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sofia3226
15.07.2019 •
Mathematics
You have a budget of $48. you want to buy fruit and granola bars. fruit costs $4 per pound, and the granola bars are $1 each. you need at least 10 granola bars. what combinations of fruit and granola bars can you buy? 1. define the variables you will use in your model. (2 points) 2. write an inequality representing the total cost of your purchase. (3 points) a. each pound of fruit costs $4. write an expression that shows the total cost of the fruit. use the variable you identified in question 1. b. each granola bar costs $1. write an expression that shows the total cost of the granola bars. use the variable you identified in question 1. c. combine the expressions from parts a and b to write an expression for the total cost. then use this expression to write an inequality that compares the total cost with the amount you have to spend. 3. write the inequality that models the number of granola bars you need to buy. (1 point) 4. describe in words what each of your inequalities means. (2 points) inequality 1:inequality 2:graph the system of inequalities 5. graph your system of inequalities. shade the half plane that represents the solution for each inequality, and then identify the area that represents the solution to the system of inequalities. (5 points: 1 point for each boundary line, 1 point for each correctly shaded half plane, 1 point for identifying the solution) interpreting the graph 6. identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution. identify the number of granola bars and pounds of fruit represented by each point, and explain why the point is or is not viable. (4 points: 1 for each point and 1 for each explanation)
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Ответ:
1)Define the variables you will use in your model.
Let
x------->total pounds of the fruit
y-------> the total number of granola bars
TC----> total cost
Tf------> total cost of the fruit
Tg----> total cost of the granola bars
2) Write an inequality representing the total cost of your purchase. (3 points)
a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1
Tf=4*x
b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.
Tg=1*y--------> Tg=y
c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.
TC=Tf+Tg
TC=4*x+y
inequality------->![4x+y \leq 48](/tpl/images/0091/0210/11ec6.png)
3. Write the inequality that models the number of granola bars you need to buy.
You need at least 10 granola bars
so
4. Describe in words what each of your inequalities means
inequality 1
the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars
inequality 2
5. Graph your system of inequalities.
using a graph tool
see the attached figure
6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution.
Let
A-------> one point on the graph that represents a viable solution
B-------> one point on the graph that does not represent a viable solution
A(4,20)
x=4-------> total pounds of the fruit
y=20------> the total number of granola bars
check point A
substitute the values of x and y in the inequality 1
substitute the values of x and y in the inequality 2
the point A represents a viable solution, because satisfies both inequalities
B(10,30)
x=10-------> total pounds of the fruit
y=30------> the total number of granola bars
check point B
substitute the values of x and y in the inequality 1
substitute the values of x and y in the inequality 2
the point B is not a viable solution because does not satisfy the inequality 1
Ответ:
a = 2, b = 0 , x =![\frac{1}{2}](/tpl/images/1404/2026/9cdae.png)
Step-by-step explanation:
Given that x = 0 and x = 2 are zeros of p(x) , then
p(0) = 0 and p(2) = 0
p(0) = 2(0)³ - 5(0)² + a(0) + b = 0 , that is
0 - 0+ 0 + b = 0, then b = 0
p(2) = 2(2)³ - 5(2)² + 2a + b = 0 , that is
16 - 20 + 2a + 0 = 0
- 4 + 2a = 0 ( add 4 to both sides )
2a = 4 ( divide both sides by 2 )
a = 2
Then
p(x) = 2x³ - 5x² + 2x ← factor out x from each term
= x(2x² - 5x + 2)
= x(2x - 1)(x - 2)
To find zeros equate p(x) to zero
x(2x - 1)(x - 2) = 0
Equate each factor to zero and solve for x
x = 0
x - 2 = 0 ⇒ x = 2
These are the 2 zeros already known (given)
2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
← third zero of p(x)