Answer:
To create function h, function f was translated 2 units to the right, translated 4 units down and reflected across the y-axis.
Step-by-step explanation:
Since f(x) = x^3 is transformed to h(x) = -(x+2)^3-4, by
1. Adding 2 to x in x³ to give f'(x) = f(x + 2) = (x + 2)³.
2. We now translate f(x + 2) down by subtracting 4 from f(x + 2) to give
f''(x) = f'(x) - 4 = f(x +2) - 4 = (x + 2)³ - 4.
3. We now reflect f'(x) across the y-axis by multiplying (x + 2)³ by -1 to get
h(x) = -(x + 2)³ - 4.
Answer:
7.2 m²
Step-by-step explanation:
Use the appropriate area formula, fill in the given values, and do the arithmetic.
A = (1/2)ab·sin(C)
where "a" and "b" represent triangle side lengths and C is the angle between them.
A = (1/2)(4 m)(8.5 m)sin(25°) ≈ 7.2 m²
Using the Empirical Rule, it is found that 49 farms in the sample have land and building values per acre between $1100 and $1700.
<h3>What does the Empirical Rule state?</h3>
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Considering the given mean and standard deviation, values between $1100 and $1700 are within 1 standard deviation of the mean, which is a percentage of 68%.
Hence, the number of farms out of 72 is:
0.68 x 72 = 49 farms.
More can be learned about the Empirical Rule at brainly.com/question/24537145
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The product is 1.786e+25
You multiply in the paranthesis on both and then you mulitpoy them together
Answer: D
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other
The slope of this line is -1/4, the reciprocal is just the flipped fraction which is -4/1 or 4. Since it is a negative reciprocal you multiply it by -1. 2 negatives multiplied equals a positive so the slope of the perpendicular line is 4
