# Examples for 8th grade - page 93

- Remainder

A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ? - Points on line segment

Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB. - Embankment

Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long. - Unknown number 17

Milada said, I am thinking of a number such that I evaluate expression x^{1}/3, the value of the expression would be 5. Which number Milada thinking? - Diagonal

he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal. - Mushrooms

Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them? - Area of iso-trap

Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other. - How far

From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse? - Candy

Peter had a sachet of candy. He wanted to share with his friends. If he gave them 30 candies, he would have 62 candies. If he gave them 40 candies, he would miss 8 candies. How many friends did Peter have? - Trapezoid - intersection of diagonals

In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area. - Unknown numbers

The sum of two consecutive natural numbers and their triple is 92. Find these numbers. - Rhombus construction

Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides... - Three painters

The three painters have painted bridge. The first would work done in 5 days, the second in 6 days, and the third in 7.5 days. How long will the bridge work if they work together? - 6 terms

Find the first six terms of the sequence. a1 = 7, an = an-1 + 6 - Fence and scale

The garden with 80 m of fencing is draw on plan as a square with a side length of 4 cm. At what scale is this plan made? - Competitors

In the first round of slalom fell 15% of all competitors and in the second round another 10 racers. Together, 40% of all competitors fell. What was the total number of competitors? - Trapezoid ABCD

ABDC is a trapezoid in which AB and CD are parallel sides measuring 6 and 9 respectively. Angles ABC and BCD are both right angles. Find the length of segment BD. - Five pumps

The water tank is filled with two pumps in 48 minutes. How long would it take to fill it with 5 same pumps? - Trapezium bases

Find the trapezium height if a = 8 cm and c = 4 cm if its content 21 square centimeters. - Square area

Complete the table and then draw each square. Provide exact lengths. Describe any problems you have. Side Length Area .

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