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2 years ago

Use mental math to decide which equations are true. Drag the true equations into the box.

Mathematics

1 answer:

AleksAgata [21]2 years ago

3 0

1.23÷10 = 0.123 is a true statement

Given the expression 1.23÷10, we need to<u> check if the expression is equal to 0.123</u>

<h3>Fractions</h3>

Fractions is a ratio of two integers a/b

Given

1.23÷10

Convert the decimal to a fraction as shown:

1.23 = 123/100

The expression becomes:

123/100 ÷10

= 123/100 * 1/10

= 123/1000

Convert back to decimal

1.23÷10 = 0.123

This shows that 1.23÷10 = 0.123 is a true statement

Learn more on division here: brainly.com/question/12957834

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The answer to this question is 4/6 because of the ratio changes to a division sign

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Each of the three friends will get one-sixth of the Thomas's enitre marble collection.

Step-by-step explanation:

Fraction of the total marble collection brought by Thomas = $\frac{1}{2}$

Now, Thomas divides these marbles equally among his three friends. So, each of the three friends will get one-third of the total marble collection brought by Thomas.

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Express the terms of the following sequence by giving a recursive formula.

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The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

Keywords: arithmetic sequence, common difference

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