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4 years ago

72b384 is a number in which one of its digits is ‘b'. If the number is a multiple of 9, what is the numerical value of ‘b'?

Mathematics

1 answer:

Maslowich4 years ago

7 0

A number is divisible by 9 if and only if the sum of its digits is divisible by 9.

So, the sum of the digits of your number is

$7+2+b+3+8+4 = 24+b$

Since b ranges from 0 to 9 (it is a digit and it can't have any other values), 24+b ranges from 24 to 33. The only multiple of 9 in this range is 27, which we obtain by choosing b=3.

So, the only way to choose a value for b in order to make your number divisible by 9 is choosing b=3 and thus getting the number 723384, and indeed we have

$\dfrac{723384}{9}=80376$

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What is 0.3636363636 to the nearest thousandth?

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3 years ago

What is the simplified expression for,

Nostrana [21]

Here are a few rules you need to know for this equation:

Multiplying exponents of the same base: $x^m\times x^n=x^{m+n}$
Dividing exponents of the same base: $\frac{x^m}{x^n}=x^{m-n}$
Turning a negative exponent to a positive one: $x^{-m}=\frac{1}{x^m};\frac{1}{x^{-m}}=x^m$

So this is our algebraic expression: $\frac{3^{-4}\times 2^3\times 3^2}{2^4\times 3^{-3}}$

Firstly, multiply 3^-4 and 3^2: $\frac{3^{-4+2}\times 2^3}{2^4\times 3^{-3}}=\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}$

Next, divide:

$\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}=3^{-2-(-3)}2^{3-4}=3^12^{-1}$

Next, turn the negative exponent into a positive one: $3^12^{-1}= \frac{3}{2}$

Your final answer is 3/2, or 1.5.

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3 years ago

Solve for x: 3 over 3 x plus 1 over quantity x plus 4 equals 10 over 7x .

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There is one last step after getting x = 3. You must check x = 3 in the original equation to be sure that x = 3 does not cause a zero denominator.

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4 years ago

What is the least common denominator (LCD) of 12 and 23?

leva [86]

Answer: none of those, 276...?

Step-by-step explanation:

You need to know the least common denominator (LCD) of 12 and 23 if you want to add or subtract two fractions with 12 and 23 as denominators.

The least common denominator, also called lowest common denominator (LCD), of 12 and 23 is 276.

Here is a math problem example where you need to know the LCD of 12 and 23 to solve:

3/12 + 2/23 = ?

Step 1) Take the LCD and divide each denominator by it as follows:

276/12 = 23

276/23 = 12

Step 2) Multiply each nominator with the respective answers from Step 1:

3 x 23 = 69

2 x 12 = 24

Step 3) Put it all together to solve the problem:

69/276 + 24/276 = 93/276

= 3/12 + 2/23 = 93/276

It's that easy! Once again, the lowest common denominator (LCD) of 12 and 23 is as follows:

276

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3 years ago