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2 years ago

Prove that any number n of the form abcabc, where a, b, and c are decimal digits, is divisible by 7, 11 and 13.

Mathematics

1 answer:

vfiekz [6]2 years ago

6 0

We can factorize abcabc as

abcabc = abc000 + abc

abcabc = abc (1000 + 1)

abcabc = abc × 1001

abcabc = abc × 7 × 11 × 13

so naturally each of 7, 11, and 13 must divide abcabc.

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The track-and-field coach wants to know whether the students in the entire school prefer track races or field events. The coach

strojnjashka [21]

All students in each grade

audience: students - counts for both boys and girls.

option (B) for teachers is irrevelant.

option (C) doesn't include girls.

option (D) doesn't include the entire school

Hence, option A is correct.

8 0

2 years ago

5/9 × 8/11 what is the answer

nikitadnepr [17]

Answer:

$\frac{5}{9} \times \frac{8}{11} = \frac{5 \times 8}{9 \times 11} = \frac{40}{99} = 0.4040$

7 0

3 years ago

Read 2 more answers

A motor club has estimated that a 325 mile car trip will take 6 1/2 hours. What is the club assuming to be the average speed mil

In-s [12.5K]

Answer:

The average speed that the club is assuming is 50 miles per hour

Solution:

We know that Distance = Speed × Time.

Here it is given that distance is 325 miles and the time to cover 325 miles is $6_{2}^{1}$ hours which is equal to $\frac{13}{2}$ hours.

Now to find the average speed mile per hour we use the formula

$\begin{aligned} \text { Speed } &=\frac{\text { Distance }}{\text { time }} \\ &=\frac{325}{\frac{13}{2}} \\ &=\frac{325 \times 2}{13} \end{aligned}$

By cancelling 325 by 13 we get 25

= 25 × 2

= 50 miles per hour

Thus the average speed that the club is assuming is 50 miles per hour.

3 0

3 years ago

Whoops i forgot to read the lesson :P 30 points

andriy [413]

Step-by-step explanation:

I'll do 2.

Alright,Alex let say we have factored a quadratic into two binomial, for example

$(5x + 3)(6x - 4)$

If we set both of those equal to zero

$(5x + 3)(6x + 4) = 0$

We can used the zero product property in this case to find the roots of the quadratic equation.

This means that

$if \: ab = 0 \: then \: a = 0 \: and \: b = 0$

This means we set each binomal equal to zero to find it root.

$5x + 3 = 0$

$5x = - 3$

$x = - \frac{3}{5}$

$6x + 4 = 0$

$6x = - 4$

$x = - \frac{2}{3}$

So our roots are negative 3/5 and negative 2/3 using zero product property

6 0

3 years ago

A veterinarian in Camperville zoo needs to weigh the big bear. Which would be the most appropriate unit of measure?

Doss [256]

Answer:

Kilograms

Step-by-step

A meter is distance

A kilogram is weight

A liter is related to ounces

A cup is how much of something

3 0

3 years ago

Read 2 more answers