Math Problem Statement

[{"Options":["a. y + 1.000 = 19.000","b. x + 1.000 > 19.000","c. x + y = 19.000","d. x = 18.000"],"Problem":"\"Uang Budi bila ditambah Rp 1.000 menjadi 19.000\". Manakah dari simbol matematika di bawah ini yang benar dalam melambangkan kalimat tersebut:"},{"Options":["a. 9","b. 6","c. 3","d. 1"],"Problem":"Budi dan Tono membeli buku di toko buku. Budi membawa 5 bungkus buku dan Tono membawa 2 bungkus buku. Jika Budi memberi 9 buku kepada Tono dan sisanya adalah banyaknya buku yang sama sebelum ditambahkan, maka berapakah jumlah buku pada setiap bungkusnya?"},{"Options":["a. (-5, 0)","b. (0, -4)","c. (0, 4)","d. (5, 0)"],"Problem":"Koordinat titik potong fungsi m(x) = 12 - 3x dengan sumbu y adalah:"},{"Options":["a. 51°","b. 61°","c. 91°","d. 119°"],"Problem":"Bila y = 29°, maka x =:"},{"Options":["a. 30°","b. 45°","c. 60°","d. 15°"],"Problem":"Nilai x pada gambar adalah:"}]

Solution

Let's go through the problems presented in the image:

  1. Problem 1:

    • Question: "uang budi bila ditambah Rp 1.000 menjadi 19.000", manakah dari simbol matematika di bawah ini yang benar dalam melambangkan kalimat tersebut:
      • a. y + 1.000 = 19.000
      • b. x + 1.000 > 19.000
      • c. x + y = 19.000
      • d. x = 18.000
    • Solution: The correct symbol is x+1.000=19.000\mathbf{x + 1.000 = 19.000}, which translates to "Budi's money plus Rp 1,000 becomes Rp 19,000." Therefore, option a is correct.
  2. Problem 2:

    • Question: Budi dan Tono membeli buku di toko buku. Budi membawa 5 bungkus buku dan Tono membawa 2 bungkus buku. Banyaknya buku pada setiap bungkus adalah sama. Jika Budi memberi 9 buku kepada Tono dan sisanya adalah banyaknya buku yang sama sebelum ditambahkan, maka berapakah jumlah buku pada setiap bungkusnya?
      • a. 9
      • b. 6
      • c. 3
      • d. 1
    • Solution: We are told that after giving 9 books, the remaining number of books in Budi's possession equals the initial number. Let the number of books in each pack be xx. Since Budi has 5 packs and Tono 2 packs, the total number of books for Budi is 5x5x, and for Tono is 2x2x. After Budi gives 9 books to Tono, both Budi and Tono have equal books. 5x9=2x+95x - 9 = 2x + 9 Solving this equation: 5x2x=9+93x=18x=65x - 2x = 9 + 9 \quad \Rightarrow \quad 3x = 18 \quad \Rightarrow \quad x = 6 Therefore, the number of books in each pack is 6, so option b is correct.
  3. Problem 3:

    • Question: Koordinat titik potong fungsi m(x)=123xm(x) = 12 - 3x dengan sumbu y adalah...
      • a. (-5, 0)
      • b. (0, -4)
      • c. (0, 4)
      • d. (5, 0)
    • Solution: To find the y-intercept of the line m(x)=123xm(x) = 12 - 3x, we set x=0x = 0. m(0)=123(0)=12m(0) = 12 - 3(0) = 12 So the y-intercept is (0,12)(0, 12), which is not listed as an option. Thus, the closest response would likely be none of the above, but the correct coordinate should be (0, 12).
  4. Problem 4:

    • Question: Given y=29y = 29^\circ, find xx.
      • a. 5151^\circ
      • b. 6161^\circ
      • c. 9191^\circ
      • d. 119119^\circ
    • Solution: Referring to the image, if y=29y = 29^\circ and the diagram shows angles forming a straight line, then the two angles are supplementary. Therefore: x+y=180x+29=180x=18029=151x + y = 180^\circ \quad \Rightarrow \quad x + 29^\circ = 180^\circ \quad \Rightarrow \quad x = 180^\circ - 29^\circ = 151^\circ The answer is not present in the options, but the closest match would be d based on supplementary angles.
  5. Problem 5:

    • Question: Nilai xx pada gambar adalah...
      • a. 3030^\circ
      • b. 4545^\circ
      • c. 6060^\circ
      • d. 1515^\circ
    • Solution: The diagram shows 2x2x^\circ and 2x2x'^\circ. Assuming the lines are symmetrical, and knowing that the sum of angles in a triangle is 180180^\circ, we solve based on the given angles.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Angles and Triangles

Formulas

x + 1,000 = 19,000
Linear equation: 5x - 9 = 2x + 9
Linear function y = 12 - 3x
Supplementary angles: x + y = 180°

Theorems

Properties of Linear Equations
Supplementary Angles Theorem

Suitable Grade Level

Grades 8-10