Catherine and Chelsie need to hire a clown for their birthday party. Clown A charges an initial $75 in addition to $12 per hour.
1 answer:
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<h2>Steps:</h2>
So for this, we will be completing the square to solve for m. Firstly, subtract 8 on both sides:
Next, divide both sides by 2:
Next, we want to make the left side of the equation a perfect square. To find the constant of this perfect square, divide the m coefficient by 2, then square the quotient. In this case:
-8 ÷ 2 = -4, (-4)² = 16
Add 16 to both sides of the equation:
Next, factor the left side:
Next, square root both sides of the equation:
Next, add 4 to both sides of the equation:
Now, while this is your answer, you can further simplify the radical using the product rule of radicals:
- Product rule of radicals: √ab = √a × √b
√12 = √4 × √3 = 2√3.
In exact form, your answer is
In approximate form, your answers are (rounded to the hundreths)
Answer:
The farmer should plant 14 additional trees, for maximum yield.
Step-by-step explanation:
Given
So, we have:
Required
The additional trees to be planted for maximum yield
The function is:
Open bracket
Rewrite as:
Differentiate
Equate to 0 and solve for x to get the maximum of x
Divide by -4
The farmer should plant 14 additional trees, for maximum yield.
The simplification form of the expression is 3x²/2 + 2x or three-halves x squared + 2 x option second is correct.
<h3>What is the area of the rectangle?</h3>It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have:
A community garden with raised beds is being redesigned. The area of the new rectangular beds can be expressed as one-half x (3 x + 4).
The expression:
By using the distributive property:
Thus, the simplification form of the expression is 3x²/2 + 2x or three-halves x squared + 2 x option second is correct.
Learn more about the rectangle here:
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