<h3>3
Answers: Choice D, Choice E, Choice F</h3>
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Explanation:
The inequality 6x - 10y ≥ 9 solves to y ≤ (3/5)x - 9/10 when you isolate y.
Graph the line y = (3/5)x - 9/10 and make this a solid line. The boundary line is solid due to the "or equal to" as part of the inequality sign. We shade below the boundary line because of the "less than" after we isolated for y.
Now graph all of the points given as I've done so in the diagram below. The points in the blue shaded region, or on the boundary line, are part of the solution set. Those points are D, E and F.
We can verify this algebraically. For instance, if we weren't sure point E was a solution or not, we would plug the coordinates into the inequality to get...
6x - 10y ≥ 9
6(5) - 10(2) ≥ 9 .... plug in (x,y) = (5,2)
30 - 20 ≥ 9
10 ≥ 9 ... this is a true statement
Since we end up with a true statement, this verifies point E is one of the solutions. I'll let you check points D and F.
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I'll show an example of something that doesn't work. Let's pick on point A.
We'll plug in (x,y) = (-1,1)
6x - 10y ≥ 9
6(-1) - 10(1) ≥ 9
-6 - 10 ≥ 9
-16 ≥ 9
The last inequality is false because -16 is smaller than 9. So this shows point A is not a solution. Choices B and C are non-solutions for similar reasons.
Answer:
y = 1/2x
Step-by-step explanation:
x - 2y = -4
x = -4 + 2y
x + 4 = 2y
2y = x + 4
y = 1/2x + 2
y = 1/2x
Answer:
23 pounds of the Gualtemala Antigua Blend and 37 pounds of the Tanzanian Blend
Step-by-step explanation:
you need to make a system of equations to solve this.
First lets make x be the pounds of Gualtemala Antigua coffee blend and y the pounds of Tanzanian coffee blend
we know we need 60 pounds total so first equation is
x+y=60
Next we will make an equation based on the money information
10.30x + 13.80y = 12.46(60)
10.30x + 13.80y = 747.60
So our system of equations is
x + y = 60
10.30x + 13.80y = 747.60
I will solve this by using substitution. first rewrite x+y=60 to y=60-x
now i can substitute that into the other equation for y and solve for x
10.30x + 13.80(60-x) = 747.60
10.30x + 828 -13.80x = 747.60
-3.5x + 828 = 747.60
-3.5x = -80.4
x = 23 (rounded from 22.9714 since they requested that)
now I can use this solution to solve for y by plugging into one of the original equations
x + y =60
23 + y =60
y = 37
Finally we can say that they must mix 23 pounds of the Gualtemala Antigua Blend and 37 pounds of the Tanzanian Blend.
Answer:
Yes
Step-by-step explanation:
A for loop basically relies on repeating the same code for a pre-set number of times. During which you can make any code repeat inside of it, including indexing through a type of list. Many times a for-loop will use the indexes in a list to calculate the number of times that the loop has to repeat. This is usually done in order to search or apply changes in an array of other types of data structures that have countless values stored in it.
