What is an equation for the linear function whose graph contains the points (2, 5) and (3, 0)?
1 answer:
Answer:
y = -5x + 15
Step-by-step explanation:
We'll look for a linear function of the form y = mx + b, where m is the slope and b is the y-intercept.
We can determine a slope from the two given points by calculating a Rise/Run. Starting at (2,5) and going to (3,0):
Rise = (0 - 5) = -5
Run = (3-2) = 1
Rise/Run = Slope, m) = -(5/1) or -5
Now we have y = -5x + b
To find b, enter either of the two points and solve for b. I'll use (3,0), because I know my zero multiplication and addition tables by heart.
y = -5x + b
0 = -5(3) + b
b = 15
The equation becomes <u>y = -5x + 15</u>
See attachment.
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<h3>Answer: 6</h3>
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Explanation:
Rule: If a set has n elements in it, then it will have 2^n subsets.
For example, there are n = 3 elements in the set {a,b,c}. This means there are 2^n = 2^3 = 8 subsets. The eight subsets are listed below.
- {a,b,c} .... any set is a subset of itself
- {a,b}
- {a,c}
- {b,c}
- {a}
- {b}
- {c}
- { } ..... the empty set
Subsets 2 through 4 are subsets with exactly 2 elements. Subsets 5 through 7 are singletons (aka sets with 1 element). The last subset is the empty set which is a subset of any set. You could use the special symbol to indicate the empty set.
For more information, check out concepts relating to the power set.
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The problem is asking what value of n will make 2^n = 64 true.
You could guess-and-check your way to see that 2^n = 64 has the solution n = 6.
Another approach is to follow these steps.
Which is fairly trivial.
Or you can use logarithms to solve for the exponent.
Due to rounding error, we don't land exactly on 6 even though we should.