The function ƒ(x) = x is vertically translated 1 unit up and then reflected across the y-axis. What's the new function g(x)?
1 answer:
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Answer:
- 108 cm^2
- 211.2 cm^2
- 308.8 mm^2
- 560 yd^2
Step-by-step explanation:
In each case, you can use the given formula to find the surface area. The area of the triangular base (B) is ...
A = 1/2bh
where b is the base of the triangle, and h is the height of the triangle perpendicular to that base.
You will notice that B is multiplied by 2 in the area formula, because there is a triangular base at either end of the prism. That means we can save some work by not multiplying by 1/2, and then by 2.
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For figures 1, 3, 4, the triangle is a right triangle, so the base and height make up two of the three sides of it. The perimeter is finished by adding the length of the hypotenuse. That sum is then multiplied by the "height" of the prism (distance between bases) to find the lateral area as part of the area formula (Ph).
In figure 3, the triangle is equilateral, so the perimeter is not the sum of the base and height and a third side. In the attached spreadsheet, we have used a value "rest of perimeter" to make the sum be the right value for use in computing the value of Ph. For figure 3, that is 6+6-5.2=6.8. Then the sum 6 +5.2 +6.8 is 18, the proper perimeter for that figure.
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The idea here is to let a spreadsheet do the tedious work of applying the same formula to different sets of numbers. The areas are ...
- 108 cm^2
- 211.2 cm^2
- 308.8 mm^2
- 560 yd^2
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By way of example, we can "show work" for problem 1:
1. S = Ph +2B
S = (4 +3 +5)(8) +2(1/2)(4)(3) = 12(8) +12 = 96 +12 = 108 . . . cm^2
Answer:
Option b
or
Step-by-step explanation:
The absolute value is a function that transforms any value x into a positive number.
Therefore, for the function x> 0 for all real numbers.
Then the equation:
has two cases
if
(i)
if
(ii)
We solve the case (i)
We solve the case (ii)
Then the solution is:
or
Answer:
B.) 2 3/4 + (-4 1/4) = -1 2/4
Step-by-step explanation:
blue line: forward with positive +
red line: backward with negative -
so the number line follows: + -
= -1 2/4