Part A: The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
Part B: the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
inequality 1 -2 <4 (-2) - 2
-2 <-10 (false)
inequality two -2> = - (5/2) (- 2) - 2
-2> = 3 (false).
An equation that models the proportional relationship between t and s.
t = 12.5s
<h3>What is proportional relationship?</h3>
Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality."
<h3>According to the given information :</h3>
1) Ticket for an art museum costs $12.50
2) In other words, the price will increase by $12.50 for each ticket purchased (or tickets).
In other words, the total expense is always 12.5 times the quantity of tickets sold.
3) This indicates that we can create this ---> t = 12.5s.
An equation that models the proportional relationship between t and s.
t = 12.5s
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Answer:
Step-by-step explanation:
5) -7 (-15w + 21) + 3(18 - 27w)
Step 2: 105w - 81w - 147 + 54
6)
step 3: 24w - 93
Answer:
This is true.
Step-by-step explanation:
Step 1: see that √27 is the same as √3*3*3 and thus 3√3
Step 2: remove parenthesis so that 2(1-3√3) becomes 2 - 6√3
Step 3: observe that the equation now becomes 6√3 + 2 - 6√3 = 2
if you simplify any further, you are left with 0=0, which is true.
Comment if there is any step that requires more details...
Answer:
A: (-9,-3)(-2,-4)(-5,-8)
B: (-5,2)(-1,-3)(3,2)
C: (4,-7)(-1,-3)(4,1)
D: (-1,-11)(-2,-4)(-6,-7)
Step-by-step explanation:
So of the transformations, translations are pretty much the easiest. x-1 just means move all coordinates left 1 and y-3 means move all coordinates down 3. So for the first one the x coordinate gets 1 subtracted from it and the y value gets 3 subtracted from it.
(-8,0) => (-8-1, 0-3) = (-9,-3)
I do recommend double checking though, for practice and in case I flubbed a calculation.
