My father taught me a method that I call, 'throwing some thing over the wall'. There is a sample equation for the first picture that shows you how it works. It's a great way to help isolate the variable and I hope that it works for you. The second picture contains the answers I got through the use of this method. I'm sorry for the messy handwriting; I was on a bus.
The function g(x) is created by applying an <em>horizontal</em> translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)
<h3>How to determine the characteristics of rigid transformations by comparing two functions</h3>
In this problem we have two functions related to each other because of the existence of <em>rigid</em> transformations. <em>Rigid</em> transformations are transformations applied to <em>geometric</em> loci such that <em>Euclidean</em> distance is conserved at every point of the <em>geometric</em> locus.
Let be f(x) = - 2 · cos (x - 1) + 3, then we use the concept of <em>horizontal</em> translation 4 units in the + x direction:
f'(x) = - 2 · cos (x - 1 + 4) + 3
f'(x) = - 2 · cos (x + 3) + 3 (1)
Now we apply a reflection over the x-axis:
g(x) = - [- 2 · cos (x + 3) + 3]
g(x) = 2 · cos (x + 3) - 3
Therefore, the function g(x) is created by applying an <em>horizontal</em> translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)
To learn more on rigid transformations: brainly.com/question/1761538
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Let, the height of the building be x ft.
Given the building casts 35ft shadow.
The height of the flagpole given which is 22ft and casts a shadow of 10ft.
Now to find the height of the building we have to equate the ratio of height and shadow of the building and the flagpole.
So we can write,
x/35 = 22/10
To find x, we have to get rid of 35 from the left side and have to move it to right side. As 35 is divided there, we will multiply 35 to both sides.
(x/35)× 35 = (22/10)×35
x = (22×35)/10
x = 770/10
x = 77
So, the height of the building is 77 ft which is the required answer here.
Answer:
Answer and explanation with steps are in the following attachments
Step-by-step explanation: