How do you find the largest 6-digit multiple of 11 such that the sum of all its digits equals 40. What is the answer?

1 answer:

8 0

There is a certain way to find the answer for your question. First, you must be familiar with the divisibility rule for 11: the difference between the sums of even digits and odd digits should either be 0 or 11 only. For example, 1430, here the odd digits are 4 and 0 (which are the 3rd and 1st digits); the even digits on the other hand are 1 and 3, placed as the 4th and 2nd digits respectively.

Adding the sums of odd and even digits will give 4 (4+0) and 4 (3+1). Now, the difference of these sums is obviously equal to 0. Therefore, 1430 is divisible by 11. Same case will hold for numbers whose sums of odd and even digits is 11.

Moving on, now let us try to find the biggest 6-digit number divisible by 11. Intuitively, the last digit should be "9" - the hundred thousands digit - for it is the biggest number among numbers from 0-9. Furthermore, since there is no restriction as to whether the same number could or could not repeat, we can still use "9" all throughout the remaining 5 digits (ten thousands down to ones digit), giving the greatest possible 6-digit number, 999,999.

To check if the number we have obtained, 999,999, is divisible by 11, we need to use the divisibility rule for 11. Sum of even digits is 18 (9+9+9); sum of odd digits is 18 (9+9+9) as well. The difference of the sums is 0. Therefore, 999,999 is divisible by 11, hence the greatest 6-digit number multiple of 11.

As for the 6-digit number whose digits' sum is 40 and multiple of 11, we can assume its first 4 digits to be as 999,9** - four 9s is already equal to 36 - we only need to find two numbers whose sum is 4 to make the sum's total be 40. These remaining numbers should also be divisible by 11 since 9999 is already divisible by 11. The remaining numbers should only be 2 and 2 since the sum of its digit is 4, and that if we put them together, 22, a multiple of 11. This is the only combination of numbers that will give a sum of 4 while maintaining its structure a multiple of 11.

At last, the greatest 6-digit number whose digits' sum equal to 40 and is a multiple of 11 is 999,922. True, for 999,922 / 11 is equal to 90,902.

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10. If x = -2, y=-6 and z= 4, find the value of 4xy<br>Z

Grace [21]

Answer:

192

Step-by-step explanation:

Given

4xyz ← substitute given values into expression

= 4 × - 2 × - 6 × 4 = - 8 × - 24 = 192

5 0

2 years ago

What is the quotient StartFraction 15 p Superscript negative 4 Baseline q Superscript negative 6 Baseline Over negative 20 p Sup

Kitty [74]

Answer:

$-\frac{3p^8}{4q^3}$

Step-by-step explanation:

$\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}$ can be broken down into three fractions, coefficients, powers of p, powers of q.

$-\frac{15}{20}\cdot\frac{p^{-4}}{p^{-12}}\cdot\frac{q^{-6}}{q^{-3}}$

Simplify the first fraction, then simplify the others by subtracting numerator exponents minus denominator exponents.

$-\frac{3}{4} p^{-4-(-12)} q^{-6-(-3)} =-\frac{3}{4} p^8 q^{-3} = \alpha -\frac{3p^8}{4q^3}$

8 0

2 years ago

I need help please

bija089 [108]

Hey There!

Lets Just Work through your answers,

ⓧ A - An isosceles triangle is a triangle with (at least) two equal sides, so this would not apply to the given triangle.

:) B - A scalene triangle is a triangle in which all three sides have different lengths so this applies to the given triangle. One side measures 10, one measures 11, and one measures 12.1

ⓧ C - A right triangle is a type of triangle that has one angle that measures 90 degrees, which this triangle does not so this does not apply.

ⓧ D - In geometry, an equilateral triangle is a triangle in which all three sides are equal, so this does not apply to the given triangle.

ⓧ E - An obtuse triangle is a triangle with one obtuse angle (greater than 90°) and two acute angles, so this does not apply to the given triangle.

:) F - An acute triangle (or acute-angled triangle) is a triangle with three acute angles less than 90 degrees. So this applies to the given triangle.

In Summary, B & F classify the given triangle correctly.

If you could rate five starts & give brainliest that would be greatly appreciated!

Hope I helped, Have a good day.

4 0

3 years ago

the time required to assemble computers varies directly as the number of computers assembled and inversely as the number of work

olga2289 [7]

Answer:

16 hours

Step-by-step explanation:

let t be time, n the number of computers and w the number of workers, then

t = $\frac{kn}{w}$ ← k is the constant of variation