Respuesta :
Answer:
1) Option D is correct.
The choice that represents the number of balloons in their bags is x² - 40x + 300 ≥ 0
2) Option A is correct
If Rob had more balloons than Loretta, the least number of balloons that Rob van have before using any = 30.
Step-by-step explanation:
Complete Question
To decorate for a party, Rob and Loretta were each given a bag of balloons. There were 40 balloons between both bags. Rob used 8 balloons from his bag, and Loretta used 8 balloons from hers. The product of the number of balloons left in each bag is no more than 44.
Let x represent the number of balloons that Rob had in his bag before he used any. Which choice represents the number of balloons left in their bags?
A. x² - 40x - 300 = 0
B. x² - 40x - 300 < 0
C. x² - 40x = 300
D. x² - 40x + 300 ≥ 0
If Rob originally had more balloons than Loretta, what is the least number of balloons that Rob could have had before using any?
A.30
B.20
C.10
Solution
If x is the number of balloons that Rob had at the start, the number of balloons that Loretta would have at the start = (40 - x)
Then, they both use 8 balloons each for their designs,
The number of balloons Rob has after the design = (x - 8)
The number of balloons Lorretta has after the design = (40 - x - 8) = (32 - x)
The product of the balloons left isn't more than 44
(x - 8) × (32 - x) ≤ 44
32x - x² - 256 + 8x ≤ 44
44 ≥ -x² + 32x + 8x - 256
44 ≥ -x² + 40x - 256
44 + x² - 40x + 256 ≥ 0
x² - 40x + 300 ≥ 0
To solve the second part of the question, we just solve the expression obtained in the first part.
x² - 40x + 300 ≥ 0
Simplifying the left hand side
(x - 30)(x - 10) ≥ 0
The solutions of the inequality is
x ≤ 10 or x ≥ 30
Hence, if Rob had more balloons than Loretta, the feasible solution for x would be x ≥ 30 and the least number of balloons that Rob van have before using any = 30.
Hope this Helps!!!
Answer:
D & A
Step-by-step explanation:
Answer:
1) Option D is the right answer.
x2 - 40x + 300 0 is the option that reflects the number of balloons in their bags.
2) Option A is the right answer.
If Rob had more balloons than Loretta, the minimum number of balloons Rob could have before using any would be 30.
Step-by-step instructions:
Question in its entirety, Rob and Loretta were each handed a bag of balloons to decorate for a party. Between the two bags, there were 40 balloons. Loretta used 8 balloons from her bag, while Rob used 8 from his.The total number of balloons left in each bag cannot exceed 44. Let x be the number of balloons in Rob's bag before he utilized any of them. Which option best depicts how many balloons they still have in their bags? x2 - 40x - 300 = 0 A. x2 - 40x - 300 0 x2 - 40x - 300 0 x2 - 40x - 300 0 x2 C. 40x - x2 = 300 x2 - 40x + 300 0 x2 - 40x + 300 0 x2 - 40x + 300 0 x2 What is the smallest number of balloons that Rob has if he started with more than Loretta? What is the smallest number of balloons Rob could have had before using any if he had more than Loretta at the start? Solution A.30 B.20 C.10 If x is the number of balloons Rob had at the start, Loretta's number of balloons at the start would be = (40 - x) Then they each use eight balloons to create their creations. After the design, the number of balloons Rob possesses Equals (x - 8) Then there was (40 - x - 8) = the amount of balloons Lorretta possesses after the design (32 - x) The product of the remaining balloons is just 44. (x - 8) (32 - x) 44 x x x x x x x x x x x 32x - x2 - 256 + 8x 44 44 -x2 + 32x + 8x - 256 44 -x2 + 32x + 8x - 256 44 -x2 + 40x - 256 x2 - 40x + 256 0 x2 - 40x + 300 0 44 + x2 - 40x + 256 0 We just solve the equation acquired in the first half of the question to solve the second portion of the question. x2 - 40x + 300 ======================== Simplifying...
(x - 30)(x - 10) 0 (x - 30)(x - 10) 0 (x - 30)(x - 10) 0 (x - 30)(x - The inequality's solutions are x 10 or x 30. As a result, if Rob has more balloons than Loretta, the viable solution for x is x 30, and the smallest number of balloons Rob may have before using any is 30. I hope this information is useful!!! ⭐️
