F(x) = 0.54 g(x) = f(x + k) for k=-2
1 answer:
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The length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.
<h3>What is the scale factor?</h3>In mathematics, a scale factor is the proportion of related dimensions of an object to a description of that object.
Given that:-
- The outside edges of the walkway form a rectangle whose length and width are proportional to the sides of the garden, increased by a scale factor of 3. the sides of the garden are (2x+4) and (3x+2)
The length and width of the outside edge will be:-
The sides are Dilated by factor 3 so the edges of the rectangle will be calculated as;-
Length = 3 ( 2x+4 ) = 6x + 12
Width = 3 ( 3x+2 ) = 9x + 6
Therefore the length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.
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So this is trig, and when it comes to right (90°) triangles, it's imperative that you know:
SOH-CAH-TOA
Sine (x) = Opposite/Hypotenuse
Cosine (x) = Adjacent/Hypotenuse
Tangent (x) = Opposite/Adjacent
*hypotenuse is always the largest side, and the one opposite the 90° angle in right triangles
therefore we'll use SOH, because the opposite of x (O) and the hypotenuse (H) are given:
Sine (x) = Opposite/Hypotenuse
Sine (x) = 32/58 = 16/29 = 0.552
Sine (x) = 0.552
now we use something called arc-sine, or
it's basically a fancy function of most advanced calculators, so we'll plug it in as:
x = 33.49° --> answer B) is correct
SOH-CAH-TOA
Sine (x) = Opposite/Hypotenuse
Cosine (x) = Adjacent/Hypotenuse
Tangent (x) = Opposite/Adjacent
*hypotenuse is always the largest side, and the one opposite the 90° angle in right triangles
therefore we'll use SOH, because the opposite of x (O) and the hypotenuse (H) are given:
Sine (x) = Opposite/Hypotenuse
Sine (x) = 32/58 = 16/29 = 0.552
Sine (x) = 0.552
now we use something called arc-sine, or
it's basically a fancy function of most advanced calculators, so we'll plug it in as:
x = 33.49° --> answer B) is correct