Write an equivalent expression to present patricia total earnings this week 7h + 135 + 5h = ?h + ?
1 answer:
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Answer:
- turning point: (0, -1)
- domain, range: all real numbers
- x-intercept: (1/27, 0)
- y-intercept: (0, -1)
- transformations: vertical expansion by a factor of 3; translation down 1
Step-by-step explanation:
There are a couple of transformations that may be of interest:
g(x) = k·f(x) . . . . vertical scaling by a factor of k
g(x) = f(x) +k . . . vertical translation by k units (up)
g(x) = f(x -k) . . . horizontal translation by k units (right); <em>not used here</em>
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Unlike the square root function, which is undefined for negative values, the cube root function is defined for all real numbers. Its domain and range are all real numbers.
The turning point of a cube-root function is the origin. Here, that has been translated down 1 unit, so it is (0, -1). That is also the y-intercept.
The x-intercept is the value of x where g(x)=0:
0 = 3∛x -1
1 = 3∛x
1/3 = ∛x
(1/3)³ = x = 1/27
The x-intercept is (1/27, 0).
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<u>Transformations</u>
As we discussed above, the addition of -1 to the parent function causes it to be translated down 1 unit.
The multiplication of the parent function by 3 causes it to be vertically expanded by a factor of 3.
4.05 with (05) repeating if converted to a fraction or mixed number will be
.
As per the question statement, we are provided with a repeating decimal, 4.05 with (05) repeating.
We are required to convert the repeating decimal into a mixed number.
To solve this question, we need to know the formula to convert any repeating decimal number to a fraction which goes as:
Where, DN denoted the concerned Decimal Number,
(F = 10) if one repeating is number, 100 if two repeating numbers, 1000 if three repeating numbers and so on.
NRP denotes the Non-repeating part of decimal number.
And, D = 9 if one repeating number, 99 if two repeating numbers, 999 if three repeating numbers, and so on, similar to F.
Then, using our given data in the above formula, we get
4.05 with (05) repeating = .
- Repeating Decimal: A repeating decimal, also called as Recurring Decimal, is a decimal number that consists of digits repeating after a fixed interval after the decimal point.
To learn more about Repeating Decimal, click on the link below.
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Given:
In triangle WXY, .
To find:
The Cotangent of .
Solution:
In a right angle triangle,
It can be written as:
For triangle WXY,
Therefore, the Cotangent of is
.