Question
If 
and 
, what is one possible value of 
?
Hint:
Hint:
is called the absolute value of x . The value of the expression is given as
To find the value of , we first find value of x and y seperately, and then find absolute value of their product. There can be four different cases here, two cases for each equation. We will take the case where both the values are positive.
The correct answer is: 1,3,4,12
We are given two equations and
To find:
Considering, the first equation, we have
As this is true for all values of x ,
We take such that 
Then
Thus, we get
Solving this equation, we have
Next, consider the equation
As this is true for all values of y ,
So, we have
Solving this equation for y , we have
Thus, we get values of x and y as
From here, we have,
As 
so by definition, we get 
Therefore, one possible value of is 3.
Note:
This problem can have different answers if solved differently. Instead of making 
positive, if we took 
, we would get a different answer. Similarly,
for , we get a different value of . If we take both negative, we will get another answer.
Thus, we can get 4 answers: 1,3, 4, 12.
Related Questions to study
In △ ABC, AB = x and BC = x + 1 . How many possible values are there for x if the perimeter of △ ABC is 14?
In △ ABC, AB = x and BC = x + 1 . How many possible values are there for x if the perimeter of △ ABC is 14?
A park has the shape of an isosceles triangle. Its sides are x − 1 and x − 2 . The length of its compound is 44 units. Find the possible values of x
A park has the shape of an isosceles triangle. Its sides are x − 1 and x − 2 . The length of its compound is 44 units. Find the possible values of x
A triangular tiffin box is to be designed such that the measure of all angles is equal. What should be the measure of each angle?
A triangular tiffin box is to be designed such that the measure of all angles is equal. What should be the measure of each angle?
Find the mistake in the given image
Find the mistake in the given image
State whether the lines y = x + 2, y = − x + 3 and y − x = 1 form a triangle or not. Explain
why or why not.
State whether the lines y = x + 2, y = − x + 3 and y − x = 1 form a triangle or not. Explain
why or why not.
A pillar 14 cm in diameter is 5 m high. How much material was used to construct it?
A pillar 14 cm in diameter is 5 m high. How much material was used to construct it?
Simplify using the laws of exponents: Find x so that 
Simplify using the laws of exponents: Find x so that
The measures of the angles of a triangle are 
.
Find the measure of each angle and classify the triangle by its angles.
The measures of the angles of a triangle are .
Find the measure of each angle and classify the triangle by its angles.
The area of parallelogram is p sq.cm and height is q cm. A second parallelogram has equal area but its base is r cm more than that of the first Obtain an expression in terms of p, q and r for the height of the second parallelogram.
The area of parallelogram is p sq.cm and height is q cm. A second parallelogram has equal area but its base is r cm more than that of the first Obtain an expression in terms of p, q and r for the height of the second parallelogram.
A poster has an area of 432 square inches. The length , in inches, of the poster is 6 inches longer than the width of the poster. Which of the following equations can be solved to determine the length, in inches, of the poster?
Note:
The question can be further extended and ask us to find the length, breadth, or the perimeter of the poster. In that case, first we would solve the above equation to find the length of the poster and then use it to find the breadth. Finally we can find the perimeter easily by using the formula: perimeter 
(length + breadth).
A poster has an area of 432 square inches. The length , in inches, of the poster is 6 inches longer than the width of the poster. Which of the following equations can be solved to determine the length, in inches, of the poster?
Note:
The question can be further extended and ask us to find the length, breadth, or the perimeter of the poster. In that case, first we would solve the above equation to find the length of the poster and then use it to find the breadth. Finally we can find the perimeter easily by using the formula: perimeter (length + breadth).
A Medicine Capsule is in the shape of a cylinder of diameter 0.5 cm with two hemi spheres stuck to each of its ends. The length of entire capsule is 2 cm. Find the capacity of capsule.
A Medicine Capsule is in the shape of a cylinder of diameter 0.5 cm with two hemi spheres stuck to each of its ends. The length of entire capsule is 2 cm. Find the capacity of capsule.
The measures of the angles of a triangle are
.
Write an equation to show the relationship of the angles and find the measure of each angle
The measures of the angles of a triangle are.
Write an equation to show the relationship of the angles and find the measure of each angle
An ecologist selected a random sample of 30 prairie dogs from a colony and found that the mean mass of the prairie dogs in the sample was 0.94 kilograms (kg) with an associated margin of error of 0.12kg. Which of the following is the best interpretation of the ecologist's findings?
Note:
There are many concepts and definitions used in solving this question. The student must be familiar with mean, sampling, random sample, margin of error and hoe any results derived from the sample relate to the population, to solve this problem correctly.
An ecologist selected a random sample of 30 prairie dogs from a colony and found that the mean mass of the prairie dogs in the sample was 0.94 kilograms (kg) with an associated margin of error of 0.12kg. Which of the following is the best interpretation of the ecologist's findings?
Note:
There are many concepts and definitions used in solving this question. The student must be familiar with mean, sampling, random sample, margin of error and hoe any results derived from the sample relate to the population, to solve this problem correctly.
