El número 18 tiene la siguiente propiedad: al sumar sus dígitos da como resultado1+8=9, y 18 se puede dividir por 9 (el valor de
1 answer:
Step-by-step explanation:
First of all, we can easily find that, for example, 63, has that particular property, therefore Jacinto is wrong.
Now we proceed to show that every (two digit) number is divisible by 3 if and only if it's sum of digits is.
Let n be a natural two digits number, and let a and b be the digits of said number, with
We can write n as
Let's call r1 the remainder of 10a/3, with, of course,
(for example, if a=1 then r1=1, because 10=3*3+1)
Now, each power of 10 leaves a remainder of 1 when divided by 3, thus r1 is equal to the remainder of a/3.
As an example, if a=3, then r1=0, because 30=3*10.
And let's call r2 the remainder of b/3.
In order for n to be divisible by 3, r1+r2 must be equal to a multiple of 3 (otherwise the division would leave a remainder).
Now, a can be written as
And similarly, b can be written as
Therefore, a+b is equal to (a multiple of 3)+r1+r2.
But since we already showed that r1+r2 needs to be equal to a multiple of 3, we have that 3 divides n if and only if the sum of its digits is a multiple of 3.
With a similar reasoning we can find that the same holds for 9.
The largest two digits multiple of 9 is 99, but it doesn't work, because 9+9=18, and 99 is odd.
Next up we have 90, which is of course good, since 90/9=10.
It is the largest two digits integer to have this property, since it's easily checked that others do not work
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Answer:
A
Step-by-step explanation:
They are basically wanting the value of x.
These are 2 secant lines drawn. Secant Line is a line that intersects the circle at 2 points.
To solve this, we have to use secant-secant theorem.
Secant-Secant Power Theorem tells us that if 2 secant lines are drawn from external point (here, E) to a circle, then, product of measure of one secant's external part and total secant is equal to other secants external part and whole secant.
In algebra, that is:
Let's multiply and find the value of x:
Hence, the correct answer choice is A
<h2>Hello!</h2>
The answers are:
A.
and
D.
and
To find which of the following pairs of numbers contains like fractions, we must remember that like fractions are the fractions that share the same denominator.
We are given two fractions that are like fractions. Those fractions are:
Option A.
and
We have that:
So, we have that the pairs of numbers
and
Share the same denominator, which is equal to 6, so, the pairs of numbers contains like fractions.
Option D.
and
We have that:
So, we have that the pair of numbers
and
Share the same denominator, which is equal to 7, so, the pairs of numbers constains like fractions.
Also, we have that the other given options are not like fractions since both pairs of numbers do not share the same denominator.
The other options are:
and
We can see that both pairs of numbers do not share the same denominator so, they do not contain like fractions.
Hence, the answers are:
A.
and
D.
and
Have a nice day!