To make lemonade following the recipe, the amounts required are 12 tablespoons of sugar and 3 cups of water (which equals 48 tablespoons).
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.
Response:
The answer is many to one
Step-by-step explanation:[[TAG_9]][[TAG_10]][[TAG_11]]
The third option is correct. Step-by-step explanation: Various transformations apply to a function f(x). If a transformation is applied downward by 'k' units, the function shifts down; if upward, it rises 'k' units. Additionally, if scaled vertically by a factor of 'b', it will stretch; if reflected over the x-axis, the operation is indicated. Thus, since the parent function has undergone reflection over the x-axis, a vertical stretch by a factor of 2, and a downward shift of three units, we can derive that the transformed function is presented.
Response:
$144,843.5
Detailed explanation:
In this scenario, we will utilize the compound interest formula
A= P(1+r)^t
A = final amount
P = initial principal
r = interest rate
t = number of periods
Given parameters
P= $27,000
R= 7.25%= 7.25/100= 0.0725
T= 24
A=27000(1+0.0725)^24
A= 27000(1.0725)^24
A= 27000*5.364
A= $144,843.5
By the end of 24 years, her account balance will reach $144,843.5
