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
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The distance from point (15,-21) to the line 5x + 2y = 4 is 27.5 units
Given the coordinate (15, -21) and the line 5x + 2y = 4
In order to get the point on the line 5x + 2y =4, we can a point on the line
Let x = 0
5(0) + 2y = 4
2y = 4
y = 2
The point (0, 2) is on the line.
Find the distance between the point (15, -21) and (0, 2) using the distance formula
Hence the distance from point (15,-21) to the line 5x + 2y = 4 is 27.5 units
Learn more here: brainly.com/question/22624745
Answer:
The width of the rectangle is 18 inches, and the length is 50 inches
Step-by-step explanation:
We can designate a variable, x, to represent the width of the rectangle. To represent the length and widths of the rectangle, we can say that the length is 3x-4 and the width is just x. We can then write an equation for the perimeter and solve:
2(3x-4) + 2x = 136
6x - 8 + 2x = 136
8x - 8 = 136
8x = 144
x = 18
To calculate the length
(3x - 4)
3(18) - 4 = 50 in
Answer:
Website 1: Y=1.5x+30
Website 2: Y=2x
Step-by-step explanation:
Website 1 has upfront cost of $30.
The cost of download will be $1.5 per download
Total cost will be 1.5X+30
Where in for Website 2, it will be multiplied by $2
so Y=2X
Answer:
See explanation
Step-by-step explanation:
Car A: Started at 0 and ended at 300, thus, car A travels 300 miles.
It travels 6 hours, so car A speed is 
mph.
Car B: Started at 100 and ended at 300, thus, car B travels 300-100=200 miles.
It travels 5 hours, so car B speed is 
mph.
Since 50>40, car A traveled faster than car B.
The graph for the car A is steeper than the graph for the car B.
