Using translation concepts, it is found that the transformations needed to form g(x) = 3(x + 2)² - 1 from f(x) = x² are given as follows:
- The graph of g(x) is narrower than f(x), and is shifted to left 2 units and down 1 unit.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the change is as follows:
f(x) = x² -> g(x) = 3(x + 2)² - 1.
f(x) is multiplied by 3 to form g(x), hence g(x) has a narrower graph. Since x -> x + 2, it was shifted left 2 units, and since y -> y - 1, it was shifted down 1 unit.
More can be learned about translation concepts at brainly.com/question/4521517
#SPJ1
Answer:
x = 9
Step-by-step explanation:
A line segment parallel to a side of a triangle and intersecting the other 2 sides divides the 2 sides in proportion, that is
= 
= 
( cross- multiply )
8(3x - 20) = 56
24x - 160 = 56 ( add 160 to both sides )
24x = 216 ( divide both sides by 24 )
x = 9
Answer:
<h2>
</h2>
Step-by-step explanation:
<em><u>Given</u></em><em><u> </u></em><em><u> </u></em>
<em><u>Since</u></em><em><u>,</u></em>
<em><u>Hence</u></em><em><u>,</u></em>
Answer:
56.3 kilometers per hour
Step-by-step explanation:
We know D = RT
where
D is distance
R is rate (speed)
T is time
Let's Bill's rate be "x". Thus using equation we can write:
D = xt
We know Eugene travelled 21.1 faster than Bill, so Eugene's rate is 21.1 + x. So we can write:
D = (21.1 + x)t
D = 21.1t + xt
Now, putting t = 1 in both since after 1 hour given, we have:
D = x(1)
D = x
and
D = 21.1(1) + x(1)
D = 21.1 + x
We know the sum of both the distance is 133.7, so we can write:
x + 21.1 + x = 133.7
Solving for x:
2x = 133.7 - 21.1
2x = 112.6
x = 112.6 / 2
x = 56.3 km/hr
This is Bill's rate: 56.3 kilometers per hour
