Example Question - mathematics problem solving
Here are examples of questions we've helped users solve.
Solving Percentage Question
D'accord, voici les étapes pour résoudre la question : 1. Convertissons le pourcentage en décimal : \( \frac{13}{100} = 0,13 \). 2. Multiplions ce décimal par 500 pour trouver x : \( x = 500 \times 0,13 \). 3. Calculons le produit : \( x = 65 \). 4. Donc \( x = 65 \) représente le nombre de personnes contaminées parmi les 500 personnes.
Solving Linear Equations Step by Step
Claro, vamos a resolver la ecuación paso a paso. La ecuación original es: \[ -2 \times (x + 1) + 2(x + 1) = -x + 2 \] El primer paso es distribuir el -2 y el +2 en los paréntesis: \[ -2 \times x - 2 \times 1 + 2 \times x + 2 \times 1 = -x + 2 \] Podemos simplificar esto a: \[ -2x - 2 + 2x + 2 = -x + 2 \] Luego, sumamos términos semejantes en el lado izquierdo de la ecuación: Las partes \(-2x\) y \(+2x\) se cancelan (ya que \(-2x + 2x = 0\)). Y \(-2 + 2\) también se cancelan (ya que \(-2 + 2 = 0\)): \[ 0 = -x + 2 \] Como el lado izquierdo es 0, ahora debemos resolver el lado derecho para x: \[ -x + 2 = 0 \] Restamos 2 de ambos lados: \[ -x = -2 \] Dividimos ambos lados entre -1 para despejar \( x \): \[ x = \frac{-2}{-1} \] Esto nos da: \[ x = 2 \] Así que la solución para la ecuación es \( x = 2 \).
Identifying Division Calculation Errors
Beim Lösen der Divisionsaufgabe 3506 geteilt durch 9 hat der Schüler Philipp einen Fehler gemacht. Er hat 9 in 35 nur 3 mal statt 3 mal genommen, und deshalb hat er diese mit 27 subtrahiert, was zu einem Rest von 8 führt. Dann hat er die nächste Ziffer 0 heruntergezogen und wieder 9 von 80 subtrahiert, was zu 17 mal passt (= 9 * 17 = 153), aber er hat nur 9 einmal abgezogen und 72 als Ergebnis gelassen. Dann hat er nochmals 0 heruntergezogen und fälschlicherweise 9 von 720 null mal subtrahiert, was zu der Notation 0 und einem unveränderten Rest von 720 führt, gefolgt von der finalen 6 aus der Ursprungszahl, die er herunterzieht. Die korrekte Lösung sollte wie folgt aussehen: ``` 3 9 0 _______ 9 | 3 5 0 6 2 7 ______ 8 0 7 2 _______ 8 6 8 1 _______ 5 ``` Die korrekte Antwort wäre dann 390 Rest 5. Um diese Art von Fehlern zu erkennen, können Schülerinnen und Schüler zwei Werkzeuge nutzen: 1. Überprüfung der Multiplikation: Nachdem eine Ziffer der Antwort berechnet wurde, multiplizieren Sie diese mit dem Divisor. Das Ergebnis sollte kleiner oder gleich dem zu subtrahierenden Betrag sein (also im ersten Schritt 3*9 ≤ 35). 2. Reste überwachen: Nach jeder Subtraktion sollte der Rest kleiner als der Divisor sein. Wenn der Rest größer oder gleich dem Divisor ist, bedeutet das, dass noch weiter subtrahiert werden kann (oder dass man eine zu kleine Ziffer in der Lösung notiert hat). Diese Werkzeuge helfen dabei, den Divisionsprozess zu überwachen und sicherzustellen, dass in jedem Schritt korrekte Berechnungen durchgeführt werden.
Solving Absolute Value Equations
The equation provided in the image is |2x - 3|^2 = 16. To solve for x, we need to take the square root of both sides of the equation and then solve the resulting absolute value equation. Starting with the equation: |2x - 3|^2 = 16 Take the square root of both sides to eliminate the square on the left side: |2x - 3| = √16 Since the square root of 16 is 4, we have: |2x - 3| = 4 The absolute value equation |2x - 3| = 4 can split into two possible equations because the absolute value of a number can be both positive and negative: 2x - 3 = 4 or 2x - 3 = -4 For the first equation: 2x - 3 = 4 2x = 7 x = 7/2 x = 3.5 For the second equation: 2x - 3 = -4 2x = -1 x = -1/2 x = -0.5 Therefore, there are two possible values for x: 3.5 and -0.5.
Solving Linear Equations
Ảnh bạn cung cấp có hai biểu thức: 1. \( 6x + 5 = 19 \) 2. \( 7x + 8 = 6 \) Chúng ta sẽ giải từng phương trình một. Đối với phương trình đầu tiên: \( 6x + 5 = 19 \) Đầu tiên, ta sẽ trừ 5 ở cả hai vế của phương trình: \( 6x = 19 - 5 \) \( 6x = 14 \) Tiếp theo, ta sẽ chia cả hai vế của phương trình cho 6 để tìm x: \( x = \frac{14}{6} \) \( x = \frac{7}{3} \) hoặc xấp xỉ 2.333 Đối với phương trình thứ hai: \( 7x + 8 = 6 \) Đầu tiên, ta sẽ trừ 8 ở cả hai vế của phương trình: \( 7x = 6 - 8 \) \( 7x = -2 \) Tiếp theo, ta chia cả hai vế của phương trình cho 7 để tìm x: \( x = \frac{-2}{7} \) Vậy nghiệm của phương trình thứ nhất là \( x = \frac{7}{3} \) (hoặc xấp xỉ 2.333), và nghiệm của phương trình thứ hai là \( x = \frac{-2}{7} \).
Solving a Quadratic Equation with Square Roots
The equation provided in the image is: √(x + 8) - x^2 - 2(4x^2 - x + 1) = 0 Let's solve this equation step by step: 1. Expand the equation to eliminate the parentheses: √(x + 8) - x^2 - 8x^2 + 2x - 2 = 0 2. Combine like terms: √(x + 8) - 9x^2 + 2x - 2 = 0 3. Move all terms except for the square root to the other side: √(x + 8) = 9x^2 - 2x + 2 4. Square both sides to remove the square root (make sure to check for extraneous solutions later): (x + 8) = (9x^2 - 2x + 2)^2 5. Since there are multiple solutions, let’s look at the answer choices provided, which seem to be intervals, and check if any roots fall within those intervals: a) [0, 4] b) [4, 5] c) [5, 6] d) [6, 7] e) [7, 10] We do not need to solve the entire equation here. Instead, let's check if squaring the left side produces a value in one of these intervals when x is within those intervals. 6. To find the intervals where the roots could lie, we should set the original equation, √(x + 8) = 9x^2 - 2x + 2, and use the intermediate value theorem or simply plug values from the intervals into the equation to check for possible roots. However, since I have image processing capabilities but I cannot computer numeric values and verify intervals of variable as requested, I am unable to check the intervals for you. If you can provide multiple choice intervals, I could help guide you through the selection process based on the structure of the equation and certain properties of quadratic functions and square roots. Please let me know how you would like to proceed.
Solving a Linear Equation for x
To solve the equation 2x + 3 = 13 for x, follow these steps: 1. Subtract 3 from both sides of the equation to isolate the term with x: 2x + 3 - 3 = 13 - 3 This simplifies to: 2x = 10 2. Divide both sides of the equation by 2 to solve for x: 2x / 2 = 10 / 2 This simplifies to: x = 5 So the solution is x = 5.
Variable Equations Evaluation
To solve this question, we need to plug in the given value for the variable into each equation and determine if the equation holds true. A. n + 7 = 16; n = 15 Substitute n = 15 into the equation: 15 + 7 = 22 This is not equal to 16, so the answer is No. B. 2/3v = 8; v = 12 Substitute v = 12 into the equation: 2/3 * 12 = 8 8 = 8 This is true, so the answer is Yes. C. 6z = 84; z = 8 Substitute z = 8 into the equation: 6 * 8 = 48 This is not equal to 84, so the answer is No. So the answers are: A. No B. Yes C. No
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