9514 1404 393
Answer:
- h = -2; k = 0; vertex = (-2, 0)
- h = 3; k = 0; vertex = (3, 0)
Step-by-step explanation:
Translation of a function to the right h units and up k units is accomplished by ...
g(x) = f(x -h) +k
Here, we have f(x) = |x|, so the translation will be ...
g(x) = |x -h| +k
or ...
y = |x -h| +k
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The function y = |x| has its vertex at (0, 0), so translation by (h, k) moves the vertex to (0 +h, 0 +k) = (h, k).
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You will notice that the given equations you are given have no "+k" added on, so k = 0 in both cases. The value of h is the opposite of the constant between the absolute value bars.
1. y = |x +2|
h = -2, k = 0
vertex: (-2, 0)
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2. y = |x -3|
h = 3, k = 0
vertex: (3, 0)
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<em>Additional comment</em>
This is all about <em>matching patterns</em>. You need to be able to identify the variable (x) and what has been added or subtracted to/from it. You need to be able to identify the "parent" function (what you have with nothing added or subtracted), and determine if something is added or subtracted to to/from that. Here, the parent function is |x|. Nothing has been added to the function (outside the absolute value bars), but something has been added to x (inside the absolute value bars).
Answer:
<h2>132.25π m²</h2>
Step-by-step explanation:
The circumference of a circle is 23π
On the other hand, The circumference of a circle = 2×π×r ; where r is the radius.
then
by equating the last two expressions we get: 23π = 2πr then r = 23/2
then
the area = π × r² = (23/2)²×π = (132.25)×π
Ok so student in cleveland walks 2.5 miles away from cleveland every hour from 8
so the distance, x is x=2.5t
the riding one rides 4 hours later, so t-4
11 mph
y=11(t-4)
A. x=2.5t
y=11(t-4)
when do they meet is when the distance when they are equal or when x=y
2.5t=x=y=11(t-4)
solve for t
2.5t=11(t-4)
2.5t=11t-44
-8.5t=-44
divide both sides by -8.5
t=5.17647
answer is 5.18 hours
A.
x=2.5t
y=11(t-4)
B. 5.18 hours
