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:
208
Step-by-step explanation:
{ed}-{3cb}+{4ba}-{2ea} = {(-15)*(-6)} - {3*5*(-2)} + {4*(-2)*4} - {2*(-15)*4}
={90} - {15*(-2)} + {16*(-2)} - {8*(-15)}
= {90} - {-30} + {-32} - {-120}
= 90 (--)30 (+-) 32 (--) 120
= 90 + 30 - 32 + 120
= 120 - 32 + 120
= 88 + 120
= 208
The decimal representation of any number is a linear combination of powers of 10. In other words, given a number like 123.456, we can expand it as
for any 
, so the above is the same as
Similarly, we can write
Now it's a question of reducing the fraction as much as possible. We have 
so
$15 more, than twice Friday's earnings
d is how much he earned on Friday
s is how much he earned on Saturday
2d + 15 = s
Answer:
The length of the line segment AC is equal to 14
Step-by-step explanation:
The triangle above is an isosceles triangle, In an Isosceles triangle the two angles; B and C are the same, hence the two sides; AB and AC are also the same.
AB=2x and AC= 3x - 7
AB = AC
which implies;
2x = 3x - 7
subtract 3x from both-side of the equation
2x - 3x = 3x -3x -7
-x = -7
Multiply through by -1
x = 7
But we were ask to find the the length of the line segment AC
AC = 3x - 7
substituting x = 7 into the above equation will yield;
AC = 3(7) - 7 = 21 - 7 =14
Therefore the length of the line segment AC is equal to 14
