Y= 3X + 1. Perpendicular means you would change the slope by flipping it and changing the sign. So the slope then becomes 3. Then you use your points to find the y-intercept by filling in the variables. 7=3(2) + B. 7=6 + B. Then subtract 6 from both sides. B=1. Then you just put your problem back into slope intercept form with your new slope and y-intercept. Y=3x + 1.
Let the speed of walking of James = x mile/hour
speed of jogging = 2x mile/hour
9/2x + 1.5/x = 2
or, (9 + 3)/2x = 2
or, 12 = 4x
or, x = 3
Average speed of walking = 3 mile/hour
Average speed of jogging = 2 * 3 = 6 mile/hour
Answer:
- f(x + 5) = |x + 5|, represents the requested change of 5 units to the left,
- f(x) - 4 = |x| - 4, represents the requested change of 4 units down.
Step-by-step explanation:
The following rules will permit you to predict the equation of a new function after applying changes, especifically translations, that shift the graph of the parent function in the vertical direction (upward or downward) and in the horizontal direction (left or right).
- <u>Horizontal shifts:</u>
Let the parent function be f(x) and k a positive parameter, then f (x + k) represents a horizontal shift of k units to the left, and f (x - k) represents a horizontal shift k units to the right.
Let, again, the parent function be f(x) and, now, h a positive parameter, then f(x) + h represents a vertical shift of h units to upward, and f(x - h) represents a vertical shift of h units downward.
- <u>Combining the two previous rules</u>, you get that f (x + k) + h, represents a vertical shift h units upward if h is positive (h units downward if h is negative), and a horizontal shift k units to the left if k is positive (k units to the right if k negative)
Hence, since the parent function is f(x) = |x|
- f(x + 5) = |x + 5|, represents the requested change of 5 units to the left,
- f(x) - 4 = |x| - 4, represents the requested change of 4 units down.
Furthermore:
- f(x + 5) - 4 = |x + 5| - 4, represents a combined shift 5 units to the left and 4 units down.
Answer:
one solution: (-1,1)
Step-by-step explanation:
we have
----> equation A
----> equation B
Solve the system by substitution
Substitute equation A in equation B
solve for x
<em>Find the value of y</em>
----> 
The solution is the point (-1,1)
therefore
one solution: (-1,1)
500mL is basically your average Dasani or Fiji water. So D) a gallon of milk is a bit too big, along with A, so we can cross those two out. B) A cup of yogurt is too small- one cup is only 200mL. So our answer would be C) A bottle of salad dressing.
