Examples for 9th grade - page 52
The length of the bases trapezium are in ratio 2:1. Length of midline is 17. How long are the bases of a trapezoid?
From station 130 km away started passenger train and after 2.8 hours after the express train, which travels 24 km an hour more. Express train finish journey 14 minutes early. Calculate the average speed of this two trains.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.
- Three workers
Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 25 days, B together with C for 16 days, A together with C for 10 days. How long it would take to complete the task every one of them alone? How long it would.
- Two runners
Two runners ran simultaneously towards each other from locations distant 21 km. The average speed of the first runner was 1/7 higher than the average speed of the second runner. How long should each ran a 21 km, if you know that they meet after 77 minute
In the country XYZ car Daewoo Leganza costs 3779 Euros including VAT; 3325.52 Eur without VAT. a) Determine the rate of VAT. b) How much is Euro VAT paid on the purchase? c) How many % of the total price of the goods is VAT? VAT = value added tax.
- Price of state
Estimate the cost of the state based on following reason. State price is expressed as a percentage respectively share in the redistribution of national GDP. Employee creates monthly value € 1121 (super-gross wage).Then tax him 35.2% employer contribution
Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″.
Diagonal of the rectangle has length 14 cm. Angle between diagonal and londer sife of rectangle is 37°. Calculate area of the rectangle.
Outer perimeter of silo is 24 m. Concrete wall is 18 cm thick. What is diameter and area of inside floor of silo?
If the segment of the line y = -8x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much?
- Trains for people
It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 50 km, with regular train leave at 6:05 and arrive at 7:20, but train is late and has departure at 9:52 and arrive at 11:05.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm2.
- Quadratic equation
Determine the numbers b, c that the numbers x1 = -7 and x2 = -4 were roots of quadratic equation: ?
- Cable car
Cable car rises at an angle 21° and connects the upper and lower station with an altitude difference of 1030 m. How long is "endless" tow rope?
- Widescreen monitor
Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 17 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha
- Glass mosaic
How many dm2 glass is nessesary to produc 50 slides of a regular 6-gon, whose side has length 7 cm? Assume that cutting glass waste is 14%.
Rhombus-shaped jewel have area of 86 mm2 and the edge in long 10 mm. Calculate the size of rhombus acute angle.
- Triangle SAA
The triangle has one side long 34 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.