# Algebra - problems - page 78

1. 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.
2. Unknown number 17
Milada said, I am thinking of a number such that I evaluate expression x1/3, the value of the expression would be 5. Which number Milada thinking?
3. Eq1
Solve equation: 4(a-3)=3(2a-5)
4. If-then equation
If 5x - 17 = -x + 7, then x =
5. Circle - AG
Find the coordinates of circle and its diameter if its equation is: ?
6. Family 8
Father is 38 years old, daughter 12, son 14. How many years will father have as many years as his children together?
7. Lcd3
What is LCD of the equation of ? ? And what is x?
8. 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?
9. Equation of circle
find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
10. Unknown numbers
The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
11. Clubhouse
There were only chairs and table in the clubhouse. Each chair had four legs, and the table was triple. Scouts came to the clubhouse. Everyone sat on their chair, two chairs were left unoccupied, and the number of legs in the room was 101. How many chairs w
12. 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?
13. Equation of circle 2
Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
14. 6 terms
Find the first six terms of the sequence. a1 = 7, an = an-1 + 6
15. Modulo
Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .
16. Unknown number
I think the number - its sixth is 3 smaller than its third.
17. Photocopier
A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?
18. Suzan
Susan's age will be after 12 years four times as much as twelve years ago. How old is Susan now?
19. Rhombus
The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
20. Simplify
Simplify the following problem and express as a decimal: 5.68-[5-(2.69+5.65-3.89) /0.5]

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