Missouri HiSET Math Version 1 Questions

Explanation

<h2>The solutions of (x - 2)(x + 4) = 0 are -2 and 4.</h2> To solve the equation, we apply the zero-product property, which states that if a product of factors equals zero, at least one of the factors must be zero. Setting each factor to zero gives us the solutions x - 2 = 0 (which leads to x = 2) and x + 4 = 0 (which leads to x = -4). <b>A) 4 and 2</b> This choice incorrectly lists the solutions as 4 and 2. While 2 is indeed a solution from the factor (x - 2), 4 is not derived from any of the factors, as solving (x + 4) = 0 yields -4, not 4. <b>B) -3 and 1</b> This choice presents -3 and 1 as solutions. However, neither value satisfies the equation (x - 2)(x + 4) = 0, making them invalid solutions. The correct solutions must stem directly from the factors of the equation. <b>C) -2 and 4</b> This choice includes -2 as a solution, which is derived from the factor (x + 4) = 0, yielding x = -4, but lists 4 incorrectly. The correct solutions are -4 and 2, making this choice partially correct but ultimately incorrect. <b>D) -1 and 1</b> This choice suggests -1 and 1 as solutions, neither of which satisfies the equation. Plugging these values into the original equation does not yield zero, confirming they are not solutions. <b>E) 0-1 and 3</b> This choice contains values that do not stem from the factors of the equation. Neither 0 nor 3 satisfies the equation (x - 2)(x + 4) = 0, thus they cannot be solutions. <b>Conclusion</b> The solutions to the equation (x - 2)(x + 4) = 0 are found by setting each factor to zero. The correct solutions are x = 2 and x = -4, derived from solving the factors independently. The incorrect choices misrepresent or do not satisfy the original equation, highlighting the importance of correctly applying the zero-product property in solving quadratic equations.

Explanation

<h2>±√10 are the solutions to the equation x² - 10.</h2> To find the solutions for the equation x² - 10 = 0, we can rearrange it to x² = 10. Taking the square root of both sides gives us x = ±√10, which are the correct solutions. <b>A) ±5</b> The value ±5 would imply that 5² = 25, which does not satisfy the original equation x² - 10 = 0. Therefore, this choice does not represent the correct solutions since it does not yield the necessary result when squared. <b>B) ±√(10)</b> This choice is correct because when we resolve the equation x² - 10 = 0, we find that x² = 10. Taking the square root of both sides yields x = ±√10, which are indeed the solutions to the equation. <b>C) ±10</b> The value ±10 would imply that 10² = 100, which is not a solution to the equation x² - 10 = 0. As a result, this choice fails to satisfy the equation, making it an incorrect answer. <b>D) ±10²</b> This choice simplifies to ±100, as 10² equals 100. Since 100 does not satisfy the equation x² - 10 = 0, this option is incorrect and does not represent the correct solutions. <b>E) ±20</b> The value ±20 would imply that 20² = 400, which is also not a solution to the equation x² - 10 = 0. Therefore, this choice does not solve the equation and is incorrect. <b>Conclusion</b> The solutions to the equation x² - 10 = 0 are found by taking the square root of 10, resulting in ±√10. Each of the other choices fails to satisfy the equation when squared, confirming that they are not valid solutions. Thus, ±√10 stands as the only correct answer in this context.

Explanation

<h2>The probability that Brandon will select a green piece of candy is 2/9.</h2> To find the probability of selecting a green piece of candy, we take the number of green candies (4) and divide it by the total number of candies (18). This gives us a probability of 4/18, which simplifies to 2/9. <b>A) 02-Jul</b> This choice does not represent any calculation related to the problem. The probability of selecting a green piece is not related to a date or numerical format that corresponds to any fraction or decimal. <br> <b>B) 02-Sep</b> This is the correct answer, as it corresponds to the simplified probability of 2/9. By calculating the ratio of the number of green candies to the total number of candies, we find 4/18 simplifies to 2/9, which is represented correctly here. <br> <b>C) 02-Nov</b> Similar to option A, this choice does not reflect a probability related to the problem. The probability calculation does not yield a result that aligns with the date format or any other number presented. <br> <b>D) 01-Aug</b> Again, this choice does not accurately represent the probability of selecting a green piece of candy. The answer requires a fractional representation of the probability, which this option does not provide. <br> <b>E) 01-Sep</b> This option also does not correspond to the calculated probability. The result of the probability calculation must be in the form of a fraction or decimal, neither of which is represented in this choice. <br> <b>Conclusion</b> The probability of selecting a green piece of candy from the bowl is calculated as 4/18, which simplifies to 2/9. This probability is accurately represented by option B, while all other choices fail to reflect the mathematical calculation necessary to determine the correct answer. Thus, understanding the calculation of probability is essential for solving such problems accurately.

Explanation

<h2>√(45) is between 6 and 7.</h2> The square root of 45 is approximately 6.7, which places it between the whole numbers 6 and 7. This can be confirmed by recognizing that 6² equals 36 and 7² equals 49, indicating that 45 lies between these two perfect squares. <b>A) 4 and 5</b> The squares of 4 and 5 are 16 and 25, respectively. Since 45 is much larger than 25, this pair of whole numbers does not enclose the square root of 45, making this option incorrect. <b>B) 5 and 6</b> The squares of 5 and 6 are 25 and 36, respectively. Again, 45 exceeds 36, meaning this interval does not contain the square root of 45, and thus this choice is incorrect. <b>C) 6 and 7</b> This choice is correct because 6² equals 36 and 7² equals 49. As such, 45 falls between these two values, confirming that the square root of 45 is indeed between 6 and 7. <b>D) 14 and 15</b> The squares of 14 and 15 are 196 and 225, respectively. Since 45 is far less than both of these values, this option is incorrect, as it does not encompass the square root of 45. <b>E) 22 and 23</b> The squares of 22 and 23 are 484 and 529, respectively. Since 45 is considerably lower than 484, this option also does not include the square root of 45, making it incorrect. <b>Conclusion</b> The square root of 45 lies between the whole numbers 6 and 7, as verified by calculating the squares of these integers. None of the other options correctly encompass the value of √(45), which further confirms that 6 and 7 is the only valid choice. Understanding the relationship between squares and square roots is essential for determining such intervals accurately.

Explanation

<h2>5x^2 + 9x + 2</h2> To find the sum of the two polynomials, we combine the like terms from each polynomial. Adding the coefficients of the same degree yields the resulting polynomial of 5x² + 9x + 2. <b>A) 4x^2 + 9x + 2</b> This option incorrectly suggests that the coefficient of x² remains 4 instead of correctly summing the coefficients from both polynomials. The correct addition of 4x² from the first polynomial and 1x² from the second results in 5x². <b>B) 5x^2 + 9x + 2</b> This is the correct answer. By adding the polynomials (4x² + 3x + 5) and (x² + 6x - 3), we correctly combine the x² terms (4 + 1 = 5), the x terms (3 + 6 = 9), and the constant terms (5 - 3 = 2), resulting in 5x² + 9x + 2. <b>C) 5x^2 + 9x + 8</b> This choice miscalculates the constant term. While the sum of the x² and x terms is correct, the constant should be 5 - 3, which equals 2, not 8. <b>D) 4x^4 + 9x^2 + 2</b> This option incorrectly introduces an x⁴ term that does not exist in either of the original polynomials. Both polynomials are of degree 2, and thus the resulting polynomial should also be of degree 2, with no x⁴ term. <b>E) 5x^4 + 9x^2 + 8</b> Similar to option D, this choice incorrectly introduces an x⁴ term. Furthermore, it also miscalculates both the x² and constant terms, leading to an entirely incorrect polynomial structure. <b>Conclusion</b> The correct sum of the two given polynomials is 5x² + 9x + 2, achieved by accurately combining like terms. Each incorrect option highlights common errors in polynomial addition, such as miscalculating coefficients and introducing non-existent terms. Understanding how to properly sum polynomials is essential in algebra for accurate expression manipulation.