We solve for the area of the original triangle and solution is shown below:
Original triangle area = LW = 5*10 = 20 squared units
If we extend this x on one side that resulted to L-shaped, we have the new area such as shown below:
New area = (L+X) (W)
126 = (5+x) * 10
126/10 = 5+x
12.6 - 5 = x
7.6 =x
I. The equation that could be used to solve for x is below:
126 = (5+x)*w
II. We arrived on this because of the statement that "x is added to one side that resulted to L-shaped rectangle, therefore it is added on 5 ft side"
III. The value of x is equal to 7.6 ft.
The length of a segment, given the extremities, is:
√[(x₂ - x₁)² + (y₂ - y₁)²]
Therefore:
RS = √[(3-1)² + (1-3)²] = √(4+4) = √8
RT = √[(5-1)² + (2-3)²] = √(16+1) = √17
ST = √[(5-3)² + (2-1)²] = √(4+1) = √5
Since the lengths are all different, the triangle is scalene.
Answer: Choice B
a_n = 10(1/2)^(n-2) is the nth term
average rate of change = -35/3
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Explanation:
Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.
If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.
Use the slope formula to find the slope of the line through (0,40) and (3,5)
m = (y2-y1)/(x2-x1)
m = (5-40)/(3-0)
m = -35/3
The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3
The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.
In other words, 20(1/2)^(n-1) is equivalent to 10(1/2)^(n-2) when n starts at n = 1.
We are told to solve for n given the equation 3(n + 4) = -6 + 15n. We can solve for n by first using the distributive property, which gives us 3n + 12 = -6 + 15n. Now, subtract 15n from both sides, giving us -12n + 12 = -6. Next, subtract 12 from both sides to get -12n = -18. Now, divide both sides by -12 to get n = 18/12, or 3/2 when simplified. Therefore, the value of n in the equation 3(n + 4) = -6 + 15n is 3/2. Hope this helped!
Answer:
The medicine treats swelling
Step-by-step explanation:
"The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of swelling. What can Andria conclude from this experiment?"
If she does not give placebo, which she should, then we can only conclude that the medication might be effective. Might, because the thought of the medicine fixing swelling might actually be what helps them.
This takes us to the next topic- placebo experiments.
Most good experiments, to elaborate, are "double blind," one group receives a placebo, and another the medication, and neither know which.
In this case, assuming that the placebo was ineffective, we can conclude that the medicine is effective in treating swelling.
