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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Answer: 30 feet per second
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x = diameter, y = speed of water
y varies inversely with respect to x, so, y = k/x for some constant k
If x = 0.6 and y = 5 pair up, then y = k/x turns into 5 = k/0.6 which solves to k = 3 when you multiply both sides by 0.6
So the equation y = k/x turns into y = 3/x
Now plug in the diameter x = 0.1 to find the speed to be...
y = 3/x
y = 3/0.1
y = 30 feet per second
Answer:
72%
Step-by-step explanation:
you can divide part of a whole by the whole to get a decimal
this decimal is the percentage when you move the decimal 2 places to the right
32 - 9 = 23 men
23/32 = .72 (rounded)
.72 = 72%
Answer:- The smaller integer is -5.
Explanation:-
Let the first consecutive integer be x and the second consecutive integer be x+1.
According to the given question:-
x+6(x+1)= -29
⇒x+6x+6= -29 [distributive law]
⇒x+6x= -29-6 [subtract 6 on the both sides]
⇒7x= -35 [combining like terms ]
⇒x= -5 [dividing 7 on both sides]
Thus the smaller integer =x= -5
larger integer =x+1= -5+1= -4
