Paul: 140 + 12x
Jacklyn: 56 + 16x
Where x is how many practice sessions he had this season
"After how many more practices will Paul and Jacklyn have completed the same number of laps?"
This means what will x be if both equations are equal to each other
140 + 12x = 56 + 16x
Isolate x in one side by subtracting both sides by 12x
140 + 12x - 12x = 56 + 16x - 12x
140 = 56 + 4x
Subtract both sides by 56 to shift the 56 from the right side to the left side
140 - 56 = 56 - 56 + 4x
84 = 4x
Divide both sides by 4 to isolate x
84/4 = 4/4x
21 = x
x = 21
They'll have completed the same number of laps after 21 practices
Hope it helps :)
Branliest would be appreciated
Answer:
See below (I hope this helps!)
Step-by-step explanation:
Because odd numbers are always 1 greater than even numbers, we can call the two odd numbers x + 1 and y + 1 where x and y are even integers. Multiplying the two gives us:
(x + 1) * (y + 1)
= x * y + x * 1 + 1 * y + 1 * 1
= xy + x + y + 1
We know that x * y will be even because x and y are also even and the sum of two even numbers will be even, and we also know that x and y are even and that 1 is odd. Since the sum of even and odd numbers is always odd, the product of any two numbers is always odd.
*NOTE: I put a limitation on x and y in my proof (the limitation was that x and y must be EVEN integers) but you don't have to do that, you could make the odd integers 2x + 1 and 2y + 1 where x and y could be any integer from the set Z like mirai123 did. I simply gave this proof because it was the first thing that came to mind. While mirai123's proof and mine are different, they are still both correct.
9514 1404 393
Answer:
(2, 11)
Step-by-step explanation:
The graph shows you the point of intersection is (x, y) = (2, 11).
Answer:
The pre-image C is (2, 5)
Step-by-step explanation:
- If the point (x, y) rotated about the origin by angle 90° clockwise, then its image is (y, -x)
- If the point (x, y) rotated about the origin by angle 180° clockwise, then its image is (-x, -y)
- If the point (x, y) rotated about the origin by angle 270° clockwise, then its image is (-y, x)
∵ Point C was rotated 270° clockwise around the origin
∵ C' = (-5, 2)
→ By using the 3rd rule above
∵ The image of the point (x, y) is (-y, x)
∴ (-y, x) = (-5, 2)
→ That means -y = -5 and x = 2
∴ x = 2
∴ -y = -5
→ Divide both sides by -1
∴ y = 5
∴ The pre-image C = (2, 5)
