Given parameters:
Equation:
(x-4)²=9
Problem: Solve the equation by both factoring and extracting the square root.
Solution:
Starting equation:
(x-4)²=9
Subtracting 9 from both sides brings us to zero;
(x-4)² - 9 = 0
(x -4)² - 3² = 0
This fits the concept of the difference of squares;
x² - y² = (x + y)(x-y)
Let x = x-4 and y = -3
Then input and solve;
(x - 4 -3)(x - 4 -(-3)) = 0
(x - 7)(x - 1) = 0
S thus,
x - 7 = 0 or x-1 = 0
x = 7 or 1
<pBy extracting the square roots;
(x-4)² = 9
√(x-4)² = √9
x - 4 = 3
x = 4 + 3 = 7; however, this is not the sole solution
Thus, direct extraction of the square root is not the method for complete solutions.
We can formulate the trajectory of the parabola using the vertex form equation: y = a (x – h)^2 + k. The coordinates for the vertex are at h and k, representing the peak height, thus h = 250 and k = 120. Consequently, the equation becomes y = a (x – 250)^2 + 120. At the starting point where x = 0 and y = 0, we find a: 0 = a (0 – 250)^2 + 120, which simplifies to 0 = a (62,500) + 120, leading to a = -0.00192. The complete equation is y = -0.00192 (x – 250)^2 + 120. To determine y when x = 400, we substitute: y = -0.00192 (400 - 250)^2 + 120, yielding y = 76.8 ft. Hence, the ball clears the tree by 76.8 ft – 60 ft = 16.8 ft.
Assuming a maximum rental duration of 8 days, if we apply this to the equation, Happy Harry's Rentals costs $500, while Smilin' Sam's charges $600. Therefore, for the 7th and 8th days, Happy Harry's Rentals is a better option, while Smilin' Sam's is preferable for the first six days.
From a distance of 300 feet, a car approaches you at a speed of 48 feet per second. The distance d (in feet) of the car from you after t seconds can be described by the equation d=|300−48t|. At what moments does the car find itself 60 feet away from you?
Response:
Step-by-step explanation:
Shift the decimal points in both the divisor and the dividend.
Transform the divisor (the number you're dividing by) into a whole number by moving its decimal to the furthest right. Simultaneously, adjust the dividend's decimal (the number being divided) the same number of places to the right.
In the quotient (the result), place a decimal point directly over where the decimal point is now located in the dividend.
Proceed with the division as normal, ensuring proper alignment so the decimal point appears correctly.
Align each digit in the quotient directly over the last digit of the dividend utilized in that step.
