Question

Вычислите удобным способом:1)38*21,5+21,8-38*1,5.2)148*6,5-31,7+24,4*6,5. 4.найдите значение выражения.1)12*(-3)-16:(-4).2)-24:(-8)+15*(-3). 5) решите уровнен ия 1)-3*(х+4)=18. 2)-3*(х+2)=6.6)на математической олимпеаде 32% участников получили грамоты.сколько школьников приняло участие в олимпиаде,если наградили 416человек? 7)В начале учебного года в школьной библиотеке было 700книг.к концу учебного года число книг увеличилось на 30%.сколько книг стало в школьной библиотеке к концу учебного года?

Answer 1

38 * 21,5 + 21,8 - 38 * 1,5 = 38 * (21,5 - 1,5) + 21,8 = 38 * 20 + 21,8 = 760 + 21,8 = 781,8

148 * 6,5 - 31,7 + 24,4 * 6,5 = 6,5 * (148 + 24,4) - 31,7 = 6,5 * 172,4 - 31,7 = 1120,6 - 31,7 = 1088,9

12 * (-3) - 16 : (-4) = - 36 - (-4) = - 36 + 4 = - 32  
- 24 : (-8) + 15 * (-3) = 3 + (-45) = - 42

- 3 * (х + 4) = 18                     - 3 * (х + 2) = 6
- 3х - 12 = 18                          - 3х - 6 = 6
- 3х = 18 + 12                         - 3х = 6 + 6
- 3х = 30                                 - 3х = 12
х = 30 : (-3)                              х = 12 : (-3)
х = - 10                                     х = - 4

416 школьников - 32%
х школьников - 100%
х = 416 * 100 : 32 = 1300 школьников приняли участие в олимпиаде

700 книг - 100%
х книг - 130%
х = 700 * 130 : 100 = 910 книг стало к концу учебного года

Answer 2

1) Вычисление выражений:

1) 38 * 21.5 + 21.8 - 38 * 1.5

To calculate this expression, we can follow the order of operations (PEMDAS/BODMAS) which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction.

38 * 21.5 + 21.8 - 38 * 1.5 can be simplified as:

= (38 * 21.5) + 21.8 - (38 * 1.5) = 817 + 21.8 - 57 = 838.8 - 57 = 781.8

Therefore, the value of the expression is 781.8.

2) 148 * 6.5 - 31.7 + 24.4 * 6.5

Following the order of operations:

= (148 * 6.5) - 31.7 + (24.4 * 6.5) = 962 - 31.7 + 158.6 = 930.3 + 158.6 = 1088.9

Therefore, the value of the expression is 1088.9.

3) 12 * (-3) - 16 / (-4)

Following the order of operations:

= (12 * (-3)) - (16 / (-4)) = -36 - (-4) = -36 + 4 = -32

Therefore, the value of the expression is -32.

4) -24 / (-8) + 15 * (-3)

Following the order of operations:

= (-24 / (-8)) + (15 * (-3)) = 3 + (-45) = -42

Therefore, the value of the expression is -42.

2) Решение уравнений:

1) -3 * (x + 4) = 18

To solve this equation, we can start by distributing the -3 to the terms inside the parentheses:

-3 * x - 3 * 4 = 18

Simplifying further:

-3x - 12 = 18

Next, we can isolate the variable x by adding 12 to both sides of the equation:

-3x - 12 + 12 = 18 + 12 -3x = 30

Finally, we can solve for x by dividing both sides of the equation by -3:

x = 30 / -3 x = -10

Therefore, the solution to the equation is x = -10.

2) -3 * (x + 2) = 6

Following the same steps as above:

-3x - 6 = 6 -3x = 12 x = 12 / -3 x = -4

Therefore, the solution to the equation is x = -4.

3) Расчет количества школьников и книг:

6) На математической олимпиаде 32% участников получили грамоты. Сколько школьников приняло участие в олимпиаде, если наградили 416 человек?

To find the total number of participants in the math olympiad, we can use the information that 32% of the participants received awards.

Let's assume the total number of participants is x.

32% of x is equal to 416:

0.32 * x = 416

To solve for x, we can divide both sides of the equation by 0.32:

x = 416 / 0.32 x ≈ 1300

Therefore, approximately 1300 students participated in the math olympiad.

7) В начале учебного года в школьной библиотеке было 700 книг. К концу учебного года число книг увеличилось на 30%. Сколько книг стало в школьной библиотеке к концу учебного года?

To find the number of books in the school library at the end of the academic year, we need to calculate a 30% increase from the initial number of books.

The initial number of books is 700.

30% of 700 is equal to:

0.30 * 700 = 210

To find the total number of books at the end of the academic year, we add the increase to the initial number:

700 + 210 = 910

Therefore, there were 910 books in the school library at the end of the academic year.