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2 years ago

If 2x+9<32 then x could be

Mathematics

2 answers:

alina1380 [7]2 years ago

8 0

Answer:

x < 11 1/2

Step-by-step explanation:

2x+9<32

Subtract 9 from each side

2x+9-9 < 32-9

2x<23

Divide by 2

2x/2 <23/2

x < 11 1/2

X is any number less than 11 1/2

Y_Kistochka [10]2 years ago

3 0

Answer:

x < 11.5

Step-by-step explanation:

2x + 9 < 32

(2x + 9) - 9 < 32 - 9

2x < 23

2x/2 < 23/2

x < 11.5

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Find the volume of the following solid figure. Use = 3.14. V = 4/3r3. A sphere has a radius of 3.5 inches. Volume (to the neares

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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. Yo

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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-------> $4x+y \leq 48$

3. Write the inequality that models the number of granola bars you need to buy.

You need at least 10 granola bars

$y\geq 10$

4. Describe in words what each of your inequalities means

inequality 1

$4x+y \leq 48$

the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars

inequality 2

$y\geq 10$

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

$4x+y \leq 48$

$4*4+20\leq 48\\ 36\leq 48$ -------> is ok

substitute the values of x and y in the inequality 2

$y\geq 10$

$20\geq 10$ --------> is ok

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

$4x+y \leq 48$

$4*10+30\leq 48\\ 70\leq 48$ -------> is not a viable solution

substitute the values of x and y in the inequality 2

$y\geq 10$

$30\geq 10$ --------> is ok

the point B is not a viable solution because does not satisfy the inequality 1

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