Answer: No
Explanation:<em> </em>Here, we want to decide if 5 is a solution
for the equation 47 = 6x.
We can do this by simply plugging in 5 for <em>x</em>. If the statement holds true when 5 is plugged in for <em>x</em>, then 5 is a solution.
Plugging in 5 for <em>x</em> we have 47 = 6 (5).
6 (5) is equal to 30 so we have 47 = 30.
Since 47 and 30 are not equal, the statement 47 = 30 is not true.
Since 47 ≠ 30, this is a false statement which means 5 is not a solution for the equation 47 = 6x.
Answer: Area of ΔABC is 2.25x the area of ΔDEF.
Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

with a as side of the triangle.
Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:
a₁ = 1.2a
Then, its area is


Triangle DEF is 20% smaller than the original, which means its side is:
a₂ = 0.8a
So, area is


Now, comparing areas:

2.25
<u>The area of ΔABC is </u><u>2.25x</u><u> greater than the area of ΔDEF.</u>
For question 6, recall that a sinusoidal function is of the form
A*sin(ω*t + φ)
where A is the amplitude, ω the angular frequency (in units of radians/second), and φ the phase (in radians). The amplitude is the magnitude of the peaks and troughs, the angular frequency inversely proportional to the period (ω = 2*π/T - the 2*π being a normalizing factor), and the phase a value between 0 and 2*π that "shifts" the graph of the function accordingly.
For question 7, you are being asked to find the composite function obtained by applying g to f, which would be
. The domain would be the values for which this function is defined, which, assuming it to be a subset of the real numbers, would be the interval (-∞, 3] (as the square root of a negative number is an imaginary number.
Answer: 112.32
Step-by-step explanation: