Which of the following operations could you perform on both sides of the given equation to solve it? check all that apply. 8x - 6 = 2x + 24
answer: 205 lbs
here are all the answers
f(x) = -3x > #6
f(x) = |x-1|+3 > #5
f(x) = √(x+3) > #3
1/2x² > #1
f(x) = (x+1)²-3 > #4
recall for transformations:adding a number outside the function moves it upsubtracting a number outside the function moves it downadding inside the function moves it to the leftsubtracting inside the function moves it to the rightmultiplying to the function by a number less than 1 compressesmultiplying to a function by a number greater than 1 stretched itmultiplying by a negative flips the graph
f(x) = -3x
this is multiplication by a number greater than 1 and a negative so this stretches and flip. this is #6, a reflection.
f(x) = |x-1|+3
subtraction inside the function shifts it to the right 1 and addition outside shifts it up 3. this is #5.
f(x) = √(x+3)
addition inside the function shifts it to the left 3. this is #3
multiplication by 1/2 which is less than 1 compresses it. this is #1.
f(x) = (x+1)²-3
addition inside the function shifts the function to the left once. this is #4.
multiplying by 4, a number greater than 1, stretches it. this is #2.
let w represent lizette's walking speed. then her running speed is w+6. the relationship between speed, time, and distance is
distance = speed × time
lizette ran for 1.5 hours, then walked for 3 hours. her total distance is
(w+6)·1.5 + w·3 = 18
4.5w + 9 = 18 . . . simplify
4.5w = 9 . . . . . subtract 9
w = 2 . . . . . . divide by 4.5
lizette's walking speed is 2 mph; her running speed is 8 mph.