Put a digit in the gap, such that the answer is a whole number:

3x+486=100...

What are all the possible digits?

The possible digits are 2,5 and 8

Step-by-step explanation:

3x +486 = 100_

From the equation in the question, we are looking for a digit to put in the gap after 100 to make sure that when we solve the question, x will be a whole number.

Therefore, since it's a single digit required, the possible digits will be from 0 to 9.

Now, from divisibilty tests, for a number from 2 digits upwards to be divisible by 3, the sum of its digits has to be divisible by 3.

Going back to the question, let's divide each term by 3 to get ;

3x/3 + 486/3 = 100_ to give ;

x + 162 = 100_ /3

Now for x to be a whole number, the value on the right hand side must be a whole number.

Therefore, since we know that for a 2 digits and above number to be divisible by 3,it's sum must be divisible by 3. We can plug in any of the digits from 0-9 into the gap and add up.

For 0; 1+0+0+0= 1

For 1; 1+0+0+1 = 2

For 2; 1+0+0+2= 3

Following the same addition pattern for digits 3,4,5,6,7,8and 9, we'll get sum of 4,5,6,7,8,9 and 10 respectively.

Inspecting the above, the only additions that are divisible by 3 are when the digit is; 2,5 and 8

answer: do we write it

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true