Step-by-step explanation:
recall for any function f(x)
Vertical translations by "a" units are given simply by
f(x) + a,
where positive values of a translates the graph in the positive y direction (i.e up) and negative values of a translates the graph in the negative y direction (i.e down)
Horizontal translations by "b" units are given by
f(x-b),
where negative values of a translates the graph in the negative x direction (i.e left) and postive values of a translates the graph in the postive x direction (i.e right)
if we combine the two above, we get the expression
g(x) = f(x-b) + a
In our case, we see that to get from the blue graph to the red graph, we need to translate 3 units in the positive x-direction (i.e b = 3) and 4 units in the negative y-direction (i.e a = -4)
Substituting b = 3, a = -4 and that f(x) = |x|,
we get
g(x) = |x-(3)| - 4
g(x) = |(x-3)| - 4
Answer: Each catalog weighs 0.87 pounds
Step-by-step explanation:
Given: Number of identical catalogs = 8
Weight of package with the catalogs= 6.96 pounds
Using division operator,
Weight of each catalog = (Weight of package ) ÷ (Number of identical catalogs)
i.e. Weight of each catalog =(6.96)÷8 pounds
⇒ Weight of each catalog = 0.87 pounds
Hence, Each catalog weighs 0.87 pounds
Answer: The scale is 5cm/m (5 cm in the drawing are equivalent to 1 meter on the actual pit)
Step-by-step explanation:
When we have an original measure M, and we redraw it with a new scale, where the new measure is m, the scale used is equal to:
scale = m/M.
In this case, we know that:
The pit is 3m, by 5m
and the drawing to scale is 15cm by 25cm
(15cm is the rescaled version of the 3m side, and 25cm is the rescaled version of the 5m side)
Using the equation above, we can find that the scale is:
Scale = 15cm/3m = 5cm/m
and, if we use the other side, we get:
Scale = 25cm/5m = 5cm/m
Both calculations give the same scale, as expected.
Then the scale is 5cm/m, which means that 5 centimeters in the drawing are equivalent to one meter in the real pit.
23, 24, 25
23+24+27 equals 72
