Answer: The ordered pair is (2,3)
Step-by-step explanation:
To solve this problem, we can use substitution. With substitution, we substitute the y in each problem with the equations. In this case, x + 1 can substitute the y in y = -x + 5. Here is what the problem looks like now:
x + 1 = -x + 5
The reason we used substitution is because we assume that these linear equations are equal. We must prove it, though. We can use algebra.
Move the variables to one side and the numerical values to another:
x + x = 5 - 1.
Simplify.
2x = 4
Simplify.
x = 2.
Now, we got our x value, we can substitute it into our problem:
y = 2 + 1
y + -2 + 5
2 + 1 = - 2 + 5 = 3
Our x is 2, and our y is 3. The ordered pair that is a solution is (2,3).
Answer:
Pattern B gets larger faster.
Step-by-step explanation:
Pattern A: 1, 4, 7, 10, 13
Pattern B: 1, 5, 9, 13, 17
The terms of pattern B are larger than those of Pattern A by 1 less than the number of the term. (Term 5 of Pattern B is 4 more than term 5 of Pattern A, for example.)
Answer:
huh?
Step-by-step explanation:
<h3>
Answers: x = -17 and x = 64</h3>
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Explanation
Consider three scenarios:
- A) The value of x is the smallest of the set (aka the min)
- B) The value of x is the largest of the set (aka the max)
- C) The value of x is neither the min, nor the max. So 8 < x < 39.
These scenarios cover all the possible cases of what x could be. It's either the min, the max, or somewhere in between the min and max.
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We'll start with scenario A.
If x is the min, then that must mean 39 is the max as it's the largest of the set {18, 36, 16, 39, 27, 8, 34}
The range is 56, so,
range = max - min
56 = 39 - x
56+x= 39
x = 39-56
x = -17 which is one possible answer
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If instead we go with scenario B, then x is the max and 8 is the min
range = max - min
56 = x - 8
56+8 = x
64 = x
x = 64 is the other possible answer
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Lastly, let's consider scenario C. If x is not the min or the max, then it's somewhere between the min 8 and max 39. in short, 8 < x < 39.
Note that range = max - min = 39-8 = 31 which is not the range of 56 that we want. So there's no way scenario C can be possible here.
