The table shows the amounts of fines established in Russia since September 1, 2013, for exceeding the maximum permitted speed, recorded using automatic fixation tools.
What fine must be paid by the owner of a car whose recorded speed was 122 km/h on a road section with a maximum permitted speed of 100 km/h?
The figure shows how the air temperature changed during one day. The horizontal shows the time of day, the vertical shows the temperature in degrees Celsius. Find smallest value temperature. Give your answer in degrees Celsius.
A ladder 3.7 m long was leaned against a tree. At what height (in meters) is its upper end, if the lower end is separated from the tree trunk
at 1.2 m?
Answer: ___________________________.
The answer to task 18 is a sequence of numbers written in any order without spaces and using other symbols, for example: 214. The answer should be written in answer form No. 1 to the right of the number of the task you are performing, starting from the first cell. Write each number in a separate box.
In your answer, write down the numbers of the chosen answers.
Answer: ___________________________.
The answer to tasks 19 - 20 must be an integer or a final decimal. The answer should be written in the answer sheet No. 1 to the right of the number of the task you are performing, starting from the first cell. Write each number, minus sign and comma in a separate box.
1. Find the value of the expression:
2. Find the value of the expression:
3. The product on sale was discounted by 35%, while it began to cost 650 rubles. How much did the item cost before the sale?
4. Volume cuboid is calculated by the formula V = abc, where a, b and c are the lengths of its three edges coming out of one vertex. Using this formula, find a if V = 27, b = 3 and c = 4.5.
5. Find tg α if
6. Installation of two water meters (cold and hot) costs 3,500 rubles. Before the installation of water meters, they paid 1,100 rubles a month for water. After installing the meters, the monthly payment for water began to be 900 rubles. In what least number of months will the savings in water bills exceed the cost of installing meters if the water tariffs do not change?
7. Find the root of the equation 2 + 2(−9 + 4x) = 10x − 8.
8. The plan indicates that the rectangular room has an area of 21.2 sq.m. Accurate measurements showed that the width of the room is 4 m, and the length is 5.4 m. square meters the area of the room differs from the value indicated in the plan?
9. Establish a correspondence between the quantities and their possible values: for each element of the first column, select the corresponding element from the second column.
VALUE VALUES
A) the area of a three-room apartment 1) 0.7 ha
B) area football field 2) 100 sq. m.
C) the area of \u200b\u200bthe territory of Russia 3) 97.5 square meters. cm.
D) the area of a banknote with a denomination 4) 17.1 million square meters. km
100 rubles
In the table, under each letter corresponding to the value, indicate the number of its possible value.
Using the table, determine what fine the owner of a car whose recorded speed was 195 km / h on a road section with a maximum permitted speed of 110 km / h must pay. Give your answer in rubles.
12. There are 5 attractions in the city park: a carousel, a Ferris wheel, an autodrome, Chamomile and a Merry Shooting Range. The box office sells 6 types of tickets, each of which is for one or two attractions. Information about the cost of tickets is presented in the table.
What tickets should Andrey buy to visit all five attractions and spend no more than 900 rubles? In your answer, indicate any one set of ticket numbers without spaces, commas, and other additional characters.
13. A box shaped like a cube with an edge of 20 cm without one face must be painted on all sides from the outside. Find the area of the surface to be painted. Give your answer in square centimeters.
14. The figure shows a graph of the function y \u003d f (x) and points A, B, C and D on the Ox axis are marked. Using the graph, match each point with the characteristics of the function and its derivative.
In the table, under each letter, indicate the corresponding number.
| BUT | AT | FROM | D |
15. In triangle ABC angle C is 90°, CH is height, BC = 15, sin A = 0.8. Find VN.
16. Given two balls with radii 6 and 1. How many times the volume larger ball more volume than a smaller one?
17. Points A, B, C and D are marked on the coordinate line.
The number m is
Each point corresponds to one of the numbers in the right column. Set the correspondence between the specified points and numbers.
Write in the table given in the answer under each letter the number corresponding to the number.
| BUT | AT | FROM | D |
18. There are 30 people in the class, 20 of them attend a circle in biology, and 16 - a circle in geography. Select the statements that are true under the given conditions.
1) There are at least two of this class who attend both circles.
2) Each student from this class attends both circles.
3) There are 11 people who do not attend any circle.
4) There will not be 17 people from this class who attend both circles.
In your answer, write down the numbers of the selected statements without spaces, commas, or other additional characters.
19. Find a four-digit natural number, greater than 3000 but less than 3200, which is divisible by each of its digits and all of whose digits are different. Give your answer as one such number.
20. There are four gas stations on the ring road: A, B, C and D. The distance between A and B is 65 km, between A and C is 50 km, between C and D is 35 km, between D and A is 45 km ( All distances are measured along ring road along the shortest path). Find the distance (in kilometers) between B and C.
Answers:
| Tasks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answers | 2,1 | 8 | 1000 | 2 | 1,2 | 18 | −4 | 0,4 | 2143 | 0,8 |
| Tasks | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answers | 5000 |
146; 164; 416; 461; 614; 641 |
2000 | 3124 | 12 | 216 | 1342 | 14 |
3126; 3162; 3168; 3195 |
15 |
Follow the tasks of this part with a record of the solution.
Solve the inequality \frac(-14)((x-5)^2-2)\geq0
Show answer
\begin(array)(l)\frac(-14)((x-5)^2-2)\geq0\\\frac(-14)((x-5-\sqrt2)(x-5+\ sqrt2))\geq0\end(array)
We solve by the interval method.
We find zeros: x 1 \u003d 5+√2, x 2 \u003d 5-√2
\begin(array)(l)\_\_\_-\_\_\__\circ\_\_\_\_+\_\_\_\_\__\circ\_\_\_ -\_\_\__(\rightarrow X)\\\;\;\;\;\;\;\;\;\;\;\;5-\sqrt2\;\;\;\;\; \;\;\;\;\;\;5+\sqrt2\\x\in(5-\sqrt2;5+\sqrt2)\end(array)
Answer: (5-√2;5+√2)
Three enterprises of the holding received applications for the purchase additional equipment. The cost of equipment at the request of the first enterprise is 40% of the application of the second enterprise, and the cost of equipment in the application of the second enterprise is 60% of the application of the third. The cost of equipment in the application of the third enterprise exceeds the application of the first by 570 thousand rubles. What is total cost equipment in the applications of all three enterprises? Give your answer in thousand rubles.
Show answer
Let the cost of equipment in the application of the third enterprise be equal to x thousand rubles. Then the cost of the application of the second is 0.6x thousand rubles, and the cost of the application of the first is 0.4 * 0.6x thousand rubles. The cost of equipment in the application of the third enterprise exceeds the application of the first by (x - 0.4 * 0.6x) thousand rubles, and according to the condition - by 570 thousand rubles. Let's make an equation: (x - 0.4 * 0.6x) \u003d 570 Having solved the equation, we get x \u003d 750. Then the total cost of equipment in the applications of all three enterprises is x + 0.6x + 0.4 * 0.6x. Substituting x = 750 into the expression, we get 1380.
Build a graph of the function y\;=\;x^2\;-\vert4x\;+\;7\vert\;and determine for what values of m the line y = m has exactly three common points.
Show answer
Let's open the module: at 4x + 7< 0 функция задаётся формулой у = х 2 + 4х + 7,
and for 4x + 7 \geq 0 - by the formula y \u003d x 2 - 4x - 7, i.e.:
y=\left\(\begin(array)(l)x^2+4x+7,\;when\;x<-\frac74\\х^2-4х-7,\;при\;х\geq-\frac74\end{array}\right.
For all x< -7/4 строим график функции у = х 2 + 4х + 7 = (х + 2) 2 + 3 - это парабола без растяжений, ветви вверх, вершина в точке (-2;3).
Now for all x \geq -7/4 we build y \u003d x 2 - 4x - 7 \u003d (x - 2) 2 - 11 - a parabola without stretching, branches up, top (-2; -11). The result should be the following.
