4 0

3 years ago

Read 2 more answers