# Algebra - examples

- Right triangle from axes

A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 sq. Units . The segment passes through the point ( 5,2). What is the slope of the line segment. ? - A clock

A clock was set right at 6:00 AM. If it gains 3 1/2 minutes per hour, what time will it show at 6:00 PM on the same day? Show your solution - Supermarket 2

A supermarket had a buko pie sale. In the morning 2/3 of the pies were sold and in the afternoon 1/6 of the pies were sold. If 150 pies were left, how many pies had been sold? Show your solution. - Gasoline tank 2

A gasoline tank is 1/6 full. When 25 liters of gasoline were added, it became 3/4 full. How many liters more is needed to fill it? Show your solution. - Reciprocal equation 2

Solve this equation: x+5/x-6=4/11 - The larger

The larger of two numbers is nine more than four times the smaller number. The sum of the two numbers is fifty-nine. Find the two numbers. - Prime factors

Write 98 as product of prime factors - Solve 2

Solve integer equation: a +b+c =30 a, b, c = can be odd natural number from this set (1,3,5,7,9,11,13,15) - Isosceles

Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area. - Three sides

Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. . - Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent was the waste. - Digit sum

How many are three-digit numbers that have a digit sum of 6? - Square into three rectangles

Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible. - Two rectangles

I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm^{2.}What dimensions can this large rectangle have? Write all options. Explain your calcu - Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - CuSO4 mixture

How many grams of solid CuSO4 we have to add to 450g of 15% CuSO4 solution to produce a 25% solution? - Sum of inner angles

Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees. - Digits

Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z. - Geometric progression 4

8,4√2,4,2√2 - Algebra

X+y=5, find xy (find the product of x and y if x+y = 5)

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