9.9 squared times 1.79
Calculating 9.9^2 gives 98.01
Then multiplying 98.01 by 1.79 results in 175.4379
We are presented with the following polynomial: The initial step is to move the variables to one side of the equation. After doing this, we have: We complete the square by adding (b / 2) ^ 2 to both sides of the equation. After doing so, we obtain: Rewriting this gives us: Therefore, the solutions are: The solution set of the equation is:
Revenue must be greater than Cost: R(x) > C(x), which translates to 0.50x > 10 + 0.20x. After simplification: 0.50x - 0.20x > 10, leading to 0.30x > 10. Therefore, x > 10/0.30 which gives x > 33.333. Rounding up, we find x = 34, meaning at least 34 cups of lemonade must be sold for revenue R(x) to exceed cost C(x). The answer is 34.
Homer made an error in step 2
When completing the square, it's necessary to apply the adjustments to both sides of the equation
Solution:
The provided equation for the circle:
First, let’s determine the center and the radius and identify where the mistake occurred
Step 1:
Group the terms
Step 2:
However, Homer’s second step is:
Thus, Homer committed an error during this step
When completing the square, the values must be added to both sides of the equation
However, Homer neglected to add 49 and 1 to the right side of the equation
Correct steps are:
By comparing with the general equation of a circle,
It follows that the center coordinates are ( 7, -1) and the radius measures 8.66
Response: Mackenzie purchased 7 bags of popcorn and 10 candies.
Step-by-step explanation:
Let x denote the number of popcorn bags bought by Mackenzie.
Let y denote the number of candies acquired by Mackenzie.
The total quantity of popcorn bags and candies combined is 17. Therefore,
x + y = 17
She spent $99.50 on popcorn bags and candies. Given that each bag costs $8.50 and each candy costs $4, we can express it as:
8.5x + 4y = 99.5 ———— 1
By substituting x = 17 - y into equation 1, we reformulate it as:
8.5(17 - y) + 4y = 99.5
144.5 - 8.5y + 4y = 99.5
- 8.5y + 4y = 99.5 - 144.5
- 4.5y = - 45
y = - 45 / - 4.5
y = 10
Now, substituting to find x, we have x = 17 - y = 17 - 10
x = 7
