Answer:
The equation 0 = 3x² + 17x - 160 might be useful in determining the length.
Step-by-step explanation:
The area of the vegetable garden is specified as 170 ft².
Now, regarding the provided equations;
1) For 0 = 3x² + 2x + 180, applying the quadratic formula results in:
x = [-2 ± √(3² - 4(3 × 180)]/(2 × 3)
x = [-2 ± √(-2151)]/6
The square root value is negative, indicating no real solution for x.
Thus, this equation does not help find the length.
2) For the equation 0 = 3x² + 10x + 180, employing the quadratic formula, the square root value is also negative, hence there's no natural root for x. This means this equation can't be used to determine the length.
3) For 0 = 3x² + 17x - 160, the roots when using the quadratic formula yield -10.67 or 5. The value 5 is viable since it is a whole number. Considering the area is also a whole number, this equation can be applied to ascertain the length.
4) For 0 = 3x² - 160, simplifying gives;
3x² = 160
x² = 160/3
x = ±√(160/3)
x = ±7.303
Since the area is a whole number but this length isn't, this equation may not accurately determine the length.
1. "The limit on John's credit card is defined by the function f(x)=15,000+1.5x," indicating that if John's monthly income is $5,000, he can spend a maximum of f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22,500 (dollars). As another example, if John's monthly income is $8,000, then he can spend up to f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars). 2. If we consider the maximum amount John can spend as y, it can be represented as y=15,000+1.5x. To express x, the monthly income, in terms of y, we rearrange this equation: y=15,000+1.5x results in 1.5x = y-15,000. Therefore, in functional notation, x is a function, referred to as g, based upon y, the maximum sum. Generally, we denote the variable of a function by x, so we redefine g as: This tells us that if the maximum amount that John can spend is $50,000, then his monthly income would be $23,333. 3. If John's limit is $60,000, his monthly income equals $30,000. Note: g is deemed as the inverse function of f because it reverses the actions of f.
Answer:
The student should have divided the amount after the discount by the percentage expressed as a decimal.
Step-by-step explanation:
Let Sanku be x. If Madhu's age is three times his, Madhu would be 3x. The age difference is 14, leading to the equation 3x - x = 14, which simplifies to 2x = 14, thus x = 7, indicating Sanku is 7 years old, while Madhu is 21.
