Takumi and Kaliska manipulated the rational expression \dfrac{-9y^2 - 3y}{-6y^2 - 6y}
−6y
2
−6y
−9y
2
−3y

start fraction, minus, 9, y, squared, minus, 3, y, divided by, minus, 6, y, squared, minus, 6, y, end fraction. Their responses are shown below.
Takumi Kaliska
\dfrac{-3y(3y+1)}{-6y(y+1)}
−6y(y+1)
−3y(3y+1)

start fraction, minus, 3, y, left parenthesis, 3, y, plus, 1, right parenthesis, divided by, minus, 6, y, left parenthesis, y, plus, 1, right parenthesis, end fraction \dfrac{3y+1}{2y+2}
2y+2
3y+1

start fraction, 3, y, plus, 1, divided by, 2, y, plus, 2, end fraction

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

let's start from the lower value, we have:

(we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

so, the range of wavelength of infrared radiation is:

it is a secret for it not to be compromised sorry

step-by-step explanation: