I graphed the equation using an online graphing calculator and got the vertex of (-5, 49) therefore y = 49
2x+3y=12
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She needs 45 more sticks of butter. This is because she already has two cakes, and 47-2=45. She can bake one more cake with each stick of butter, which means the answer is indeed 45.
Total time taken by Jon was 4.5 hours
Time taken by Sam was 5.5 hours
This implies that John traveled faster than Sam because he took shorter time to get to the camp, thus we conclude that from the given information, the correct answer is:
Sam and Jon traveled at the same rate of speed to camp.
When a function is shifted to the right by 1 unit it is moved towards the negative side so we would be adding -1 to the value of x. The function f(x) would be f(x-1). To determine the resulting function, we substitute to the parent function (x-1) to x. We do as follows:
<span>f (x) = x^3 + 2x^2 − 3x − 5
</span>f (x-1) = (x-1)^3 + 2(x-1)^2 − 3(x-1) − 5
f (x-1) = x^3 - 3x^2 + 3x - 1 + 2(x^2 - 2x + 1) - 3x + 3 - 5
f (x-1) = x^3 - 3x^2 + 2x^2 + 3x - 4x - 3x - 1 + 2 + 3 - 5
f (x-1) = <span>x^3 - x^2 - 4x - 1
Therefore, the correct answer is the last option.</span>
