Recent questions tagged absolute-value

1
The number of distinct pairs of integers $(m,n)$ satisfying $|1 + mn| < |m + n| < 5$ is
2
If $3x + 2|y| + y = 7$ and $x + |x| + 3y = 1,$ then $x + 2y$ is$\frac{8}{3}$$1$$ – \frac{4}{3}$$0 1 answer 3 For a real number x the condition |3x – 20| + |3x – 40| = 20 necessarily holds if9 < x < 14$$6 < x < 11$$7 < x < 12$$10 < x < 15$
4
If $r$ is a constant such that $|x^{2} – 4x -13| = r$ has exactly three distinct real roots, then the value of $r$ is$15$$18$$17$$21 0 answers 5 The area, in \text{sq. units}, enclosed by the lines x = 2, y = |x – 2| + 4, the X-axis and the Y-axis is equal to 8$$12$$10$$6$
6
The area of the region satisfying the inequilities $\left | x \right |-y\leq 1,y\geq 0$ and $y\leq 1$ is
7
The area of the closed region bounded by the equation $\mid x \mid+\mid y \mid= 2$ in the two-dimensional plane is $4\pi$$4$$8$$2\pi 1 answer 8 The shortest distance of the point \left ( \frac{1}{2}, 1 \right ) from the curve y=\mid x-1 \mid+\mid x+1 \mid is 1$$0$$\sqrt{2}$$\sqrt{\dfrac{3}{2}}$
If $x^{2}+y^{2}= 0.1$ and $\left | x-y \right |=0.2$, then $\left | x \right |+\left | y \right |$ is equal to$0.3$$0.4$$0.2$$0.6 1 answer 10 Let \text{S} be the set of all points (x,y) in the x-y plane such that |x|+|y|\leq 2 and |x|\geq 1. Then, the area, in square units, of the region represented b... 1 answer 11 The product of the distinct roots of |x^{2}-x-6|=x+2 is-8$$-24$$-4$$-16$
The number of solutions to the equation $|x|(6x^{2}+1)=5x^{2}$ is _________
If $a, b$ and $c$ are three real numbers, then which of the following is not true?$\mid a+b \mid\leq \mid a \mid+\mid b \mid$$\mid a – b \mid \leq \mid a \mid + \mid b... 2 answers 14 The area bounded by the three curves |x + y| = 1, |x| = 1, and |y| = 1, is equal to4 3$$2$$1 2 answers 15 If x^2 + y^2 = 0.1 and |x – y| = 0.2, then | x | + | y | is equal to0.3$$0.4$$0.2$$0.6$
In the $\text{X-Y}$ plane, the area of the region bounded by the graph $|x+y| + |x-y| =4$ is$8$$12$$16$$20$