Answer:
Step-by-step explanation:
Length of:
First piece = x
Second piece = 4x
Third piece = 5x
Equation: 30 = 4x + 5x + x
Solving the Equation:
10x = 30
x = 3
Lengths of:
First piece = 3 inches
Second piece = 12 inches
Third piece = 15 inches
Answer:
y=2
Step-by-step explanation:
(y+7)÷3=3y-3
y+7=9y-9
7+9=9y-y
16=8y
2=y
The vertex is (7,-50)
***rewrite in standard form***
Ok, here we go. Pay attention. The formula for the arc length is

. That means that to use that formula we have to find the derivative of the function and square it. Our function is y = 4x-5, so y'=4. Our formula now, filled in accordingly, is

(that 1 is supposed to be negative; not sure if it is til I post the final answer). After the simplification we have the integral from -1 to 2 of

. Integrating that we have

from -1 to 2.

gives us

. Now we need to do the distance formula with this. But we need 2 coordinates for that. Our bounds are x=-1 and x=2. We will fill those x values in to the function and solve for y. When x = -1, y=4(-1)-5 and y = -9. So the point is (-1, -9). Doing the same with x = 2, y=4(2)-5 and y = 3. So the point is (2, 3). Use those in the distance formula accordingly:

which simplifies to

. The square root of 153 can be simplified into the square root of 9*17. Pulling out the perfect square of 9 as a 3 leaves us with

. And there you go!
Answer:the function representing profit, P = 3n + 200
Step-by-step explanation:
The function C = 2n + 200 represents his costs, in dollars, for producing n jars of salsa.
The revenue, or the amount he receives for selling n jars, can be represented by the function R = 5n.
Profit = revenue - cost or expenses.
Therefore,
The function representing Dominic's profit, P, for selling n jars of salsa will be
P = 5n - 2n + 200 = 3n + 200