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eduard
3 years ago
11

Show that 30.1111... is a rational number.

Mathematics
1 answer:
nexus9112 [7]3 years ago
8 0

We know that 30.1111... is a rational number because it ends in repeating decimals. We can show this by writing the number as a fraction using algebra.

x = 30.1111....

10x = 301.1111....

Subtract both sides by x

10x - x = 301.1111.... - 30.1111...

9x = 271

x = 271/9

The number can be rewritten as 271/9, which you can verify is the same number by checking on a calculator.

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Which of the following could be the equation of the line passing through (8, 3) parallel to y = -2.
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3 years ago
Rita finds the quotient of 584 divide by 17
Serga [27]

Answer:

Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.

Step-by-step explanation:

Quotient is the required answer if 584 is divided by 17

584 will be the dividend and 17 is the divisor.

To calculate 584/17, 17 will go in 58 3times with 7 as remainder. This remainder 7 will combine with 4 to make 74, 17 will also go in 74 4times with remainder of 6.

The final answer by combining the number of times 17 goes in 584 which is 34 with final remainder of 6. This means that;

584/17 = 34 remainder 6 i.e 34R6

This shows that Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.

5 0
4 years ago
2x+3y=12 and y=x+1.5 in substitution form
Sonbull [250]

Answer:

(1.5, 3)

Step-by-step explanation:

Given the 2 equations

2x + 3y = 12 → (1)

y = x + 1.5 → (2)

Substitute y = x + 1. 5 into (1)

2x + 3(x + 1.5) = 12 ← distribute and simplify left side

2x + 3x + 4.5 = 12

5x + 4.5 = 12 ( subtract 4.5 from both sides )

5x = 7.5 ( divide both sides by 5 )

x = 1.5

Substitute x = 1.5 into (2) for corresponding value of y

y = 1.5 + 1.5 = 3

Solution is (1.5, 3)

4 0
3 years ago
How many different arrangements can be made with the letters from the word space
alekssr [168]
120 different arrangements
4 0
3 years ago
Read 2 more answers
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