sample response: The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.
Where y represents the total number of coins and 0.5x represents the number of 5 cent coins and x represents the number of 1 cent coins...
y = 0.5x + x
= 1.5x
1/2x + 2x = 2.5x
If he exchanged 1 cent coins for 2 cent coins, he would have half the same number of 2 cent coins as he had for 5 cent coins. Instead of 2x, you would have "x" and...
y = 0.5x + 0.5x = x
y = 1x
Divide slopes..
1 / 1.5 = 2/3 or 0.67.
The answer is 2/3 so Choice B is the answer.
Suppose the equation went like this
-12 -24= x
You would essentially just add them together and put a negative sign in front of it so the answer would be -36. But once you start dealing with parentheses and brackets it get more complicated than that. Comment if you have any more questions :)
Answer:
slope = 3/2, y-interecept = -.5
Step-by-step explanation:
To find a perpendicular line, just take the current slope (-2/3) and find the opposite reciprocal of 3/2. Then, you can just slowly find your way to the y-intercept through subtraction (or division if you'd rather, both are much quicker than the way most textbooks would tell you - remember, in math, there is no one set way!)
3x + 6 = 21...subtract 6 from both sides
3x + 6 - 6 = 21 - 6
3x = 15...divide both sides by 3
x = 15/3
x = 5....answer is D