Absolute value - practice problems
The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. Denoted by vertical bars |x|, it equals x when x ≥ 0 and -x when x < 0. Absolute value transforms negative numbers to positive while leaving positive numbers unchanged. Equations and inequalities involving absolute value often split into multiple cases based on the sign of the expression inside. Graphically, y = |x| creates a V-shape centered at the origin. Applications include measuring distances, errors, deviations, and defining metrics in various mathematical contexts.Remember: Solve each problem thoughtfully and make sure to show your complete solution for every question.
Number of problems found: 150
- Distance - number line
What is the distance between -93 and 114 on a number line? - Parallel lines - dist
Find the distance between the parallel lines 3x – 4y +7 = 0 and 3x – 4y + 5 = 0 - Submarine and plane
A submarine is floating 900 m below the sea level. And at the opposite point, right above the submarine, an aeroplane is flying at the height of 4800 m above the sea level. What is the vertical distance between the two? - Clock error
How much does a watch lose per day, if its hands coincide every 64 minutes? - Hands of a clock
At what time between 11 and 12 O'clock will the hands of a clock be at an angle of 180°? - The dimensions
The dimensions of a rectangular piece of paper are 22 cm × 14 cm. It is rolled once across the breadth and once across the length to form right circular cylinders of biggest possible surface area. Find the difference in volumes of the two cylinders that w - Length measurement
Choose the measurement closest to 60 cm: ... - A surveyor A surveyor estimated the distance across a river to be 300 m. The actual distance across the river was 286.4 m. Find the absolute error and the percent error of the surveyor's estimate. If necessary, round to the nearest tenth.
- Same distance
What decimal is the same distance from 7.1 and 7.4? - Write 7 Write an expression representing the distance between −7 and 3 on a number line.
- Chemical experiment
For an experiment, a chemical solution starts at a temperature of 25°C, falls to −3°C, rises to 15°C and then falls again to −8°C. What is the total change in temperature? Add all the changes together for each rise and fall. - Two chords 2
The length of one of two chords of a circle is 12cm. If the chords are 6cm and 7cm away from the center of the circle, calculate the length of the second chord. - Same remainder
Find the greatest number that will divide 43, 91, and 183 so as to leave the same the remainder in each case. - In the middle 2
In the middle between the unknown number and the number 30 is the number 12. Determine the unknown number. - Calculate 449
Calculate the size of the angle formed by 2 lines on the dial and formed by connecting the points 7.2 and 1.4. - Multiplying Absolute Value and Reciprocal
What do we get by multiplying the absolute value by the number -0.7 and the reciprocal of the number by the number 10? - Coordinates of line points
I have a point A=[2,1] and a line y+x-5=0. How do I determine the coordinates of point A', which is the image of point A according to the given straight line? - Mark statistics frequency
Marks with equal weight 2,1,3,2,2,3,1,3,1,1,2,4,2,2,3,1,1,2,1,3 specify: 1) arithmetic mean 2) absolute and relative frequency 3) mode and median 4) create a chart - Point plane distance
Calculate the distance of point A[ 4; 2; -3 ] from the plane : 2x - 2y + z + 5 = 0 - Sound Doppler observer
A sound source emits a tone with an absolute pitch of 500 Hz and moves towards the observer at a speed of 5 m/s. Sound travels at a speed of 340 m/s. How fast is an observer moving who hears a tone with an absolute pitch of 522 Hz?
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