Реши задание на изображении
Solving equations
I'm looking at a list of equations that I need to solve carefully. For the first set, I’ll solve for variables x and y, and I have four equations to consider. Then, I’ll handle the second set, where I need to tackle more equations involving multiple variables like c and b. I’ve made some calculations already, but I’ll double-check my work to ensure accuracy. It’s crucial to be thorough!Verifying results and substitutions
I need to verify the result. It might help to show substitution examples or refer back to the original equality. I should mention each solution obtained through inverse operations and possibly verify them all. The task indicates to "solve the equations (80–83)," but since the user didn't specify, solving all visible ones seems best. I'll also pay attention to notation, especially with how "c" is presented in the image for exercise 83.4.Examining equations
I'm working on some equations and need to make sure my variables are clear. For example, I need to solve equations like:
- 43x + 72 = 502
- 67 - 21y = 25
I have to be careful about signs and isolate the variables correctly. It's essential to use inverse operations correctly. When showing derivations, I find that x and y values can be computed by rearranging terms properly. It's all about clarity and keeping track of each step to avoid confusion!Solving equations
I'm focusing on solving some equations. For the second equation, I have y - 7 = 200 - 122, which simplifies to y = 85. For the third equation, x + 29 = 204 - 100, leading me to x = 75.
It's all about carefully rearranging the terms to isolate the variables — sometimes these small steps can trip me up, but I'm keeping track of everything to ensure clarity and accuracy!Clarifying division equations
I’m processing division problems like \( 82.4 \) and \( 83 \). I want to note the correct notation in LaTex, using ":" or "\div". I’ll explain division equations clearly: first, find the whole parenthesized divisor by dividing the dividend by the quotient. For example, with \( (200+x):12=32 \), I’d multiply each side by \( 12 \). I’ll verify all equations by checking if my found numbers fit, ensuring readability while presenting the verifications compactly, maybe using semicolons.Проверка уравнений на изображении
Мне нужно проверить изображение на наличие уравнений, которые я ранее правильно извлёк. Посмотрим, что у меня получилось:
- Для первого уравнения, 43x + 72 = 502, я получил x = 10.
- Во втором уравнении 67 - 21y = 25, у меня получилось y = 2.
- Третье уравнение, 19y - 200 = 47, дало y = 13.
- Наконец, для 83 + 29x = 982 у меня получилось x = 31.
Я перепроверю их, чтобы убедиться, что они точны!
На фото упражнения 80–83, поэтому решу все уравнения.
Краткий ответ
80.
- \(x=10\); 2) \(y=2\); 3) \(y=13\); 4) \(x=31\).
81.
- \(x=70\); 2) \(y=51\); 3) \(y=84\); 4) \(z=2\).
82.
- \(x=116\); 2) \(y=85\); 3) \(x=75\); 4) \(y=42\).
83.
- \(x=27\); 2) \(x=184\); 3) \(y=32\);
- \(c=24\); 5) \(b=67\); 6) \(z=77\).
Решение
Главный принцип: применяем обратные действия, чтобы оставить неизвестную одну.
№ 80
\[ 43x+72=502 \] \[ 43x=502-72=430,\qquad x=430:43=10. \]
\[ 67-21y=25 \] \[ -21y=25-67=-42,\qquad y=2. \]
\[ 19y-200=47 \] \[ 19y=47+200=247,\qquad y=13. \]
\[ 83+29x=982 \] \[ 29x=982-83=899,\qquad x=31. \]
№ 81
\[ (x+58)-37=91 \] \[ x+21=91,\qquad x=70. \]
\[ (63-y)+109=121 \] \[ 172-y=121,\qquad y=51. \]
\[ 69-(y-28)=13 \] \[ y-28=69-13=56,\qquad y=84. \]
\[ 103-(z+47)=54 \] \[ z+47=103-54=49,\qquad z=2. \]
№ 82
\[ 321+(x+13)=450 \] \[ x+13=450-321=129,\qquad x=116. \]
\[ 122+(y-7)=200 \] \[ y-7=200-122=78,\qquad y=85. \]
\[ 204-(x+29)=100 \] \[ x+29=204-100=104,\qquad x=75. \]
\[ 53-(y-13)=24 \] \[ y-13=53-24=29,\qquad y=42. \]
№ 83
\[ (x-23)\cdot14=56 \] \[ x-23=56:14=4,\qquad x=27. \]
\[ (200+x):12=32 \] \[ 200+x=32\cdot12=384,\qquad x=184. \]
\[ 205:(y-27)=41 \] \[ y-27=205:41=5,\qquad y=32. \]
\[ 729:(c-15)=81 \] \[ c-15=729:81=9,\qquad c=24. \]
\[ 89\cdot(b+13)=7120 \] \[ b+13=7120:89=80,\qquad b=67. \]
\[ 12\cdot(97-z)=240 \] \[ 97-z=240:12=20,\qquad z=77. \]
Проверка
Например, для № 83:
\[ (27-23)\cdot14=4\cdot14=56; \]
\[ (200+184):12=384:12=32; \]
\[ 205:(32-27)=205:5=41; \]
\[ 12\cdot(97-77)=12\cdot20=240. \]
Во всех уравнениях после подстановки получаются верные равенства.
Да, теперь фото видно хорошо. Это упражнения 80–83, и ответы из предыдущего сообщения верные:
- 80: \(10;\ 2;\ 13;\ 31\)
- 81: \(70;\ 51;\ 84;\ 2\)
- 82: \(116;\ 85;\ 75;\ 42\)
- 83: \(27;\ 184;\ 32;\ 24;\ 67;\ 77\)
Принцип: сначала выполняем действие, обратное последнему, чтобы постепенно оставить неизвестное одну. Например: \[ 43x+72=502 \Rightarrow 43x=430 \Rightarrow x=10. \]
Обсуждение
1 сообщениеНу
